# Assistant conversation KWCP67

- Canonical URL: <https://m.sheaf.less.rest/KWCP67>
- Resource IRI: <https://m.sheaf.less.rest/KWCP67>
- Type: assistant conversation
- Mode: chat

## Transcript

### 1. User

Import the attached PDF documents.

[Uploaded PDFs]
- aameri-cheong-beck-2019-generative-design-assembly-ontology.pdf: Sheaf file #EMWWDC
- kim-2008-ontology-assembly-joint-topology.pdf: Sheaf file #93BFKH
- vagner-spivak-lerman-2015-open-dynamical-systems-wiring-diagrams.pdf: Sheaf file #8Z29DX
- van-der-schaft-maschke-2013-port-hamiltonian-systems-on-graphs.pdf: Sheaf file #JJPX6P
- desbrun-et-al-2005-discrete-exterior-calculus.pdf: Sheaf file #PPTKMN
- brisson-1993-geometric-structures-topology-order.pdf: Sheaf file #3XQ9VT
- arnold-falk-winther-2010-finite-element-exterior-calculus.pdf: Sheaf file #Y6UFY2
- fong-spivak-2018-seven-sketches-in-compositionality.pdf: Sheaf file #GMXXUV
- rachuri-et-al-2003-nistir-7057-open-assembly-model.pdf: Sheaf file #8AKLVL
- jain-2011-graph-theoretic-foundations-multibody-dynamics-part-ii.pdf: Sheaf file #P4PEF8

### 2. Assistant tool calls

#### Tool call: `document_import`

```json
{
  "action": "stage",
  "file_ids": [
    "EMWWDC",
    "93BFKH",
    "8Z29DX",
    "JJPX6P",
    "PPTKMN",
    "3XQ9VT",
    "Y6UFY2",
    "GMXXUV",
    "8AKLVL",
    "P4PEF8"
  ],
  "name": "Batch import: assembly ontology, port-Hamiltonian, DEC, compositionality"
}
```

### 3. Tool result: document_import

{
  "status": {
    "counts": {
      "pending": 10
    },
    "files": [
      {
        "error": null,
        "status": "pending",
        "file_id": "3XQ9VT",
        "execution_id": null
      },
      {
        "error": null,
        "status": "pending",
        "file_id": "8AKLVL",
        "execution_id": null
      },
      {
        "error": null,
        "status": "pending",
        "file_id": "8Z29DX",
        "execution_id": null
      },
      {
        "error": null,
        "status": "pending",
        "file_id": "93BFKH",
        "execution_id": null
      },
      {
        "error": null,
        "status": "pending",
        "file_id": "EMWWDC",
        "execution_id": null
      },
      {
        "error": null,
        "status": "pending",
        "file_id": "GMXXUV",
        "execution_id": null
      },
      {
        "error": null,
        "status": "pending",
        "file_id": "JJPX6P",
        "execution_id": null
      },
      {
        "error": null,
        "status": "pending",
        "file_id": "P4PEF8",
        "execution_id": null
      },
      {
        "error": null,
        "status": "pending",
        "file_id": "PPTKMN",
        "execution_id": null
      },
      {
        "error": null,
        "status": "pending",
        "file_id": "Y6UFY2",
        "execution_id": null
      }
    ]
  },
  "sources": [],
  "action": "stage",
  "run_id": "PJB3ZU",
  "file_ids": [
    "EMWWDC",
    "93BFKH",
    "8Z29DX",
    "JJPX6P",
    "PPTKMN",
    "3XQ9VT",
    "Y6UFY2",
    "GMXXUV",
    "8AKLVL",
    "P4PEF8"
  ],
  "run_iri": "https://m.sheaf.less.rest/PJB3ZU"
}

### 4. Assistant

Staged as run #PJB3ZU. Now extracting.

#### Tool call: `document_import`

```json
{
  "action": "extract",
  "run_id": "PJB3ZU"
}
```

### 5. Tool result: document_import

{
  "status": {
    "counts": {
      "completed": 10
    },
    "files": [
      {
        "error": null,
        "status": "completed",
        "file_id": "3XQ9VT",
        "execution_id": "pex_CCma43jcwzm2"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "8AKLVL",
        "execution_id": "pex_Wk9SAUioQudD"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "8Z29DX",
        "execution_id": "pex_WqXS-P9daP7M"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "93BFKH",
        "execution_id": "pex_28kzmZi0c80D"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "EMWWDC",
        "execution_id": "pex_0rdvZLcI_wum"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "GMXXUV",
        "execution_id": "pex_nLxgP2eG8uB8"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "JJPX6P",
        "execution_id": "pex_b2DIWRxatwuX"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "P4PEF8",
        "execution_id": "pex_vCzUxDHfjRtp"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "PPTKMN",
        "execution_id": "pex_NwdOTKuRjyzq"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "Y6UFY2",
        "execution_id": "pex_06YXPVYLyGut"
      }
    ]
  },
  "action": "extract",
  "completed": 1,
  "run_id": "PJB3ZU",
  "submitted": 10
}

### 6. Assistant

All extractions completed. Now inspecting before import.

#### Tool call: `document_import`

```json
{
  "action": "inspect",
  "run_id": "PJB3ZU"
}
```

### 7. Tool result: document_import

{
  "status": {
    "counts": {
      "completed": 10
    },
    "files": [
      {
        "error": null,
        "status": "completed",
        "file_id": "3XQ9VT",
        "execution_id": "pex_CCma43jcwzm2"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "8AKLVL",
        "execution_id": "pex_Wk9SAUioQudD"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "8Z29DX",
        "execution_id": "pex_WqXS-P9daP7M"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "93BFKH",
        "execution_id": "pex_28kzmZi0c80D"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "EMWWDC",
        "execution_id": "pex_0rdvZLcI_wum"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "GMXXUV",
        "execution_id": "pex_nLxgP2eG8uB8"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "JJPX6P",
        "execution_id": "pex_b2DIWRxatwuX"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "P4PEF8",
        "execution_id": "pex_vCzUxDHfjRtp"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "PPTKMN",
        "execution_id": "pex_NwdOTKuRjyzq"
      },
      {
        "error": null,
        "status": "completed",
        "file_id": "Y6UFY2",
        "execution_id": "pex_06YXPVYLyGut"
      }
    ]
  },
  "action": "inspect",
  "run_id": "PJB3ZU",
  "files": [
    {
      "status": "completed",
      "file_id": "3XQ9VT",
      "quality": {
        "blocks": 153,
        "pages": 10,
        "math_expressions": 530,
        "page_continuations": 3,
        "block_types": {
          "Caption": 12,
          "Equation": 8,
          "Figure": 6,
          "Footnote": 2,
          "ListGroup": 5,
          "PageFooter": 11,
          "Picture": 6,
          "SectionHeader": 14,
          "Text": 89
        },
        "empty_equation_blocks": 0,
        "equation_blocks": 8,
        "pages_with_math": 10
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/3XQ9VT.datalab.json"
    },
    {
      "status": "completed",
      "file_id": "8AKLVL",
      "quality": {
        "blocks": 609,
        "pages": 97,
        "math_expressions": 233,
        "page_continuations": 20,
        "block_types": {
          "Caption": 89,
          "Equation": 8,
          "Figure": 54,
          "Footnote": 2,
          "ListGroup": 14,
          "PageFooter": 93,
          "Picture": 17,
          "SectionHeader": 71,
          "Table": 26,
          "TableOfContents": 5,
          "Text": 230
        },
        "empty_equation_blocks": 0,
        "equation_blocks": 8,
        "pages_with_math": 29
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/8AKLVL.datalab.json"
    },
    {
      "status": "completed",
      "file_id": "8Z29DX",
      "quality": {
        "blocks": 342,
        "pages": 26,
        "math_expressions": 678,
        "page_continuations": 6,
        "block_types": {
          "Caption": 14,
          "Equation": 75,
          "Figure": 13,
          "Footnote": 1,
          "ListGroup": 2,
          "PageFooter": 2,
          "PageHeader": 38,
          "SectionHeader": 7,
          "Table": 1,
          "Text": 189
        },
        "empty_equation_blocks": 0,
        "equation_blocks": 75,
        "pages_with_math": 25
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/8Z29DX.datalab.json"
    },
    {
      "status": "completed",
      "file_id": "93BFKH",
      "quality": {
        "blocks": 91,
        "pages": 9,
        "math_expressions": 138,
        "page_continuations": 4,
        "block_types": {
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          "Figure": 2,
          "ListGroup": 3,
          "PageFooter": 9,
          "PageHeader": 12,
          "Picture": 3,
          "SectionHeader": 15,
          "Table": 2,
          "Text": 39
        },
        "empty_equation_blocks": 0,
        "equation_blocks": 0,
        "pages_with_math": 5
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/93BFKH.datalab.json"
    },
    {
      "status": "completed",
      "file_id": "EMWWDC",
      "quality": {
        "blocks": 333,
        "pages": 24,
        "math_expressions": 165,
        "page_continuations": 3,
        "block_types": {
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          "Equation": 79,
          "Figure": 3,
          "Footnote": 6,
          "ListGroup": 10,
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          "PageHeader": 48,
          "Picture": 3,
          "SectionHeader": 41,
          "Text": 136
        },
        "empty_equation_blocks": 0,
        "equation_blocks": 79,
        "pages_with_math": 12
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/EMWWDC.datalab.json"
    },
    {
      "status": "completed",
      "file_id": "GMXXUV",
      "quality": {
        "blocks": 4547,
        "pages": 353,
        "math_expressions": 10350,
        "page_continuations": 74,
        "block_types": {
          "ComplexRegion": 3,
          "Equation": 340,
          "Figure": 318,
          "Footnote": 58,
          "ListGroup": 379,
          "PageFooter": 12,
          "PageHeader": 630,
          "Picture": 3,
          "SectionHeader": 174,
          "Table": 50,
          "TableOfContents": 5,
          "Text": 2575
        },
        "empty_equation_blocks": 0,
        "equation_blocks": 340,
        "pages_with_math": 313
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/GMXXUV.datalab.json"
    },
    {
      "status": "completed",
      "file_id": "JJPX6P",
      "quality": {
        "blocks": 511,
        "pages": 32,
        "math_expressions": 866,
        "page_continuations": 5,
        "block_types": {
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          "Figure": 2,
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          "ListGroup": 6,
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          "Text": 242
        },
        "empty_equation_blocks": 0,
        "equation_blocks": 99,
        "pages_with_math": 29
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/JJPX6P.datalab.json"
    },
    {
      "status": "completed",
      "file_id": "P4PEF8",
      "quality": {
        "blocks": 567,
        "pages": 35,
        "math_expressions": 487,
        "page_continuations": 3,
        "block_types": {
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          "Figure": 7,
          "Footnote": 4,
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          "SectionHeader": 41,
          "Text": 181
        },
        "empty_equation_blocks": 0,
        "equation_blocks": 103,
        "pages_with_math": 32
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/P4PEF8.datalab.json"
    },
    {
      "status": "completed",
      "file_id": "PPTKMN",
      "quality": {
        "blocks": 838,
        "pages": 53,
        "math_expressions": 1042,
        "page_continuations": 6,
        "block_types": {
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          "Picture": 23,
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        },
        "empty_equation_blocks": 0,
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        "pages_with_math": 48
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/PPTKMN.datalab.json"
    },
    {
      "status": "completed",
      "file_id": "Y6UFY2",
      "quality": {
        "blocks": 1077,
        "pages": 74,
        "math_expressions": 2676,
        "page_continuations": 27,
        "block_types": {
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          "Figure": 7,
          "ListGroup": 10,
          "PageFooter": 1,
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          "Picture": 1,
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          "Table": 2,
          "TableOfContents": 2,
          "Text": 584
        },
        "empty_equation_blocks": 0,
        "equation_blocks": 299,
        "pages_with_math": 69
      },
      "output_path": "/home/mbrock/sheaf.mikael/var/datalab/PJB3ZU/Y6UFY2.datalab.json"
    }
  ]
}

### 8. Assistant

All 10 files inspected cleanly with no empty equation blocks or errors. Proceeding to import.

#### Tool call: `document_import`

```json
{
  "action": "import",
  "run_id": "PJB3ZU"
}
```

### 9. Tool result: document_import

{
  "next": "Resolve metadata and validate reader pages. Search indexing is continuing in the background.",
  "action": "import",
  "documents": [
    {
      "status": "imported",
      "title": null,
      "file_id": "3XQ9VT",
      "document_id": "NHJEJG",
      "document_iri": "https://m.sheaf.less.rest/NHJEJG"
    },
    {
      "status": "imported",
      "title": null,
      "file_id": "8AKLVL",
      "document_id": "6PYNP3",
      "document_iri": "https://m.sheaf.less.rest/6PYNP3"
    },
    {
      "status": "imported",
      "title": null,
      "file_id": "8Z29DX",
      "document_id": "TA7A6Y",
      "document_iri": "https://m.sheaf.less.rest/TA7A6Y"
    },
    {
      "status": "imported",
      "title": null,
      "file_id": "93BFKH",
      "document_id": "KSLF8E",
      "document_iri": "https://m.sheaf.less.rest/KSLF8E"
    },
    {
      "status": "imported",
      "title": null,
      "file_id": "EMWWDC",
      "document_id": "KT87MS",
      "document_iri": "https://m.sheaf.less.rest/KT87MS"
    },
    {
      "status": "imported",
      "title": null,
      "file_id": "GMXXUV",
      "document_id": "A6DBK8",
      "document_iri": "https://m.sheaf.less.rest/A6DBK8"
    },
    {
      "status": "imported",
      "title": null,
      "file_id": "JJPX6P",
      "document_id": "RT6CVD",
      "document_iri": "https://m.sheaf.less.rest/RT6CVD"
    },
    {
      "status": "imported",
      "title": null,
      "file_id": "P4PEF8",
      "document_id": "PB725Y",
      "document_iri": "https://m.sheaf.less.rest/PB725Y"
    },
    {
      "status": "imported",
      "title": null,
      "file_id": "PPTKMN",
      "document_id": "AX2VJD",
      "document_iri": "https://m.sheaf.less.rest/AX2VJD"
    },
    {
      "status": "imported",
      "title": null,
      "file_id": "Y6UFY2",
      "document_id": "LTESUF",
      "document_iri": "https://m.sheaf.less.rest/LTESUF"
    }
  ],
  "run_id": "PJB3ZU"
}

### 10. Assistant

All 10 documents imported. Now resolving metadata and validating each.

#### Tool call: `document_import`

```json
{
  "action": "metadata",
  "run_id": "PJB3ZU"
}
```

#### Tool call: `document_import`

```json
{
  "action": "validate",
  "run_id": "PJB3ZU"
}
```

### 11. Tool result: document_import

{
  "action": "metadata",
  "documents": [
    {
      "match": {
        "reason": "title match score below 0.78",
        "source": "isbn",
        "identifier": "0897913183",
        "score": 0.0,
        "doi": "10.1145/73833",
        "accept?": false,
        "crossref_title": "Proceedings of the fifth annual symposium on Computational geometry  - SCG '89",
        "crossref_type": "proceedings"
      },
      "metadata": {
        "title": "Representing Geometric Structures in d Dimensions: Topology and Order",
        "usage": {
          "cost": {
            "total": 6.75e-4,
            "tokens": 6.75e-4,
            "tools": 0.0,
            "storage": 0.0,
            "images": 0.0,
            "input_cost": 4.35e-4,
            "output_cost": 2.4e-4,
            "reasoning_cost": 0.0,
            "line_items": [
              {
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                "kind": "tokens",
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                "cost": 4.35e-4,
                "quantity": 1741
              },
              {
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                "id": "token.output",
                "kind": "tokens",
                "component": "token.output",
                "cost": 2.4e-4,
                "quantity": 160
              }
            ]
          },
          "output_tokens": 160,
          "input_tokens": 1741,
          "total_cost": 6.75e-4,
          "reasoning_tokens": 0,
          "input_cost": 4.35e-4,
          "output_cost": 2.4e-4,
          "reasoning_cost": 0.0,
          "cached_tokens": 0,
          "total_tokens": 1901,
          "tool_usage": {},
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          "cache_creation_tokens": 0
        },
        "year": "1989",
        "model": "google:gemini-3.1-flash-lite-preview",
        "notes": "The ISBN is derived from the ACM copyright line at the bottom of the first page: 0-89791-318-3.",
        "issue": null,
        "pages": "218-220",
        "authors": [
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        ],
        "doi": null,
        "volume": null,
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        "publication": "Proceedings of the fifth annual symposium on Computational geometry",
        "confidence": "high"
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      "document_id": "NHJEJG",
      "wrote": false
    },
    {
      "match": {
        "reason": "no DOI or ISBN found",
        "source": "none",
        "score": 0.0,
        "accept?": false
      },
      "metadata": {
        "title": "Object-Oriented Representation of Electro-Mechanical Assemblies Using UML",
        "usage": {
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            "tokens": 6.82e-4,
            "tools": 0.0,
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            "line_items": [
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              },
              {
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                "id": "token.output",
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                "quantity": 165
              }
            ]
          },
          "output_tokens": 165,
          "input_tokens": 1741,
          "total_cost": 6.82e-4,
          "reasoning_tokens": 0,
          "input_cost": 4.35e-4,
          "output_cost": 2.47e-4,
          "reasoning_cost": 0.0,
          "cached_tokens": 0,
          "total_tokens": 1906,
          "tool_usage": {},
          "image_usage": {},
          "cache_creation_tokens": 0
        },
        "year": "2003",
        "model": "google:gemini-3.1-flash-lite-preview",
        "notes": "Published by the National Institute of Standards and Technology",
        "issue": null,
        "pages": null,
        "authors": [
          "Sudarsan Rachuri",
          "Young-Hyun Han",
          "Shaw C Feng",
          "Utpal Roy",
          "Fujun Wang",
          "Ram D Sriram",
          "Kevin W Lyons"
        ],
        "doi": null,
        "volume": null,
        "isbn": null,
        "source_filename": "33bd9468fce6fecbe190b621614999a2107117ad2c7ef0ec4d9031a2a7a46e47.pdf",
        "publication": "NISTIR 7057",
        "confidence": "high"
      },
      "document_id": "6PYNP3",
      "wrote": false
    },
    {
      "match": {
        "reason": "no DOI or ISBN found",
        "source": "none",
        "score": 0.0,
        "accept?": false
      },
      "metadata": {
        "title": "ALGEBRAS OF OPEN DYNAMICAL SYSTEMS ON THE OPERAD OF WIRING DIAGRAMS",
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        "year": "2018",
        "model": "google:gemini-3.1-flash-lite-preview",
        "notes": "The document is a book manuscript or preprint, last updated October 12, 2018. No specific ISBN or DOI was found within the text.",
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        "accept?": true,
        "crossref_title": "Port-Hamiltonian Systems on Graphs",
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        "year": "2013",
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        "accept?": true,
        "crossref_title": "Graph theoretic foundations of multibody dynamics",
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      "metadata": {
        "title": "DISCRETE EXTERIOR CALCULUS",
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        "year": "2005",
        "model": "google:gemini-3.1-flash-lite-preview",
        "notes": "Published as arXiv:0508341v2 [math.DG] on 18 Aug 2005. It is a chapter or article rather than a full book.",
        "issue": null,
        "pages": "1-51",
        "authors": [
          "MATHIEU DESBRUN",
          "ANIL N. HIRANI",
          "MELVIN LEOK",
          "JERROLD E. MARSDEN"
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      "metadata": {
        "title": "FINITE ELEMENT EXTERIOR CALCULUS: FROM HODGE THEORY TO NUMERICAL STABILITY",
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        "issue": null,
        "pages": "1-71",
        "authors": [
          "DOUGLAS N. ARNOLD",
          "RICHARD S. FALK",
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        "confidence": "high"
      },
      "document_id": "LTESUF",
      "wrote": false
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  ],
  "run_id": "PJB3ZU"
}

### 12. Tool result: document_import

{
  "action": "validate",
  "documents": [
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "NHJEJG",
      "readable_chunks": 139,
      "reader_path": "/NHJEJG",
      "source_pages": 10
    },
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "6PYNP3",
      "readable_chunks": 494,
      "reader_path": "/6PYNP3",
      "source_pages": 95
    },
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "TA7A6Y",
      "readable_chunks": 296,
      "reader_path": "/TA7A6Y",
      "source_pages": 26
    },
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "KSLF8E",
      "readable_chunks": 66,
      "reader_path": "/KSLF8E",
      "source_pages": 9
    },
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "KT87MS",
      "readable_chunks": 281,
      "reader_path": "/KT87MS",
      "source_pages": 24
    },
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "A6DBK8",
      "readable_chunks": 3829,
      "reader_path": "/A6DBK8",
      "source_pages": 344
    },
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "RT6CVD",
      "readable_chunks": 377,
      "reader_path": "/RT6CVD",
      "source_pages": 32
    },
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "PB725Y",
      "readable_chunks": 371,
      "reader_path": "/PB725Y",
      "source_pages": 35
    },
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "AX2VJD",
      "readable_chunks": 727,
      "reader_path": "/AX2VJD",
      "source_pages": 53
    },
    {
      "title": "Untitled thesis",
      "valid": true,
      "document_id": "LTESUF",
      "readable_chunks": 902,
      "reader_path": "/LTESUF",
      "source_pages": 74
    }
  ],
  "search_index_status": "search",
  "run_id": "PJB3ZU",
  "embedding_status": "updating",
  "embedding_errors": 0,
  "search_index_message": "Updating text search · another refresh is queued"
}

### 13. Assistant

All documents imported and validated successfully. Three got auto-matched DOIs (Kim 2008, van der Schaft & Maschke 2013, Jain 2011). Setting metadata for the remaining seven from the reliable extracted bibliographic data.

#### Tool call: `update_document_metadata`

```json
{
  "authors": [
    "Erik Brisson"
  ],
  "document_id": "NHJEJG",
  "kind": "journal_article",
  "micro_abstract": "Formalizes geometric structures in d dimensions via combinatorial topology and order relations, a foundation for cell-complex representations used in assembly/geometric modeling.",
  "title": "Representing Geometric Structures in d Dimensions: Topology and Order",
  "venue": "Proceedings of the fifth annual symposium on Computational geometry",
  "year": "1993"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "authors": [
    "Sudarsan Rachuri",
    "Young-Hyun Han",
    "Shaw C. Feng",
    "Utpal Roy",
    "Fujun Wang",
    "Ram D. Sriram",
    "Kevin W. Lyons"
  ],
  "corporate_authors": [
    "National Institute of Standards and Technology"
  ],
  "document_id": "6PYNP3",
  "kind": "report",
  "micro_abstract": "NIST report proposing the Open Assembly Model, a UML-based object-oriented representation for electro-mechanical assembly information exchange.",
  "title": "Object-Oriented Representation of Electro-Mechanical Assemblies Using UML",
  "venue": "NISTIR 7057",
  "year": "2003"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "authors": [
    "Dmitry Vagner",
    "David I. Spivak",
    "Eugene Lerman"
  ],
  "document_id": "TA7A6Y",
  "kind": "research_paper",
  "micro_abstract": "Develops an operad-algebra formalism for open dynamical systems composed via wiring diagrams, underpinning compositional systems theory.",
  "title": "Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams",
  "venue": "arXiv:1408.1598",
  "year": "2015"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "authors": [
    "Bahar Aameri",
    "Hyunmin Cheong",
    "J. Christopher Beck"
  ],
  "document_id": "KT87MS",
  "kind": "journal_article",
  "micro_abstract": "Proposes a formal ontology of mechanical assembly structure intended to support generative design systems.",
  "title": "Towards an Ontology for Generative Design of Mechanical Assemblies",
  "venue": "Applied Ontology",
  "year": "2019"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "authors": [
    "Brendan Fong",
    "David I. Spivak"
  ],
  "document_id": "A6DBK8",
  "kind": "book",
  "micro_abstract": "A textbook introducing applied category theory (orders, monoidal categories, operads, sheaves, etc.) through seven worked \"sketches\" connecting math to systems modeling.",
  "title": "Seven Sketches in Compositionality: An Invitation to Applied Category Theory",
  "year": "2018"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "authors": [
    "Mathieu Desbrun",
    "Anil N. Hirani",
    "Melvin Leok",
    "Jerrold E. Marsden"
  ],
  "document_id": "AX2VJD",
  "kind": "research_paper",
  "micro_abstract": "Introduces discrete exterior calculus, a coordinate-free discretization of differential forms on simplicial complexes for computational modeling.",
  "title": "Discrete Exterior Calculus",
  "venue": "arXiv:math/0508341",
  "year": "2005"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "authors": [
    "Douglas N. Arnold",
    "Richard S. Falk",
    "Ragnar Winther"
  ],
  "document_id": "LTESUF",
  "kind": "research_paper",
  "micro_abstract": "Surveys finite element exterior calculus, unifying Hodge theory and mixed finite element stability analysis for PDE discretization.",
  "title": "Finite Element Exterior Calculus: From Hodge Theory to Numerical Stability",
  "venue": "arXiv:0906.4325 / Bulletin of the AMS",
  "year": "2010"
}
```

### 14. Tool result: update_document_metadata

Updated metadata for #NHJEJG: kind, title, authors, year, venue, micro_abstract

### 15. Tool result: update_document_metadata

Updated metadata for #6PYNP3: kind, title, authors, corporate_authors, year, venue, micro_abstract

### 16. Tool result: update_document_metadata

Updated metadata for #TA7A6Y: kind, title, authors, year, venue, micro_abstract

### 17. Tool result: update_document_metadata

Updated metadata for #KT87MS: kind, title, authors, year, venue, micro_abstract

### 18. Tool result: update_document_metadata

Updated metadata for #A6DBK8: kind, title, authors, year, micro_abstract

### 19. Tool result: update_document_metadata

Updated metadata for #AX2VJD: kind, title, authors, year, venue, micro_abstract

### 20. Tool result: update_document_metadata

Updated metadata for #LTESUF: kind, title, authors, year, venue, micro_abstract

### 21. Assistant

All 10 documents imported and validated successfully:

| Title | Doc ID | Metadata source |
|---|---|---|
| Brisson, *Representing Geometric Structures in d Dimensions* (1993) | #NHJEJG | manual (Crossref match rejected as proceedings-level) |
| Rachuri et al., *Open Assembly Model* (NISTIR 7057, 2003) | #6PYNP3 | manual |
| Vagner, Spivak, Lerman, *Algebras of Open Dynamical Systems...* (2015) | #TA7A6Y | manual |
| Kim, *Ontology and Assembly Joint Topology Representation* (2008) | #KSLF8E | auto (DOI matched, Crossref) |
| Aameri, Cheong, Beck, *Towards an Ontology for Generative Design...* (2019) | #KT87MS | manual |
| Fong & Spivak, *Seven Sketches in Compositionality* (2018) | #A6DBK8 | manual |
| van der Schaft & Maschke, *Port-Hamiltonian Systems on Graphs* (2013) | #RT6CVD | auto (DOI matched) |
| Jain, *Graph Theoretic Foundations of Multibody Dynamics, Part II* (2011) | #PB725Y | auto (DOI matched) |
| Desbrun, Hirani, Leok, Marsden, *Discrete Exterior Calculus* (2005) | #AX2VJD | manual |
| Arnold, Falk, Winther, *Finite Element Exterior Calculus* (2010) | #LTESUF | manual |

All are valid with no extraction errors; search index is still finishing a background refresh but readable chunks are already available for each document.

### 22. User

Really nice, thank you. Let's now write micro abstracts and make artworks for these, so skim them and read them enough to write good micro abstracts and make cool artworks for them. Also place them in folder(s)

### 23. Assistant tool calls

#### Tool call: `list_documents`

```json
{}
```

#### Tool call: `get_document`

```json
{
  "id": "KSLF8E"
}
```

#### Tool call: `get_document`

```json
{
  "id": "RT6CVD"
}
```

#### Tool call: `get_document`

```json
{
  "id": "PB725Y"
}
```

### 24. Tool result: list_documents

FOLDERS
- Accounting Algebra & Property Theory
- Living Structure, Wholeness & Beauty
- Living Structure, Wholeness &amp; Beauty
- ontology
- Procedural Generation & Co-Creation
- Roads, Trails & Movement
- Scenario-Based & Behavioral Programming
- Technology, Scale & Conviviality
- Terrain, Hydrology & Erosion
- Water Simulation & Rendering

Accounting Algebra & Property Theory (4)
- #GANFP9 A Fundamental Duality in the Mathematical and Natural Sciences: From Logic to Biology - 2024 | David Ellerman | 53 pp.
  Micro abstract: Traces an overlooked subset–partition duality—from logic and category theory through entropy and quantum indefiniteness to selectionist and generative mechanisms in biology.
- #NBH3BE Algebraic Models for Accounting Systems - 2010 | Derek J. S. Robinson, José García Pérez, Robert A. Nehmer, Salvador Cruz Rambaud | World Scientific | 255 pp.
  Micro abstract: Develops accounting theory algebraically: balance vectors as modules, transactions as a group, and whole accounting systems as automata with quotients, homomorphisms, and decision algorithms for audit and control.
- #7ESDBJ Economics, Accounting, and Property Theory - 1982 | David P. Ellerman | Lexington Books | 110 pp.
  Micro abstract: Ellerman's vector-accounting monograph: double entry generalized to property vectors ("accounting without valuation"), grounding a property-theoretic account of appropriation, the firm, and goodwill.
- #C8FHDZ On implication and negation in partition logic - 2025 |  , David Ellerman | Open Journal of Mathematical Sciences | 9 pp. | doi:10.30538/oms2025.0250
  Micro abstract: Develops implication as a refinement-sensitive operation on set partitions, showing how relative negation yields local Boolean cores within the non-distributive algebra of partitions.

Living Structure, Wholeness & Beauty (9)
- #MH5J8D Beautimeter: Harnessing GPT for Assessing Architectural and Urban Beauty Based on the 15 Properties of Living Structure - 2025 | Bin Jiang | AI | 12 pp. | doi:10.3390/ai6040074
  Micro abstract: Presents Beautimeter, a GPT-based tool that scores buildings and urban scenes against Christopher Alexander’s 15 properties of living structure to assess their coherence and beauty.
- #XW22YY Generative Codes: The Path to Building Welcoming, Beautiful, Sustainable Neighborhoods - 2005 | Brian Hanson, Christopher Alexander, Maggie Moore Alexander, Michael Mehaffy, Randall Schmidt | Center for Environmental Structure | 21 pp.
  Micro abstract: Argues that living neighborhoods arise from generative codes: ordered, participatory steps that let buildings and public spaces unfold from local people, land, and context.
- #SKRF4C Geography as a Science of the Earth’s Surface Founded on the Third View of Space - 2022 | Bin Jiang | Annals of GIS | 14 pp. | doi:10.1080/19475683.2021.1966502
  Micro abstract: Recasts geography around an organismic view of space, using scaling and spatial dependence to understand—and deliberately create—places with greater living structure.
- #PXG56P Harmony-Seeking Computations: A Science of Non-Classical Dynamics Based on the Progressive Evolution of the Larger Whole - 2009 | Christopher Alexander | Unpublished manuscript | 66 pp.
  Micro abstract: Proposes harmony-seeking computation as a creative process that repeatedly strengthens latent centers in a configuration while preserving and deepening the larger whole.
- #MJKTBB Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space - 2023 | Bin Jiang, Chris de Rijke | Annals of the American Association of Geographers | 19 pp. | doi:10.1080/24694452.2023.2178376
  Micro abstract: Measures an image’s structural beauty by recursively extracting its nested substructures, revealing a compact hierarchy that also captures visual saliency.
- #3XSLTA Structural Beauty: A Structure-Based Computational Approach to Quantifying the Beauty of an Image - 2021 | Bin Jiang, Chris de Rijke | Journal of Imaging | 15 pp. | doi:10.3390/jimaging7050078
  Micro abstract: Proposes a quantitative measure of structural beauty based on how many substructures an image contains and how strongly they form a hierarchy across scales.
- #ZU8GZV Structure-Preserving Transformations - 2002 | Christopher Alexander | The Nature of Order, Book Two: The Process of Creating Life | 4 pp. | doi:10.2307/j.ctv27ftw6c.5
  Micro abstract: Explains structure-preserving transformations: incremental changes that extend the centers and relationships already present in a place rather than weakening its wholeness.
- #AULNWD The Nature of Poetic Order - 1998 | Richard P. Gabriel | Warren Wilson Alumni Conference, Mount Holyoke | 99 pp.
  Micro abstract: Gabriel's slide essay relating poetry's formal order to Christopher Alexander's ideas of generative structure, exploring how constraint and pattern produce living order in creative work.
- #BYG3BQ Wholeness as a Hierarchical Graph to Capture the Nature of Space - 2015 | Bin Jiang | International Journal of Geographical Information Science | 14 pp. | doi:10.1080/13658816.2015.1038542
  Micro abstract: Models spatial wholeness as a hierarchical graph of mutually reinforcing centers, using PageRank and scaling depth to quantify the life of parts and wholes.

ontology (36)
- #LRK6E2 A Taxonomy of Granular Partitions - 2001 | Barry Smith, Thomas Bittner | Spatial Information Theory: Foundations of Geographic Information Science | 16 pp. | doi:10.1007/3-540-45424-1_3
  Micro abstract: Formalizes partitions as tree-structured cognitive devices projected onto reality, then classifies how accurately, structurally, and completely their cells recognize objects, with applications to cadastral and geographic data.
- #FQCWKV A Theory of Granular Partitions - 2003 | Barry Smith, Thomas Bittner | Foundations of Geographic Information Science | 33 pp.
  Micro abstract: Formalizes granular partitions as hierarchical cell systems projected onto reality, combining cognitive selectivity with mereological structure for naming, classifying, mapping, and representation.
- #SF7KYZ About the Unreal - 2025 | Barry Smith, Jim Logan, John Beverley | Proceedings of the Joint Ontology Workshops (JOWO), Episode XI | 14 pp.
  Micro abstract: Models fiction, blueprints, simulations, and other information about unreal entities through logical combinations of actual classes, avoiding commitments to nonexistent dummy instances.
- #CGE2NC Against Fantology - 2005 | Barry Smith | Experience and Analysis | 22 pp.
  Micro abstract: Critiques the idea that first-order logic reveals reality’s ontology, tracing its atomism, timelessness, Booleanism, and reductionism before proposing a six-category ontology and an enhanced Davidsonian formal language.
- #JZG4PM Against Fantology Again - 2016 | Ingvar Johansson | The Theory and Practice of Ontology | 12 pp.
  Micro abstract: Extends the critique of fantology through default ontologization, arguing that Quine’s canonical notation is incoherent about classes and excludes intentional phenomena and distinct modes of existence.
- #E5CLFY Agglomerations - 1999 | Barry Smith | Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science | 16 pp. | doi:10.1007/3-540-48384-5_18
  Micro abstract: Defines agglomerations as geographically dispersed yet unified aggregates—populations, cultures, organizations, and diasporas—and develops a realist mereotopology for their boundaries, identity, and change.
- #3CCZ4A Bodily Systems and the Spatial-Functional Structure of the Human Body - 2004 | Barry Smith, Igor Papakin, Katherine Munn | Ontologies in Medicine | 26 pp. | doi:10.3233/978-1-60750-945-5-39
  Micro abstract: Integrates anatomy and physiology by modeling the body as a nested spatial-functional hierarchy whose parts are demarcated as system elements through the functions they bear and realize.
- #7YZU95 Boundaries: An Essay in Mereotopology - 1997 | Barry Smith | The Philosophy of Roderick Chisholm | 32 pp.
  Micro abstract: Reconstructs and extends the Brentano–Chisholm mereotopology in which dependent, coincident boundaries account for contact and the continuum across points, lines, surfaces, and bodies.
- #3TZK66 Capabilities: An Ontology - 2024 | Barry Smith, David Limbaugh, Eric Merrell, John Beverley, Peter M. Koch | Proceedings of the Joint Ontology Workshops (JOWO), Episode X | 14 pp.
  Micro abstract: Defines a capability as a disposition in whose realization an organism or group has or had an interest, placing capabilities between dispositions and functions in Basic Formal Ontology.
- #XYERFR Carving Up Reality - 2004 | Barry Smith | Categories: Historical and Systematic Essays | 14 pp.
  Micro abstract: Explains how context-sensitive, coarse-grained partitions guide reference and perception while preserving transitive parthood and distinguishing fiat demarcations from boundaries grounded in reality.
- #88BVY3 Categories in Top-Level Ontologies: Revisiting the Aristotelian Background - Barry Smith, Ludger Jansen | 31 pp.
  Micro abstract: Reconstructs Aristotle’s categories as the philosophical basis of BFO, extending the ontological square with processes into a six-category framework for continuants, occurrents, dependence, and multiple scientific granularities.
- #9G4F42 CLASSIFYING PROCESSES: AN ESSAY IN APPLIED ONTOLOGY - 2012 | Barry Smith | Ratio | 21 pp. | doi:10.1111/j.1467-9329.2012.00557.x
  Micro abstract: Extends Basic Formal Ontology to scientific process data through process profiles—quality, rate, and cyclical aspects that ground measurements, time-series graphs, and representations of dynamic systems.
- #GSLMP8 Diagrams, Documents, and the Meshing of Plans - 2013 | Barry Smith | Visual Learning, vol. 3: How to Do Things with Pictures: Skill, Practice, Performance | 14 pp.
  Micro abstract: Shows how diagrams and evolving networks of documents mesh plans, obligations, and specialized labor to enable coordinated collective action beyond the limits of linear text.
- #M8BQ3S Do Mountains Exist? Towards an Ontology of Landforms - 2003 | Barry Smith, David M. Mark | Environment and Planning B: Planning and Design | 22 pp.
  Micro abstract: Argues that mountains are object-like in everyday thought but elevation fields in environmental science, motivating a geospatial ontology that supports both perspectives.
- #KSESR8 Drawing Boundaries - 2019 | Barry Smith | The Philosophy of GIS | 26 pp. | doi:10.1007/978-3-030-16829-2_7
  Micro abstract: Updates the distinction between human-demarcated fiat boundaries and physically grounded bona fide boundaries, tracing its uses in geography, property, ecology, and Basic Formal Ontology.
- #56MWAA Environmental Metaphysics - 2001 | Achille C. Varzi, Barry Smith | Metaphysics in the Post-Metaphysical Age: Proceedings of the 22nd International Wittgenstein Symposium | 12 pp.
  Micro abstract: Develops an ontology of token niches as tenant–medium–retainer structures, using physical and fiat boundaries to explain environmental fit, protection, movement, and niche construction.
- #K6JC2J Layers: A New Approach to Locating Objects in Space - 2003 | Barry Smith, Maureen Donnelly | Spatial Information Theory: Foundations of Geographic Information Science | 16 pp. | doi:10.1007/978-3-540-39923-0_4
  Micro abstract: Extends mereotopology with layers that distinguish material objects, holes, and processes from the spatial and spatiotemporal regions they occupy, supporting dynamic geospatial reasoning beyond static map overlays.
- #KG5TBB Making space: the natural, cultural, cognitive and social niches of human activity - 2021 | Barry Smith | Cognitive Processing | 11 pp. | doi:10.1007/s10339-021-01049-y
  Micro abstract: Shows how legal decisions, plans, historical reasoning, and language create fiat spatial and spatiotemporal entities, then draws limits and practical lessons for ontology-supported AI.
- #FJ5KCA More Things in Heaven and Earth - 1995 | Barry Smith | Grazer Philosophische Studien | 15 pp.
  Micro abstract: Develops an ontology of spatial regions and boundaries, arguing that political territories are historically created fiat objects through performative maps while also recognizing vague, overlapping, and incomplete geographic objects.
- #KY3Y9U Naïve Physics: An Essay in Ontology - 1994 | Barry Smith, Roberto Casati | Philosophical Psychology | 22 pp. | doi:10.1080/09515089408573121
  Micro abstract: Reconstructs naïve physics as a realist ontology of the common-sense world—objects, processes, stuffs, boundaries, media, and values—drawing on Gestalt psychology and phenomenology to broaden AI’s set-theoretic models.
- #TQPVBD New Foundations for Qualitative Physics - 1990 | Barry Smith, Jean Petitot | Evolving Knowledge in Natural Science and Artificial Intelligence | 13 pp.
  Micro abstract: Argues for a scientific ontology of the qualitative common-sense world, using morphological discontinuities to connect physical substrates, sensible qualities, Aristotelian categories, and ecologically constrained cognition.
- #B98HVX Objects and Their Environments: From Aristotle to Ecological Ontology - 2001 | Barry Smith | The Life and Motion of Socio-Economic Units | 26 pp. | doi:10.1201/9781482268096-14
  Micro abstract: Extends Aristotelian substance–accident ontology into a realist theory of behavioral settings and ecological niches as nested, bounded wholes in which organisms, objects, and activities mutually fit.
- #9GWUC8 On Classifying Material Entities in Basic Formal Ontology - 2012 | Barry Smith | Interdisciplinary Ontology: Proceedings of the Third Interdisciplinary Ontology Meeting | 13 pp.
  Micro abstract: Clarifies BFO’s material entities by distinguishing objects, aggregates, and fiat object parts, and analyzes objects through causal unity by covering, physical forces, or engineered assembly without claiming exhaustivity.
- #KYQGNH On Credentials - 2020 | Barry Smith, Giuseppe Lorini, Olimpia Giuliana Loddo | Journal of Social Ontology | 21 pp. | doi:10.1515/jso-2019-0034
  Micro abstract: Provides a social ontology of credentials as portable, inspectable institutional documents that certify identity or status and give bearers the practical deontic power to exercise rights, with a typology of their forms and functions.
- #BV47YZ On Drawing Lines on a Map - 1995 | Barry Smith | Spatial Information Theory: A Theoretical Basis for GIS | 10 pp. | doi:10.1007/3-540-60392-1_31
  Micro abstract: Builds a typology of spatial boundaries around the fiat–bona fide distinction, applying it to maps, political and property divisions, scattered objects, linguistic framing, and truthmakers.
- #D8LRQM Ontological Foundations for Geographic Information Science - 2004 | Barry Smith, David M. Mark, Max J. Egenhofer, Stephen C. Hirtle | A Research Agenda for Geographic Information Science | 8 pp. | doi:10.1201/9781420038330.ch12
  Micro abstract: Sets a research agenda for geospatial ontology, linking formal accounts of geographic objects, processes, scale, and vagueness to human concepts, interoperable data, and ontology-driven GIS.
- #GN66WW Ontologies of Common Sense, Physics and Mathematics - 2023 | Barry Smith, Jobst Landgrebe | arXiv | 32 pp. | doi:10.48550/arXiv.2305.01560
  Micro abstract: Proposes linked upper ontologies for common sense, physics, and mathematics, arguing that classical models connect real magnitudes to mathematics whereas modern physics relates measurements to entities lacking commonsense universals.
- #WYP3G6 Ontology and Geographic Kinds - 1998 | Barry Smith, David M. Mark | Proceedings of the 8th International Symposium on Spatial Data Handling (SDH ’98) | 7 pp.
  Micro abstract: Argues that geographic kinds are intrinsically spatial and boundary-centered, requiring mereology and topology to connect physical reality, cultural categorization, cognition, and GIS representation.
- #9YMD2E SNAP and SPAN: Towards Dynamic Spatial Ontology - 2004 | Barry Smith, Pierre Grenon | Spatial Cognition & Computation | 35 pp. | doi:10.1207/S15427633SCC0401_5
  Micro abstract: BFO's bicategorial framework: SNAP snapshot ontologies of continuants and a SPAN ontology of processes in spacetime, linked by trans-ontological relations to capture change — demonstrated on the ontology of geodynamics.
- #KWFTKJ Surrounding Space: The Ontology of Organism-Environment Relations - 2002 | Achille C. Varzi, Barry Smith | Theory in Biosciences | 29 pp. | doi:10.1078/1431-7613-00053
  Micro abstract: Develops a formal ontology of token niches as tenant–medium–retainer structures, extending static organism–environment fit into a dynamic account of vacant niches, movement, interaction, and niche construction.
- #DLY2WP The Cognitive Geometry of War - 1997 | Barry Smith | Current Issues in Political Philosophy: Justice in Society and World Order | 26 pp.
  Micro abstract: Argues that modern ideals of compact, contiguous national territory help drive conflict, and proposes perforated, non-contiguous, and geometrically flexible borders as alternatives to displacement and ethnic cleansing.
- #4QQD4A The Logic of Systems of Granular Partitions - 2005 | Barry Smith, Maureen Donnelly, Thomas Bittner | IFOMIS Reports | 23 pp.
  Micro abstract: Builds a sound S4-style modal logic for labeled, typed granular partitions, modeling refinement and cross-partition counterparts so differently selective views can reason about the same mereologically structured reality.
- #2F8T3H Toward a Realistic Science of Environments - 2009 | Barry Smith | Ecological Psychology | 11 pp.
  Micro abstract: Defends Gibsonian ecological realism: organisms directly perceive affordances in physically real niches, while granular partitions show how different species inhabit perspectives on one world, not separate constructed worlds.
- #DT9Y7X True Grid - 2002 | Barry Smith | Spatial Information Theory: Foundations of Geographic Information Science | 17 pp.
  Micro abstract: Generalizes Alberti’s perspectival grid into a realist theory of projection: pictures, maps, names, concepts, and databases are “true grids” when their cells preserve relevant structure and refer transparently to reality.
- #PHAFYA Truth and the Visual Field - 1997 | Barry Smith | Naturalizing Phenomenology: Issues in Contemporary Phenomenology and Cognitive Science | 8 pp.
  Micro abstract: Uses mereotopology and Gibsonian ecology to treat perception and language as carving transient fiat boundaries in reality, defining a judgment field as the truth-making portion of the world selected by a true sentence.
- #XZX6PE Vague Reference and Approximating Judgments - 2003 | Barry Smith, Thomas Bittner | Spatial Cognition and Computation | 20 pp.
  Micro abstract: Formalizes vague reference as multiple crisp candidate referents within granular partitions, then explains approximation as using familiar spatial or temporal reference grids to constrain vagueness without truth-value indeterminacy.

Procedural Generation & Co-Creation (14)
- #ABD2B8 Between Tech and Art: The Vegetation of Horizon Zero Dawn - 2018 | Gilbert Sanders, Guerrilla Games | Game Developers Conference (GDC) 2018 | 87 pp.
  Micro abstract: A production breakdown of Horizon Zero Dawn’s vegetation pipeline, covering global wind simulation, layered foliage motion, coverage-preserving alpha mipmaps, shading, asset LODs, placement, and cascaded shadows.
- #4TH488 Explainable AI for Designers: A Human-Centered Perspective on Mixed-Initiative Co-Creation - 2018 | Antonios Liapis, G. Michael Youngblood, Jichen Zhu, Rafael Bidarra, Sebastian Risi | 2018 IEEE Conference on Computational Intelligence and Games (CIG) | 8 pp. | doi:10.1109/CIG.2018.8490433
  Micro abstract: Defines explainable AI for game designers, mapping co-creative systems by their explainability, initiative, and domain overlap so explanations serve concrete design tasks.
- #9NQ94D Extracting Physics from Blended Platformer Game Levels - 2020 | Adam Summerville, Anurag Sarkar, Joseph C. Osborn, Sam Snodgrass | Joint Proceedings of the AIIDE 2020 Workshops (CEUR Workshop Proceedings, Vol. 2862) | 7 pp.
  Micro abstract: Infers playable jump physics from generated platformer levels, including hybrid physics models for levels that blend the geometry and style of multiple games.
- #66Q3W3 Ghost of Tsushima: Procedural Grass - 2021 | Eric Wohllaib, Sucker Punch Productions | Game Developers Conference (GDC) 2021 | 55 pp.
  Micro abstract: Explains Ghost of Tsushima’s compute-driven grass pipeline, from tiled placement and culling to indirect drawing, cubic Bézier blade geometry, variable LOD, wind animation, and material shading.
- #QHMFH2 Improved Alpha Testing Using Hashed Sampling - 2019 | Chris Wyman, Morgan McGuire | IEEE Transactions on Visualization and Computer Graphics | 12 pp. | doi:10.1109/TVCG.2017.2739149
  Micro abstract: Develops hashed alpha testing, a stable quasi-random thresholding method that preserves distant alpha-mapped foliage and hair while controlling flicker, anisotropy, and interactions with TAA and alpha-to-coverage.
- #7GR3AQ Procedural Content Generation through Quality Diversity - 2019 | Ahmed Khalifa, Antonios Liapis, Daniele Gravina, Georgios N. Yannakakis, Julian Togelius | 2019 IEEE Conference on Games (CoG) | 8 pp. | doi:10.1109/CIG.2019.8848053
  Micro abstract: Argues for quality-diversity algorithms in procedural generation, producing broad collections of varied, playable content while exposing the design space for exploration and co-creation.
- #CQBDX4 Procedural Content Generation via Machine Learning (PCGML) - 2018 | Aaron Isaksen, Adam Summerville, Amy K. Hoover, Andy Nealen, Christoffer Holmgård, Julian Togelius, Matthew Guzdial, Sam Snodgrass | IEEE Transactions on Games | 15 pp. | doi:10.1109/TG.2018.2846639
  Micro abstract: Defines and surveys PCGML: generating functional game content directly from models trained on existing examples, with uses spanning creation, completion, repair, critique, and compression.
- #EARFEK Procedural Generation of Villages on Arbitrary Terrains - 2012 | Adrien Bernhardt, Adrien Peytavie, Arnaud Emilien, Eric Galin, Marie-Paule Cani | The Visual Computer | 10 pp. | doi:10.1007/s00371-012-0699-7
  Micro abstract: Presents a three-stage procedural model that grows terrain-responsive village roads and settlements, partitions land into plausible parcels, and generates slope-adapted buildings with open shape grammars.
- #EDURTK Real-Time GPU Tree Generation - 2025 | Bastian Kuth, Carsten Faber, Dominik Baumeister, Max Oberberger, Pirmin Pfeifer, Quirin Meyer, Seyedmasih Tabaei | High-Performance Graphics – Symposium Papers | 10 pp. | doi:10.2312/hpg.20251168
  Micro abstract: Introduces a GPU work-graph pipeline that generates, animates, edits, and continuously LODs detailed seasonal trees every frame, replacing gigabytes of baked geometry with kilobytes of parameters.
- #GBXEP3 Realistic Modeling and Rendering of Plant Ecosystems - 1998 | Bernd Lintermann, Matt Pharr, Oliver Deussen, Pat Hanrahan, Przemyslaw Prusinkiewicz, Radomír Měch | Proceedings of SIGGRAPH ’98 | 12 pp. | doi:10.1145/280814.280898
  Micro abstract: Presents a foundational pipeline for authoring plant ecosystems through terrain design, ecological simulation, procedural plant models, approximate instancing, and efficient rendering of billion-primitive scenes.
- #BDBBL6 Real‐time Realistic Rendering and Lighting of Forests - 2012 | Eric Bruneton, Fabrice Neyret | Computer Graphics Forum | 11 pp. | doi:10.1111/j.1467-8659.2012.03016.x
  Micro abstract: Combines detailed z-field trees with terrain shader-maps to render immense forests in real time, preserving sun, sky, canopy, and ground-lighting effects through seamless, scale-consistent transitions.
- #PQ68ZH Responsive Real-Time Grass Rendering for General 3D Scenes - 2017 | Klemens Jahrmann, Michael Wimmer | Proceedings of the 2017 Symposium on Interactive 3D Graphics and Games (I3D ’17) | 10 pp. | doi:10.1145/3023368.3023380
  Micro abstract: Renders every grass blade as responsive tessellated geometry on arbitrary 3D surfaces, with per-blade wind, gravity, and collision physics plus aggressive culling that retains dense fields in real time.
- #WZ8DHP Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents - 2026 | Rishabh Kar | arXiv | 25 pp. | doi:10.48550/arXiv.2605.01783
  Micro abstract: Integrates procedural generation and validation in an endless runner, using aerial and ground agents to detect blocked or unnavigable content before the player reaches it.
- #NRBMD5 Towards Friendly Mixed Initiative Procedural Content Generation: Three Pillars of Industry - 2020 | Frederic Fol Leymarie, Gorm Lai, William Latham | Proceedings of the International Conference on the Foundations of Digital Games (FDG '20) | 4 pp. | doi:10.1145/3402942.3402946
  Micro abstract: Distills three requirements for industry-friendly co-creative PCG tools: preserve designer control, keep feedback loops short, and fit into existing production pipelines.

Roads, Trails & Movement (8)
- #G3TBNG A Sequential Two-Step Algorithm for Fast Generation of Vehicle Racing Trajectories - 2016 | J. Christian Gerdes, John Subosits, Nitin R. Kapania | Journal of Dynamic Systems, Measurement, and Control | 12 pp. | doi:10.1115/1.4033311
  Micro abstract: Generates near-optimal racing trajectories quickly by alternating between a minimum-time speed profile and a convex path update that reduces curvature.
- #B6P8L4 Active walker model for the formation of human and animal trail systems - 1997 | Dirk Helbing, Frank Schweitzer, Joachim Keltsch, Péter Molnár | Physical Review E | 34 pp. | doi:10.1103/physreve.56.2527
  Micro abstract: Models trail systems as self-organization: walkers reinforce attractive routes while unused traces fade, producing dendritic ant trails and low-detour pedestrian networks.
- #V4TQYB Interactive procedural street modeling - 2008 | Eugene Zhang, Gregory Esch, Guoning Chen, Pascal Müller, Peter Wonka | ACM Transactions on Graphics | 10 pp. | doi:10.1145/1360612.1360702
  Micro abstract: Lets designers generate and edit large street networks through tensor fields, combining procedural speed with brush-like global and local control over street patterns.
- #UYLTYJ Modelling the Evolution of Human Trail Systems - 1997 | Dirk Helbing, Joachim Keltsch, Péter Molnár | Nature | 11 pp. | doi:10.1038/40353
  Micro abstract: Shows how pedestrian trails emerge through feedback between destination-seeking walkers, existing paths, and vegetation recovery, yielding a compromise between directness and shared infrastructure.
- #GY93FG Mountain Trail Formation and the Active Walker Model - 2009 | J. P. Hague, S. J. Gilks | International Journal of Modern Physics C | 22 pp. | doi:10.1142/S0129183109014059
  Micro abstract: Extends the active-walker model to steep terrain, explaining zigzag mountain trails through slope avoidance, directional persistence, and mutual reinforcement by ascending and descending walkers.
- #LXV9AT Principles of Trail Layout and Design - 2019 | California State Parks | California State Parks Trails Handbook | 64 pp.
  Micro abstract: A field-oriented guide to durable trail design, emphasizing curvilinear alignment, natural drainage, sustainable grades, control points, and close reading of landform and soils.
- #XDEFZS Procedural Generation of Roads - 2010 | A. Peytavie, E. Galin, E. Guérin, N. Maréchal | Computer Graphics Forum | 10 pp. | doi:10.1111/j.1467-8659.2009.01612.x
  Micro abstract: Automatically routes and constructs roads with an anisotropic shortest-path method that weighs slope and obstacles while treating surface segments, bridges, and tunnels consistently.
- #ARP5U7 The Topography of Minoan Peak Sanctuaries - 1983 | A. A. D. Peatfield | The Annual of the British School at Athens | 8 pp. | doi:10.1017/s0068245400019729
  Micro abstract: Argues that Minoan peak sanctuaries were chosen for visibility and proximity to local settlements, forming a beacon-like sacred network whose contraction tracked settlement abandonment rather than cultic collapse.

Scenario-Based & Behavioral Programming (8)
- #P2W4J5 Adaptive Behavioral Programming - 2011 | David Harel, Nir Eitan | 8 pp. | doi:10.1109/ictai.2011.109
  Micro abstract: Adds reinforcements to live sequence charts and BPJ so scenario-based programs can learn from their environment, specifying goals to pursue and scenarios to avoid, with modular learning decompositions.
- #XQ5NKX Challenges in Modeling and Unmodeling Emergence, Rule Composition, and Networked Interactions in Complex Reactive Systems - 2023 | Assaf Marron, David Harel, Guy Frankel, Irun Cohen, Smadar Szekely | 8 pp. | doi:10.5220/0011728900003402
  Micro abstract: Position paper on modeling emergence, rule composition, and networked interactions in complex reactive systems, introducing "unmodeling"—explicitly excluding entities and behaviors from model execution.
- #D4VB7S Distributing Scenario-Based Models: A Replicate-and-Project Approach - 2017 | Assaf Marron, Daniel Gritzner, David Harel, Guy Katz, Joel Greenyer, Shlomi Steinberg | MODELSWARD 2017 | 16 pp. | doi:10.5220/0006271301820195
  Micro abstract: Distributes scenario-based models by replicating the full specification on every component and projecting it per component, mimicking centralized behavior while sharply reducing synchronization.
- #CSJARA Enhancing Scenario-Based Modeling Using Large Language Models - 2026 | Assaf Marron, David Harel, Guy Katz, Smadar Szekely | Communications in Computer and Information Science | Springer Nature Switzerland | pp. 43-68 | 26 pp. | doi:10.1007/978-3-031-96841-9_3
  Micro abstract: Extended methodology for combining LLM chatbots with scenario-based modeling: iterative generation of stand-alone scenarios checked by analysis and human review, framed as a step toward Wise Computing.
- #3JCRAD On Augmenting Scenario-Based Modeling with Generative AI - 2024 | Assaf Marron, David Harel, Guy Katz, Smadar Szekely | MODELSWARD 2024 | 12 pp. | doi:10.5220/0012427100003645
  Micro abstract: Outlines a structured method for using generative-AI chatbots in modeling: iteratively generate scenario-based model fragments, then analyze and inspect them to converge on an accurate system model.
- #QV3BWZ On tracing reactive systems - 2011 | David Harel, Shahar Maoz | Software &amp; Systems Modeling | 22 pp. | doi:10.1007/s10270-010-0151-2
  Micro abstract: Introduces model-based trace visualization and exploration for reactive systems, using scenario-based (LSC) abstractions and the Tracer prototype, demonstrated on a PacMan game.
- #TDS4H2 Relaxing Synchronization Constraints in Behavioral Programs - 2013 | Amir Kantor, David Harel, Guy Katz | LPAR 2013 (Logic for Programming, Artificial Intelligence, and Reasoning) | 17 pp. | doi:10.1007/978-3-642-45221-5_25
  Micro abstract: Proposes eager execution for behavioral programs: fast b-threads run ahead when synchronization outcomes are predictable, improving performance, modularity, and distributability, shown in a C++ BP framework.
- #M5788P Towards Behavioral Programming in Distributed Architectures - 2015 | Amir Kantor, Assaf Marron, David Harel, Gera Weiss, Guy Katz, Guy Wiener | Science of Computer Programming | 58 pp. | doi:10.1016/j.scico.2014.03.003
  Micro abstract: Extends behavioral programming to distributed architectures: b-threads as Erlang processes, eager execution to relax synchronization, and modular distributed execution, demonstrated on simulations and a quadrotor.

Technology, Scale & Conviviality (2)
- #WYH36B The City as Convivial Centre - 1974 | Leopold Kohr | Tract, no. 12 (Gryphon Press) | 18 pp.
  Micro abstract: Kohr's essay arguing that cities exist for convivial life rather than economic function, and that human-scale size is what lets a city serve as a centre of leisure, culture, and encounter.
- #67REFX The Question Concerning Technology - 1977 | Martin Heidegger | The Question Concerning Technology and Other Essays (Harper & Row) | 23 pp.
  Micro abstract: Heidegger's essay on the essence of technology as Enframing (Gestell), a mode of revealing that reduces the world to standing-reserve, and on art as a possible saving power.

Terrain, Hydrology & Erosion (8)
- #NV2YRW FastFlow: GPU Acceleration of Flow and Depression Routing for Landscape Simulation - 2024 | Aryamaan Jain, Bernhard Kerbl, Brandon Finley, Guillaume Cordonnier, James Gain | Computer Graphics Forum | 13 pp. | doi:10.1111/cgf.15243
  Micro abstract: A GPU framework for routing surface flow through terrain and its depressions fast enough to make erosion, river, lake, and ecosystem simulations interactive.
- #2284QZ From features to fingerprints: A general diagnostic framework for anthropogenic geomorphology - 2019 | Damian Evans, Erle C Ellis, Giulia Sofia, Paolo Tarolli, Wenfang Cao | Progress in Physical Geography: Earth and Environment | 34 pp. | doi:10.1177/0309133318825284
  Micro abstract: Integrates geomorphology, archaeology, and high-resolution remote sensing into a framework for reading anthropogenic landforms as landscape-scale sociocultural fingerprints.
- #96ZMGK Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion - 2016 | Adrien Peytavie, Bedrich Benes, Guillaume Cordonnier, Jean Braun, Marie-Paule Cani, Éric Galin, Éric Guérin | Computer Graphics Forum | 11 pp. | doi:10.1111/cgf.12820
  Micro abstract: Generates large, controllable mountain terrains by coupling user-painted tectonic uplift with fluvial erosion, then turning the resulting stream graph into detailed landforms.
- #K82AS7 Legacy sediment: Definitions and processes of episodically produced anthropogenic sediment - 2013 | L. Allan James | Anthropocene | 11 pp. | doi:10.1016/j.ancene.2013.04.001
  Micro abstract: Broadens legacy sediment to episodically produced anthropogenic alluvium and colluvium, and explains its deposition, storage, and remobilization through sediment delivery–transport capacity dynamics.
- #DWXKYQ Physically-based analytical erosion for fast terrain generation - 2024 | Boris Gailleton, Guillaume Cordonnier, Petros Tzathas, Philippe Steer | Computer Graphics Forum | 14 pp. | doi:10.1111/cgf.15033
  Micro abstract: Turns the stream power law into an interactive terrain tool, replacing thousands of erosion time steps with analytical solutions and a direct control for landscape age.
- #MTDKDE Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models - 2014 | Clarence Lehman, David Mulla, Richard Barnes | Computers & Geosciences | 17 pp. | doi:10.1016/j.cageo.2013.04.024
  Micro abstract: Introduces Priority-Flood, a simple, optimal algorithm that removes drainage-blocking depressions from elevation models and can also derive watersheds and flow directions.
- #AK7NGE Procedural Riverscapes - 2019 | A. Peytavie, B. Benes, E. Galin, E. Guérin, J. Gain, T. Dupont, Y. Cortial | Computer Graphics Forum | 12 pp. | doi:10.1111/cgf.13814
  Micro abstract: Builds editable, animated riverscapes from bare terrain by carving hydrologically plausible channels and blending real-time procedural water primitives instead of simulating fluids.
- #DMTA8Y Terrain Generation Using Procedural Models Based on Hydrology - 2013 | Adrien Peytavie, Bedřich Beneš, Jean-David Génevaux, Éric Galin, Éric Guérin | ACM Transactions on Graphics | 10 pp. | doi:10.1145/2461912.2461996
  Micro abstract: Generates controllable, multiscale terrain from a sketched drainage network, representing rivers and landforms as an editable hierarchy of continuous procedural primitives.

Water Simulation & Rendering (12)
- #RBS5K6 A Layered Particle-Based Fluid Model for Real-Time Rendering of Water - 2010 | Daniel Scherzer, Florian Bagar, Michael Wimmer | Computer Graphics Forum | 7 pp. | doi:10.1111/j.1467-8659.2010.01734.x
  Micro abstract: Renders particle-based water and volumetric foam in real time using perspective-aware surface smoothing, physically guided foam formation, and layered depth compositing.
- #C4AY2M A Survey of Ocean Simulation and Rendering Techniques in Computer Graphics - 2011 | B. Crespin, D. Ghazanfarpour, E. Darles, J.-C. Gonzato | Computer Graphics Forum | 17 pp. | doi:10.1111/j.1467-8659.2010.01828.x
  Micro abstract: Surveys ocean graphics from spectral deep-water models to near-shore fluid simulation, then covers the foam, spray, and light transport needed for convincing rendering.
- #WZMZGY Advected river textures - 2009 | Dirk Arnold, Stephen Brooks, Tim Burrell | Computer Animation and Virtual Worlds | 11 pp. | doi:10.1002/cav.288
  Micro abstract: Combines a 2D Navier–Stokes solver, hydrostatic pressure columns, and advected procedural textures to render detailed, terrain-responsive rivers at real-time frame rates.
- #92XRH7 Lagrangian Texture Advection: Preserving both Spectrum and Velocity Field - 2011 |  Qizhi Yu, E. Bruneton, F. Neyret, N. Holzschuch | IEEE Transactions on Visualization and Computer Graphics | 13 pp. | doi:10.1109/tvcg.2010.263
  Micro abstract: Advects fluid textures with deformable particle grids, preserving both the input texture’s visual spectrum and exact motion along the velocity field without cumulative stretching.
- #8SERGP Real-time Breaking Waves for Shallow Water Simulations - 2007 | Markus Gross, Matthias Müller-Fischer, Nils Thürey, Simon Schirm | 15th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2007) | 8 pp. | doi:10.1109/PG.2007.33
  Micro abstract: Adds real-time overturning waves to shallow-water heightfields by detecting steep fronts and spawning connected particle sheets that collapse into splashes and foam.
- #CWC7H9 Real-time Rendering of Enhanced Shallow Water Fluid Simulations - 2013 | Antonio Susín, Jesús Ojeda | Computers & Graphics | 9 pp.
  Micro abstract: Builds a real-time rendering pipeline for shallow-water simulations, adding fine surface detail, advected foam, photon-based caustics, and screen-space reflection and refraction.
- #MVUJ8Z Real-time Rendering of River Networks - 2010 | Quintijn Hendrickx, Rafael Bidarra, Ruben M. Smelik | Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games | 1 pp.
  Micro abstract: Renders branching river networks efficiently with quadratic Bézier curves, GPU distance fields, and streaming normal maps instead of dense geometry or particle simulation.
- #5MGCZ5 Real-time River Representation by Dynamic Control of Data on Waves - 2008 | Makoto Kosugi, Nobuhiko Mukai, Yasuhiro Kato | 4 pp. | doi:10.3169/itej.62.2063
  Micro abstract: Dynamically switches river-wave models by viewing distance, preserving nearby reflection and wave detail while retaining wind-driven motion across the full landscape.
- #XDESU9 Scalable real‐time animation of rivers - 2009 | Eric Bruneton, Fabrice Neyret, Nicolas Holzschuch, Qizhi Yu | Computer Graphics Forum | 11 pp. | doi:10.1111/j.1467-8659.2009.01363.x
  Micro abstract: Animates rivers across vast terrains by computing steady flow locally and advecting fine surface detail only where visible, at a screen-space sampling density.
- #869NHK Very Fast Real-Time Ocean Wave Foam Rendering Using Halftoning - 2011 | Ian Parberry, Jennifer R. Alford, Mary Yingst | Proceedings of the 6th International North American Conference on Intelligent Games and Simulation (GAMEON-NA) | 7 pp.
  Micro abstract: Uses a spectrally controlled halftone mask to make texture-based ocean foam dissipate as clumped bubbles that pop, rather than merely fading transparently.
- #A2QB8L Water Flow in Portal 2 - 2010 | Alex Vlachos | ACM SIGGRAPH 2010 Course: Advances in Real-Time Rendering in 3D Graphics and Games | 54 pp.
  Micro abstract: Explains Portal 2’s production-friendly water shader: artist-painted flow maps advect layered normal maps, while offsets and noise suppress repetition and pulsing on limited hardware.
- #PBM2TC Water surface wavelets - 2018 | Chris Wojtan, Matthias Müller-Fischer, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, Tomáš Skřivan | ACM Transactions on Graphics | 13 pp. | doi:10.1145/3197517.3201336
  Micro abstract: Represents water waves as spatially varying directional amplitudes, enabling vast interactive simulations with fine detail, moving obstacles, solid coupling, and direct artistic control.

Unfiled (11)
- #TA7A6Y Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams - 2015 | David I. Spivak, Dmitry Vagner, Eugene Lerman | arXiv:1408.1598 | 26 pp.
  Micro abstract: Develops an operad-algebra formalism for open dynamical systems composed via wiring diagrams, underpinning compositional systems theory.
- #AX2VJD Discrete Exterior Calculus - 2005 | Anil N. Hirani, Jerrold E. Marsden, Mathieu Desbrun, Melvin Leok | arXiv:math/0508341 | 53 pp.
  Micro abstract: Introduces discrete exterior calculus, a coordinate-free discretization of differential forms on simplicial complexes for computational modeling.
- #LTESUF Finite Element Exterior Calculus: From Hodge Theory to Numerical Stability - 2010 | Douglas N. Arnold, Ragnar Winther, Richard S. Falk | arXiv:0906.4325 / Bulletin of the AMS | 74 pp.
  Micro abstract: Surveys finite element exterior calculus, unifying Hodge theory and mixed finite element stability analysis for PDE discretization.
- #PB725Y Graph theoretic foundations of multibody dynamics - 2011 | Abhinandan Jain | Multibody System Dynamics | 35 pp. | doi:10.1007/s11044-011-9267-6
- #3CV92Z moppe
- #6PYNP3 Object-Oriented Representation of Electro-Mechanical Assemblies Using UML - 2003 | Fujun Wang, Kevin W. Lyons, National Institute of Standards and Technology, Ram D. Sriram, Shaw C. Feng, Sudarsan Rachuri, Utpal Roy, Young-Hyun Han | NISTIR 7057 | 97 pp.
  Micro abstract: NIST report proposing the Open Assembly Model, a UML-based object-oriented representation for electro-mechanical assembly information exchange.
- #KSLF8E Ontology and Assembly Joint Topology Representation - 2008 | Kyoung-Yun Kim | Computer-Aided Design and Applications | 9 pp. | doi:10.3722/cadaps.2008.630-638
- #RT6CVD Port-Hamiltonian Systems on Graphs - 2013 | A. J. van der Schaft, B. M. Maschke | SIAM Journal on Control and Optimization | 32 pp. | doi:10.1137/110840091
- #NHJEJG Representing Geometric Structures in d Dimensions: Topology and Order - 1993 | Erik Brisson | Proceedings of the fifth annual symposium on Computational geometry | 10 pp.
  Micro abstract: Formalizes geometric structures in d dimensions via combinatorial topology and order relations, a foundation for cell-complex representations used in assembly/geometric modeling.
- #A6DBK8 Seven Sketches in Compositionality: An Invitation to Applied Category Theory - 2018 | Brendan Fong, David I. Spivak | 353 pp.
  Micro abstract: A textbook introducing applied category theory (orders, monoidal categories, operads, sheaves, etc.) through seven worked "sketches" connecting math to systems modeling.
- #KT87MS Towards an Ontology for Generative Design of Mechanical Assemblies - 2019 | Bahar Aameri, Hyunmin Cheong, J. Christopher Beck | Applied Ontology | 24 pp.
  Micro abstract: Proposes a formal ontology of mechanical assembly structure intended to support generative design systems.

### 25. Tool result: get_document

DOCUMENT #KSLF8E
Title: Ontology and Assembly Joint Topology Representation

Outline:
  - 1 #XZX8KP Ontology and Assembly Joint Topology Representation
    - 1.1 #VYJGTF ABSTRACT
    - 1.2 #TB653C 1. INTRODUCTION
    - 1.3 #2RMD6K 2. BACKGROUND
      - 1.3.1 #BMFPPU 2.1 Ontology
      - 1.3.2 #QD5BYD 2.2 Mereotopology
    - 1.4 #T8MDVH 3. ASSEMBLY DESIGN ONTOLOGY IMPLEMENTATION
    - 1.5 #44NN72 4. ASSEMBLY JOINT TOPOLOGY REPRESENTATION
      - 1.5.1 #DPWAA7 4.1 Assembly Hierarchical Relationships
      - 1.5.2 #9JUREE 4.2 Mereotopological Representation of Assembly/joining Relations
      - 1.5.3 #KVSB3J 4.3 SWRL Modeling of Assembly Joints
    - 1.6 #86YQRL 5. CASE STUDY
    - 1.7 #Z2JH96 6. CONCLUSION AND FUTURE RESEARCH
    - 1.8 #3AXEVM 7. ACKNOWLEDGEMENT
    - 1.9 #KU8JX4 8. REFERENCES

### 26. Tool result: get_document

DOCUMENT #RT6CVD
Title: Port-Hamiltonian Systems on Graphs

Outline:
  - 1 #9LKTB3 PORT-HAMILTONIAN SYSTEMS ON GRAPHS*
    - 1.1 #37Z7LS 4.1. Equilibria and Casimirs.
  - 2 #WFHULX REFERENCES

### 27. Tool result: get_document

DOCUMENT #PB725Y
Title: Graph theoretic foundations of multibody dynamics

Outline:
  - 1 #ZMAZUL Graph Theoretic Foundations of Multibody Dynamics Part II: Analysis and Algorithms
    - 1.1 #TRNF2U Abstract
    - 1.2 #9TY92W 1 Introduction
    - 1.3 #ZLM3JT 2 SKO models
      - 1.3.1 #D43DAZ 2.1 Definition of SKO models
      - 1.3.2 #77YGP5 2.2 Existence of SKO models
      - 1.3.3 #JDCJMC 2.3 Generalizations of SKO models
    - 1.4 #KWNWJK 3 SPO operator/vector products for trees
      - 1.4.1 #246DL4 3.1 SKO model O(\mathcal{N}) Newton-Euler inverse dynamics
        - 1.4.1.1 #J9FRR2 Algorithm 3.1 Newton-Euler inverse dynamics algorithm for an SKO model
    - 1.5 #9ZEVAZ 4 Lyapunov equations for SKO models
      - 1.5.1 #ESEQDW 4.1 Forward Lyapunov recursions for SKO models
      - 1.5.2 #9T9V4V 4.2 Mass matrix computation for an SKO model
        - 1.5.2.1 #DZWFFN Algorithm 4.1 Recursive computation of composite body inertias for an SKO model
        - 1.5.2.2 #9B6ZG8 Algorithm 4.2 Recursive computation of the SKO model mass matrix—
      - 1.5.3 #WK7AC5 4.3 Backward Lyapunov recursions for SKO models
    - 1.6 #TX8AHY 5 Riccati equations for SKO models
      - 1.6.1 #HFQPG8 5.1 The \mathcal{E}_\psi and \psi SKO and SPO operators
      - 1.6.2 #5A6P9L 5.2 Operator identities
        - 1.6.2.1 #TFU9KT Lemma 9 Useful spatial operator identities
          - 1.6.2.1.1 #N2HGUL Proof
        - 1.6.2.2 #QKKKLC Lemma 10 Additional spatial operator identities
          - 1.6.2.2.1 #D3LDLU Proof
    - 1.7 #DMJJQB 6 SKO model mass matrix factorization and inversion
      - 1.7.1 #JLG8HF Proof
      - 1.7.2 #CXEUVA Corollary 6.1 Determinant of the mass matrix
      - 1.7.3 #E7QPWD Proof
      - 1.7.4 #7SP9RY 6.1 O(N) AB forward dynamics
        - 1.7.4.1 #KH34LE Algorithm 6.1 O(N) AB forward dynamics for SKO models
      - 1.7.5 #MVU64Z 6.2 Application: Tree Operational Space Inertia
    - 1.8 #3FFEPF 7 SPO operator sparsity structure
      - 1.8.1 #ZNPKFX 7.1 Decomposition into serial-chain segments
      - 1.8.2 #JCX29D 7.2 Sparsity structure of the \mathcal{E}_k SKO matrix
      - 1.8.3 #L3RV5K 7.3 Sparsity structure of the \mathbf{A} matrix
      - 1.8.4 #PBGZPU 7.4 Sparsity structure of the \mathbf{M} mass matrix
    - 1.9 #NR3MU6 8 Generalized SKO formulation process
      - 1.9.1 #CUPUWV 8.1 Procedure for developing an SKO model
      - 1.9.2 #64W7CF 8.2 Potential non-tree topology generalizations
    - 1.10 #NVNJHG 9 Conclusions
    - 1.11 #F9PC6B Acknowledgments
    - 1.12 #2Y7G5C References

### 28. Assistant tool calls

#### Tool call: `read`

```json
{
  "blocks": [
    "VYJGTF",
    "9LKTB3",
    "TRNF2U"
  ]
}
```

### 29. Tool result: read

SECTION #VYJGTF
Document: #KSLF8E Ontology and Assembly Joint Topology Representation
Context:
  #KSLF8E Ontology and Assembly Joint Topology Representation
    #XZX8KP Ontology and Assembly Joint Topology Representation
      #VYJGTF ABSTRACT

Children:
  - #5P627X excerpt - This paper presents an ontology-based assembly joint topology representation framework, which is illustrated with a fixture assembly case study. Joints within the physical structu…
  - #L628VQ excerpt - Keywords: mereotopology, ontology, topology, SWRL, and collaborative design.
  - #CY6ZFD excerpt - DOI: 10.3722/cadaps.2008.630-638

SECTION #9LKTB3
Document: #RT6CVD Port-Hamiltonian Systems on Graphs
Context:
  #RT6CVD Port-Hamiltonian Systems on Graphs
    #9LKTB3 PORT-HAMILTONIAN SYSTEMS ON GRAPHS*

Children:
  - #LAATHN excerpt - A. J. VAN DER SCHAFT† AND B. M. MASCHKE‡
  - #TDQKG8 excerpt - Abstract. In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. The …
  - #RFUAWF excerpt - Key words. physical systems, Hamiltonian dynamics, Dirac structures, network dynamics, stability, symmetry reduction
  - #TNQRD7 excerpt - AMS subject classifications. 05C21, 37J99, 53D20, 70H05, 93A15, 93A30, 93C15, 93D20
  - #CYSS4J excerpt - DOI. 10.1137/110840091
  - #Z3C2SH excerpt - 1. Introduction. Discrete topological structures arise abundantly in physical systems modeling. The classical approach to the analysis of electrical circuits, dating back to Kirch…
  - #RKTVQ4 excerpt - During the last two decades the study of network dynamics has received ever-increasing attention, with input from, among others, the fields of graph theory, multiagent systems, dy…
  - #W566DU excerpt - *Received by the editors July 8, 2007; accepted for publication (in revised form) November 28, 2012; published electronically March 14, 2013.
  - #M7B5TG excerpt - http://www.siam.org/journals/sicon/51-2/84009.html
  - #824RVX excerpt - †Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, 9700 AK, Groningen, The Netherlands (A.J.van.der.Schaft@rug.nl). The research of this au…
  - #DB622P excerpt - ‡Laboratoire d'Automatique et de Génie des Procédés, Université Claude Bernard Lyon-1, F-69622 Villeurbanne, Cedex, France (maschke@lagep.univ-lyon1.fr).
  - #922JRF excerpt - 1 Note that this does not include the (random) evolution of the graphs themselves, as studied in random graph theory and statistical mechanics.
  - #9J4B5A excerpt
  - #3SJWSF excerpt
  - #GCGSVJ excerpt
  - #AP6NRZ excerpt
  - #JQ2NVU excerpt
  - #W27DVC excerpt - [36, 10, 32, 37, 14].
  - #9DWHS8 excerpt - From a geometric point of view the generalized Hamiltonian structure of the network dynamics is defined, apart from its Hamiltonian function and energy-dissipating relations, by a…
  - #CEHM3R excerpt - We will illustrate this framework on some of the physical examples mentioned above. Furthermore, we will show how the same port-Hamiltonian structure is shared by network dynamics…
  - #7YL4WB excerpt - While all examples given in the paper are simple, and could be approached from other angles as well, we believe that a major contribution of the paper resides in the identificatio…
  - #M9K4XX excerpt - In a companion paper we will describe how the geometric framework as developed in this paper for graphs can be extended to arbitrary k -complexes. Among others, this will allow fo…
  - #PGFZSB excerpt - Preliminary work regarding sections 3.4 and 3.5 can be found in [40, 38, 39].
  - #CDJZSA excerpt - 2. From directed graphs to Dirac structures. As a guiding example let us consider a mass-spring-damper system, for example, the one depicted in Figure 1.
  - #FTMD3L excerpt - The underlying directed graph of such a system is defined by vertices corresponding to the masses and edges corresponding to the springs and dampers, leading to the graph in Figur…
  - #YHGWBZ excerpt - How do we formalize such a system as a port-Hamiltonian system? A key ingredient in the definition of a port-Hamiltonian system is the geometric notion of a Dirac structure , gene…
  - #FKJ3Z3 excerpt - graph LR m1[m1] ---|spring 1| m2[m2] m1 ---|damper 1| m2 m2 ---|damper 2| m3[m3] m1 ---|spring 2| m3 Diagram of a mass-spring-damper system with three masses m1, m2, and m3. Mass …
  - #MJNCAD excerpt - FIG. 1. Mass-spring-damper system.
  - #2ZF463 excerpt
  - #KWRE4H excerpt
  - #M867C9 excerpt
  - #9XDJGE excerpt
  - #ZBVRF2 excerpt - A directed graph with three vertices arranged horizontally. The leftmost and middle vertices are connected by two curved edges: one above and one below. The middle and rightmost v…
  - #MMFNDZ excerpt - FIG. 2. The corresponding graph.
  - #H3HU4F excerpt - We first recall some basic notions of graph theory (see, e.g., [4]) and Dirac structures (see, e.g., [9, 13, 10]).
  - #CP6GWE excerpt - 2.1. Directed graphs and their vertex and edge spaces. A directed graph \mathcal{G} = (\mathcal{V}, \mathcal{E}) consists of a finite set \mathcal{V} of vertices (nodes) and a fin…
  - #8U4KFV excerpt - A directed graph is completely specified by its incidence matrix \hat{B} , which is an N \times M matrix, where N is the number of vertices and M is the number of edges, with the …
  - #GTCAMC excerpt - Given a graph, we define its vertex space \Lambda_0 as the vector space of all functions from \mathcal{V} to some linear space \mathcal{R} . In the examples, \mathcal{R} will be m…
  - #NJL7ZW excerpt - The dual spaces of \Lambda_0 and \Lambda_1 will be denoted by \Lambda^0 and \Lambda^1 , respectively. The duality pairing between f \in \Lambda_0 and e \in \Lambda^0 is given as
  - #QNLC4P excerpt - \langle f | e \rangle = \sum_{v \in \mathcal{V}} \langle f(v) | e(v) \rangle,
  - #CU6EYH excerpt - where \langle \cdot | \cdot \rangle on the right-hand side denotes the duality pairing between \mathcal{R} and \mathcal{R}^* , and a similar expression holds for f \in \Lambda_1 a…
  - #LPC2HD excerpt - The incidence matrix \hat{B} of the graph induces a linear map B from the edge space to the vertex space as follows. Define B : \Lambda_1 \rightarrow \Lambda_0 as the linear map w…
  - #TKU4P2 excerpt - 2 In principle we could also associate with the edges a linear space \mathcal{R}' which is different from the space \mathcal{R} associated with the vertices. In that case the defi…
  - #MRG698 excerpt
  - #YN4HX4 excerpt
  - #S373PU excerpt
  - #HJ53B6 excerpt
  - #NVEZ22 excerpt - B is denoted as
  - #DVL8F5 excerpt - B^* : \Lambda^0 \rightarrow \Lambda^1
  - #3ZNWUX excerpt - and is called the coincidence operator . For \mathcal{R} = \mathbb{R}^3 the coincidence operator is given by \hat{B}^T \otimes I_3 , while for \mathcal{R} = \mathbb{R} the coincid…
  - #NT58FZ excerpt - We will use the terminology 3 flows for the elements of \Lambda_0 and \Lambda_1 (notation f_0 and f_1 ) and efforts for the elements of their dual spaces \Lambda^0 and \Lambda^1 (…
  - #XPC9NU excerpt - 2.2. Open graphs. An open graph \mathcal{G} is obtained from an ordinary graph with a set of vertices \mathcal{V} by identifying a subset \mathcal{V}_b \subset \mathcal{V} of N_b …
  - #S4FSDE excerpt - The splitting of the vertices into internal and boundary vertices induces a splitting of the vertex space and its dual, given as
  - #TM8YL6 excerpt - \begin{aligned}\Lambda_0 &= \Lambda_{0i} \oplus \Lambda_{0b}, \\ \Lambda^0 &= \Lambda^{0i} \oplus \Lambda^{0b},\end{aligned}
  - #4YTQ2T excerpt - where \Lambda_{0i} is the vertex space corresponding to the internal vertices and \Lambda_{0b} the vertex space corresponding to the boundary vertices. Consequently, the incidence…
  - #JP77R5 excerpt - B = B_i \oplus B_b
  - #SU3B23 excerpt - with B_i : \Lambda_1 \rightarrow \Lambda_{0i} and B_b : \Lambda_1 \rightarrow \Lambda_{0b} .
  - #UJGW58 excerpt - Furthermore, we will define the boundary space \Lambda_b as the linear space of all functions from the set of boundary vertices \mathcal{V}_b to the linear space \mathcal{R} . Not…
  - #AL42L8 excerpt - B_b : \Lambda_1 \rightarrow \Lambda_b
  - #T68G2Z excerpt - called the boundary incidence operator . Nevertheless, we will be careful in distinguishing the two isomorphic linear spaces \Lambda_b and \Lambda_{0b} because of their different …
  - #YNFA3F excerpt - 3 This terminology stems from port-based and bond-graph modeling [27], where it has a slightly more specific connotation than in our case. The space \Lambda_0 is also called the s…
  - #8W4SZP excerpt
  - #JJB29K excerpt
  - #5MWZLG excerpt
  - #XBVD6V excerpt
  - #A6L78S excerpt - 2.3. Dirac structures. Recall (see [36, 9, 32]) the definition of a (constant 4 ) Dirac structure. Consider a vector space \mathcal{F} with dual space \mathcal{F}^* . As before, t…
  - #7E2TVQ excerpt - \langle\langle (f_a, e_a), (f_b, e_b) \rangle\rangle := \langle e_a | f_b \rangle + \langle e_b | f_a \rangle, \quad f_a, f_b \in \mathcal{F}, \quad e_a, e_b \in \mathcal{F}^*,
  - #5G43PW excerpt - where \langle \cdot | \cdot \rangle denotes the duality product between \mathcal{F} and \mathcal{F}^* .
  - #XBS7A2 excerpt - DEFINITION 2.1. A subspace \mathcal{D} \subset \mathcal{F} \times \mathcal{F}^* is a Dirac structure if \mathcal{D} = \mathcal{D}^\perp , where ^\perp denotes the orthogonal compl…
  - #7FVU8G excerpt - In the finite-dimensional case an equivalent, and often easier, characterization of Dirac structures is given as follows (see, e.g., [8, 14] for a proof).
  - #X8LGBL excerpt - PROPOSITION 2.2. A subspace \mathcal{D} \subset \mathcal{F} \times \mathcal{F}^* is a Dirac structure if and only if the following two conditions are satisfied:
  - #73TF55 excerpt - (1) \langle e | f \rangle = 0 \quad \text{for all } (f, e) \in \mathcal{D}, (ii) \dim \mathcal{D} = \dim \mathcal{F}.
  - #BL9JA3 excerpt - Note that the first equation in (1) can be regarded as a power-conservation property . The second equation states that a Dirac structure has maximal dimension with respect to this…
  - #QLYY7J excerpt - While Dirac structures thus formalize power-conserving interconnections of maximal dimension, the following special type of Dirac structure can be seen to be a generalization of T…
  - #RKQ54W excerpt - DEFINITION 2.3. A Dirac structure \mathcal{D} \subset \mathcal{F} \times \mathcal{F}^* is separable if
  - #MWJC4W excerpt - (2) \langle e_a | f_b \rangle = 0 \quad \text{for all } (f_a, e_a), (f_b, e_b) \in \mathcal{D}.
  - #M9LFXQ excerpt - Separable Dirac structures have the following simple geometric characterization, similar to Kirchhoff's current and voltage laws.
  - #8U6YN2 excerpt - PROPOSITION 2.4. Consider a separable Dirac structure \mathcal{D} \subset \mathcal{F} \times \mathcal{F}^* . Then
  - #87FPEW excerpt - (3) \mathcal{D} = \mathcal{K} \times \mathcal{K}^\perp
  - #H86PD9 excerpt - for some subspace \mathcal{K} \subset \mathcal{F} , where \mathcal{K}^\perp = \{e \in \mathcal{F}^* \mid \langle e | f \rangle = 0 \text{ for all } f \in \mathcal{K}\} . Conversel…
  - #SQRYU7 excerpt - Proof. It is immediately seen that any subspace \mathcal{K} \times \mathcal{K}^\perp satisfies (2) and is a Dirac structure since it satisfies (1). Conversely, let the Dirac struc…
  - #QQM6K8 excerpt - \begin{aligned} \mathcal{F}_0 &= \{f \in \mathcal{F} \mid (f, 0) \in \mathcal{D}\}, & \mathcal{F}_1 &= \{f \in \mathcal{F} \mid \exists e \in \mathcal{F}^* \text{ such that } (f, …
  - #S674PH excerpt - 4 This definition can be extended [13, 9] to (nonconstant) Dirac structures on manifolds: a Dirac structure \mathcal{D} on a manifold \mathcal{M} is defined as a vector subbundle …
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  - #4PAP28 excerpt - It is readily seen [10] that for any Dirac structure \mathcal{E}_1 = (\mathcal{F}_0)^\perp, \mathcal{E}_0 = (\mathcal{F}_1)^\perp . We will now show that (2) implies that \mathcal…
  - #Z5877Y excerpt - \langle (f_a, 0), (f_b, e_b) \rangle := \langle e_b | f_a \rangle + \langle 0 | f_b \rangle = \langle e_b | f_a \rangle = 0
  - #4K54TG excerpt - by (2). Hence, also (f_a, 0) \in \mathcal{D} and thus f_a \in \mathcal{F}_0 . By definition \mathcal{F}_0 \times \mathcal{E}_0 \subset \mathcal{D} , and hence \mathcal{K} \times \…
  - #WEZCFV excerpt - A typical instance of a separable Dirac structure, which will be frequently used in the remainder, is the following.
  - #K8QDHR excerpt - PROPOSITION 2.5. Let A : \mathcal{V} \rightarrow \mathcal{W} be a linear map between the linear spaces \mathcal{V} and \mathcal{W} with adjoint mapping A^* : \mathcal{W}^* \righta…
  - #463L8J excerpt - (4) \quad \langle w^* | Av \rangle = \langle A^* w^* | v \rangle
  - #APH3TS excerpt - for all v \in \mathcal{V}, w^* \in \mathcal{W}^* (where, as before, \langle \cdot | \cdot \rangle denotes the duality product between the dual spaces \mathcal{W} and \mathcal{W}^*…
  - #35X7E8 excerpt - (5) \quad \begin{aligned} \mathcal{D} &:= \{(v, w, v^*, w^*) \in (\mathcal{V} \times \mathcal{W}) \times (\mathcal{V}^* \times \mathcal{W}^*) \mid \\ &Av = w, v^* = -A^* w^*\} \en…
  - #WCNQ64 excerpt - is a separable Dirac structure.
  - #RADC65 excerpt - Proof. Define \mathcal{K} := \{(v, w) \in \mathcal{V} \times \mathcal{W} \mid Av = w\} . Then \mathcal{K}^\perp = \{(v^*, w^*) \in \mathcal{V}^* \times \mathcal{W}^* \mid v^* = -A…
  - #LQNG72 excerpt - A key feature of Dirac structures is that their composition is again a Dirac structure (in contrast with symplectic or Poisson structures, where this is not generally the case). L…
  - #4ZG3ME excerpt - (6) \quad \begin{aligned} \mathcal{D}_A \circ \mathcal{D}_B &= \{(f_A, e_A, f_B, e_B) \in \mathcal{F}_A \times \mathcal{F}_B \times \mathcal{F}_A^* \times \mathcal{F}_B^* \mid \ex…
  - #LZJHKM excerpt - It has been shown in [8, 31] that \mathcal{D}_A \circ \mathcal{D}_B is again a Dirac structure. Separable Dirac structures turn out to have the following special compositional pro…
  - #XPZJ7V excerpt - PROPOSITION 2.6. Let \mathcal{D}_A \subset \mathcal{F}_A \times \mathcal{F}_c \times \mathcal{F}_A^* \times \mathcal{F}_c^* and \mathcal{D}_B \subset \mathcal{F}_B \times \mathcal…
  - #QAZTRE excerpt - \mathcal{D}_i = \mathcal{K}_i \times \mathcal{K}_i^\perp \quad i = A, B,
  - #PVW65Q excerpt - where \mathcal{K}_i \subset \mathcal{F}_i \times \mathcal{F}_c, i = A, B . Define the composition
  - #FZ6TRW excerpt - \mathcal{K}_A \circ \mathcal{K}_B = \{(f_A, f_B) \in \mathcal{F}_A \times \mathcal{F}_B \mid \exists f \in \mathcal{F}_c \text{ such that } (f_A, f) \in \mathcal{K}_A, (f_B, -f) \…
  - #B4QBF9 excerpt - Then the composition \mathcal{D}_A \circ \mathcal{D}_B is the separable Dirac structure
  - #WUPSJY excerpt - (7) \quad \mathcal{D}_A \circ \mathcal{D}_B = (\mathcal{K}_A \circ \mathcal{K}_B) \times (\mathcal{K}_A \circ \mathcal{K}_B)^\perp.
  - #HWBAT4 excerpt - For explicit equational representations of compositions of Dirac structures we refer the reader to [8].
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  - #ZJJ44X excerpt - The compositionality property of Dirac structures is a key ingredient of port-Hamiltonian systems theory, and implies that the standard interconnection of port-Hamiltonian systems…
  - #RS9STW excerpt - 2.4. The graph Dirac structures. We now have all ingredients to define Dirac structures corresponding to the incidence structure of a directed graph.
  - #WFLJ5W excerpt - DEFINITION 2.7. Consider an open graph \mathcal{G} with vertex, edge, and boundary spaces, incidence operator B , and boundary incidence operator B_b . The flow-continuous 5 graph…
  - #PK53MY excerpt - \begin{aligned} \mathcal{D}_f(\mathcal{G}) &:= \{(f_1, e^1, f_{0i}, e^{0i}, f_b, e^b) \\ (8) \quad &\in \Lambda_1 \times \Lambda^1 \times \Lambda_{0i} \times \Lambda^{0i} \times \…
  - #UV7GPA excerpt - The effort-continuous graph Dirac structure \mathcal{D}_e(\mathcal{G}) is defined as
  - #JZY9MF excerpt - \begin{aligned} \mathcal{D}_e(\mathcal{G}) &:= \{(f_1, e^1, f_0, e^0, f_b, e^b) \\ (9) \quad &\in \Lambda_1 \times \Lambda^1 \times \Lambda_0 \times \Lambda^0 \times \Lambda_b \ti…
  - #2ETBAZ excerpt - By Proposition 2.5 both \mathcal{D}_f(\mathcal{G}) and \mathcal{D}_e(\mathcal{G}) are separable Dirac structures. Note that \mathcal{D}_f(\mathcal{G}) and \mathcal{D}_e(\mathcal{G…
  - #JCZHPJ excerpt - 2.5. Interconnection of open graphs and composition of graph Dirac structures. Interconnection of two open graphs \mathcal{G}^\alpha and \mathcal{G}^\beta is performed by identify…
  - #PCMQZQ excerpt - The incidence operator of the interconnected (closed) graph is obtained as follows. For simplicity of notation consider the case where \mathcal{R} = \mathbb{R} . Let \mathcal{G}^j…
  - #CMB8MR excerpt - B^j = \begin{bmatrix} B_i^j \\ B_b^j \end{bmatrix}, \quad j = \alpha, \beta.
  - #R9HFVY excerpt - 5 The terminology flow-continuous and effort-continuous stems from the fact that in the first case the boundary flows f_b are exclusively linked to the edge flows f_1 , while in t…
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  - #CYQVSK excerpt - The incidence operator B of the interconnected graph is then given as
  - #C5N39F excerpt - (10) \quad B = \begin{bmatrix} B_i^\alpha & 0 \\ 0 & B_i^\beta \\ B_b^\alpha & B_b^\beta \end{bmatrix},
  - #RXV8JJ excerpt - corresponding to the interconnection constraints on the boundary potentials and currents given by
  - #ZE98ET excerpt - (11) \quad e^{b\alpha} = e^{b\beta}, \quad f_b^\alpha + f_b^\beta = 0.
  - #BACCTC excerpt - Of course, several extensions are possible. For example, one may retain the set of shared boundary vertices \mathcal{V}_b := \mathcal{V}_b^\alpha = \mathcal{V}_b^\beta as being bo…
  - #GD6VQQ excerpt - (12) \quad e^{b\alpha} = e^{b\beta} = e^b, \quad f_b^\alpha + f_b^\beta + f_b = 0,
  - #WSV799 excerpt - with f_b, e^b the boundary flows and efforts of the interconnected graph.
  - #SE8PXB excerpt - Comparing the interconnection of open graphs with the composition of their graph Dirac structures (see, e.g., Proposition 2.6) it is readily seen that the flow/effort-continuous g…
  - #P4PVTM excerpt - 2.6. Derived graph Dirac structures. Other Dirac structures can be derived from the flow/effort-continuous Dirac structure by constraining some of the flows and the efforts to zer…
  - #XW6JMT excerpt - \{(f_{0i}, e^{0i}) \in \Lambda_{0i} \times \Lambda^{0i} \mid f_{0i} = 0\}
  - #H88U3R excerpt - will result by Proposition 2.6 in another separable Dirac structure called the Kirchhoff–Dirac structure , which will be discussed in detail in section 6.
  - #KAF29T excerpt - However, there are other possibilities which we will only indicate. One, somewhat dual to the Kirchhoff–Dirac structure, is to constrain (some of) the edge efforts in the flow/eff…
  - #N2FBQX excerpt - 3. Port-Hamiltonian systems on graphs. First (section 3.1) we will describe how port-Hamiltonian systems can be defined with respect to the canonical graph Dirac structures define…
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  - #PWC977 excerpt - 3.1. Definition of port-Hamiltonian systems with regard to the graph Dirac structures. In this subsection we will apply the general definition of port-Hamiltonian systems with reg…
  - #YNAK7M excerpt - For clarity of exposition throughout we consider the effort-continuous graph Dirac structure \mathcal{D}_e(\mathcal{G}) involving the flow and effort variables
  - #G34EK9 excerpt - (f_1, e^1, f_0, e^0, f_b, e^b) \in \Lambda_1 \times \Lambda^1 \times \Lambda_0 \times \Lambda^0 \times \Lambda_b \times \Lambda^b
  - #7VXZRB excerpt - (the exposition is directly repeated for the flow-continuous graph Dirac structure \mathcal{D}_f(\mathcal{G}) ). A port-Hamiltonian system is specified by defining, between all th…
  - #TGYJHY excerpt - \dot{x} = -f, \quad e = \frac{\partial H}{\partial x}(x),
  - #PFHRDM excerpt - or dually,
  - #5XQ6F3 excerpt - \dot{x} = e, \quad f = -\frac{\partial H}{\partial x}(x),
  - #7UH2UM excerpt - where x is a vector of energy variables (of the same dimension as f and e ), and H(x) is any function, representing the energy stored in the system.
  - #9ZLS4U excerpt - Furthermore, a dissipative relation between a vector of flow variables f and a conjugate vector of effort variables e is any static relation
  - #L8TGDQ excerpt - R(f, e) = 0
  - #KGACJY excerpt - with the property that \langle e | -f \rangle \geq 0 for all (f, e) satisfying R(f, e) = 0 .
  - #2TRKDH excerpt - In the case of a mass-spring-damper system with boundary masses (see subsection 3.2) the vertex flow and effort variables f_0, e^0 will be related by energy-storing relations \dot…
  - #BC4JRG excerpt - Thus a port-Hamiltonian system on a graph is defined by adding to the linear relations imposed by the graph Dirac structure constitutive relations between all the internal effort …
  - #DCJR5V excerpt - 6 Throughout this paper \frac{\partial H}{\partial x}(x) will denote the column vector of partial derivatives of H , with \frac{\partial^T H}{\partial x}(x) denoting the row vecto…
  - #TWYP6Y excerpt - 7 Hence port-Hamiltonian dynamics generalizes both classical Hamiltonian dynamics (with no energy-dissipation), and gradient systems (where there is in general no oscillation betw…
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  - #86S5W7 excerpt - The interpretation of the flow/effort-continuous graph Dirac structure as describing discrete conservation or balance laws becomes clearer from the above description of port-Hamil…
  - #3NW9EZ excerpt - \begin{aligned} \dot{x}^1 &= e^1, & f_1 &= -\frac{\partial H}{\partial x^1}(x^1, x_0), \\ \dot{x}_0 &= -f_0, & e^0 &= \frac{\partial H}{\partial x_0}(x^1, x_0) \end{aligned}
  - #9PEF48 excerpt - for state variables x^1 \in \Lambda^1 and x_0 \in \Lambda_0 , and energy function H . Then the relations imposed by the effort-continuous graph Dirac structure imply
  - #NVSAZJ excerpt - \dot{x}_0 + B_i f_1 = 0, \quad \dot{x}^1 + B^* e^0 = 0,
  - #KRHGY4 excerpt - expressing discrete conservation (or balance) laws between the storage of the quantities x_0 associated to the vertices and the flow f_1 through the edges, respectively, between t…
  - #TK276N excerpt - Furthermore, it is well known [36, 10, 32] that port-Hamiltonian systems may easily entail algebraic constraints on their state variables. Indeed, whenever some of the effort vari…
  - #P3TRCS excerpt - Finally, we note a fundamental property of any port-Hamiltonian dynamics. Let H(x) denote the total energy of the port-Hamiltonian system. Then because of the power-conserving pro…
  - #4MKEWF excerpt - (13) \quad \frac{d}{dt}H(x) = \left\langle \frac{\partial^T H}{\partial x}(x) \mid \dot{x} \right\rangle = \langle e^R \mid f_R \rangle + \langle e^b \mid f_b \rangle \leq \langle…
  - #A3TM8S excerpt - Hence the total energy itself satisfies a conservation law: its increase is equal to the externally supplied power \langle e^b \mid f_b \rangle minus the dissipated power -\langle…
  - #W7M5YB excerpt - Remark 3.1. One may directly extend the definition of port-Hamiltonian systems on graphs to the case where the graphs are dynamically changing in time, as briefly indicated in sec…
  - #4UBLTK excerpt - 3.2. Mass-spring-damper systems. The basic way of modeling a mass-spring-damper system as a port-Hamiltonian system on a graph is to associate the masses to the vertices , and the…
  - #CQPEQ3 excerpt - 3.2.1. Mass-spring systems. Consider a graph \mathcal{G} with N vertices (masses) and M edges (springs), specified by an incidence operator B . First, consider the situation where…
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  - #VJN4Y9 excerpt - (14) \quad \begin{bmatrix} \dot{q} \\ \dot{p} \end{bmatrix} = \begin{bmatrix} 0 & B^T \\ -B & 0 \end{bmatrix} \begin{bmatrix} \frac{\partial H}{\partial q}(q, p) \\ \frac{\partial…
  - #XNV24Y excerpt - defined with respect to the graph Dirac structure \mathcal{D}_e(\mathcal{G}) = \mathcal{D}_f(\mathcal{G}) . Note that in fact the skew-symmetric matrix
  - #9NBZS5 excerpt - (15) \quad J := \begin{bmatrix} 0 & B^T \\ -B & 0 \end{bmatrix}
  - #QRLBKP excerpt - defines a Poisson structure on the state space \Lambda^1 \times \Lambda_0 .
  - #RJRE46 excerpt - The inclusion of boundary vertices, and thereby of external interaction, can be done in different ways. The first option is to associate boundary masses to the boundary vertices. …
  - #E42QRM excerpt - (16) \quad \begin{aligned} \dot{q} &= B^T \frac{\partial H}{\partial p}(q, p), \\ \dot{p} &= -B \frac{\partial H}{\partial q}(q, p) + E f_b, \\ e^b &= E^T \frac{\partial H}{\parti…
  - #YZUDXL excerpt - Here E is a matrix with as many columns as there are boundary vertices; each column consists of zeros except for exactly one 1 in the row corresponding to the associated boundary …
  - #P2TTP4 excerpt - Another possibility is to start from the flow-continuous graph Dirac structure \mathcal{D}_f(\mathcal{G}) . In this case there are no masses associated to the boundary vertices, a…
  - #6YHZ8H excerpt - (17) \quad \begin{aligned} \dot{q} &= B_i^T \frac{\partial H}{\partial p}(q, p) + B_b^T e^b, \\ \dot{p} &= -B_i \frac{\partial H}{\partial q}(q, p), \\ f_b &= B_b \frac{\partial H…
  - #5X386W excerpt - with e^b \in \Lambda^b the velocities of the massless boundary vertices and f_b \in \Lambda_b the forces at the boundary vertices as experienced by the environment. Note that in t…
  - #XCZZAH excerpt - 8 One can also consider the hybrid case where some of the boundary vertices are associated to masses while the remaining ones are massless.
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  - #EMAWAQ excerpt - The above formulation of mass-spring systems in \mathcal{R} = \mathbb{R} directly extends to \mathcal{R} = \mathbb{R}^3 by using the incidence operator B = \tilde{B} \otimes I_3 a…
  - #R4LS2K excerpt - 3.2.2. Mass-damper systems. Replacing springs by dampers leads to mass-damper systems . In the case of the flow-continuous graph Dirac structure this yields the equations
  - #5U496E excerpt - \begin{aligned} B_i f_1 &= -\dot{p}, \\ B_b f_1 &= f_b, \\ e^1 &= -B_i^T \frac{\partial H}{\partial p}(p) - B_b^T e^b, \end{aligned} \quad (18)
  - #WPGCHV excerpt - where f_1, e^1 are the flows and efforts corresponding to the dampers (damping forces, respectively, velocities). For example, for linear dampers f_1 = -R e^1 , where R is the pos…
  - #HTXUPL excerpt - \begin{aligned} \dot{p} &= -B_i R B_i^T \frac{\partial H}{\partial p}(p) - B_i R B_b^T e^b, \\ f_b &= B_b R B_i^T \frac{\partial H}{\partial p}(p) + B_b^T R B_b^T e^b, \end{aligne…
  - #228N3T excerpt - where, as before, the inputs e^b are the boundary velocities and f_b are the forces as experienced at the massless boundary vertices.
  - #9RZER8 excerpt - 3.2.3. Mass-spring-damper systems. For a mass-spring-damper system the edges will correspond partly to springs and partly to dampers. Thus a mass-spring-damper system is described…
  - #5ZEF2C excerpt - \begin{bmatrix} \dot{q} \\ \dot{p} \end{bmatrix} = \begin{bmatrix} 0 & B_s^T \\ -B_s & -B_d R B_d^T \end{bmatrix} \begin{bmatrix} \frac{\partial H}{\partial q}(q, p) \\ \frac{\par…
  - #RWXU9S excerpt - In the presence of boundary vertices we may distinguish, as above, between massless boundary vertices, with inputs being the boundary velocities and outputs being the boundary (re…
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  - #NJJBPF excerpt - 3.3. Spatial mechanisms. In this section we briefly discuss the extension of mass-spring-damper systems in \mathbb{R} or \mathbb{R}^3 to spatial mechanisms , that is, networks of …
  - #K7F4NT excerpt - The basic topology of the mechanism is described by a directed graph, called the primary graph , whose vertices correspond to the rigid bodies and whose edges are associated with …
  - #YB94E5 excerpt - 3.3.1. The rigid body element. The configuration space of a rigid body is the Lie group of isometries in Euclidean space \mathbb{R}^3 , called the special Euclidean group and deno…
  - #NSSWES excerpt - The kinetic energy of a rigid body is defined by
  - #4BJJM7 excerpt - (21) \quad K(P) = \frac{1}{2} \left\langle P, \left( I^b \right)^{-1} (P) \right\rangle,
  - #V3MKMJ excerpt - where I^b : se(3) \rightarrow se^*(3) is a symmetric, positive-symmetric isomorphism, called the inertia operator of the rigid body in the body frame . The potential energy of the…
  - #JY8G4A excerpt - We assume that the rigid body is subject to an external force expressed as an element W_e \in se^*(3) , called force in fixed frame [18] or wrench in fixed frame [17], which is ob…
  - #5CHT92 excerpt - The dynamical equations of the rigid body elements may then be written as a port-Hamiltonian system [36], [20, eq. (1.37)]:
  - #5TD45Z excerpt - (22) \quad \begin{aligned} \frac{d}{dt} \begin{pmatrix} Q \\ P \end{pmatrix} &= \begin{pmatrix} 0 & TL_Q \\ -T^*L_Q & -P^\times \end{pmatrix} \begin{pmatrix} dU(Q) \\ (I^b)^{-1}(P…
  - #C5RZBG excerpt - where TL_Q denotes the tangent map to the left translation (mapping the velocities T \in se(3) in body frame into the velocities v \in T_Q SE(3) ), T^*L_Q denotes its dual map (ma…
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  - #F4D4AD excerpt - (23) \quad \begin{aligned} \mathcal{D}_{RB}(Q) = & \left\{ (v, W, T_e, F, T, W_e) \right. \\ & \left. \in T_QSE(3) \times se^*(3) \times se(3) \times T_Q^*SE(3) \times se(3) \time…
  - #SL3KYL excerpt - In this way we have associated with every vertex of the primary graph of the spatial mechanism a dynamical system (22) with inputs and outputs (W_e, T_e) \in se^*(3) \times se(3) .
  - #XMAF9C excerpt - 3.3.2. The kinematic pair. Constraints between the rigid bodies of the mechanism will be specified by kinematic pairs corresponding to each edge of the primary graph. A kinematic …
  - #HMVPWB excerpt - We have defined the spaces of freedom twists and constraint wrenches as subspaces of the Lie algebra se(3) and its dual. However, these spaces express constraints on the twists an…
  - #LPFW2J excerpt - (24) \quad Ad_{Q_{KP}}^* W_{KP} \in CW \quad \text{and} \quad Ad_{Q_{KP}^{-1}} T_{KP} \in \mathcal{FT}.
  - #9RTKAQ excerpt - Hence the constitutive equations of a kinematic pair may be expressed as the following nonconstant separable Dirac structure:
  - #P3LDA5 excerpt - (25) \quad \mathcal{D}_{CW}(Q_{KP}) = \left\{ (T_{KP}, W_{KP}) \in T_{Q_{KP}}SE(3) \times T_{Q_{KP}}^*SE(3) \mid \right. \\ \left. Ad_{Q_{KP}}^* W_{KP} \in CW \quad \text{and} \qu…
  - #XQZGAH excerpt - 9 Note that this is a nonconstant Dirac structure on SE(3) .
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  - #8D39J6 excerpt - The kinematic pair introduced above represents ideal kinematic constraints; in general, however, mechanical work may be produced at the kinematic pair due to the presence of actua…
  - #TJL7WZ excerpt - \begin{aligned} \mathcal{D}_{\mathcal{CW}}^I(Q_{KP}) &= \{(T_{KP}, W_{KP}, T_I, W_I) \\ (26) \quad &\in T_{Q_{KP}}SE(3) \times T_{Q_{KP}}^*SE(3) \times \mathcal{CW}^\perp \times s…
  - #5HLCL4 excerpt - It is easy to check that for W_I = 0 the interacting kinematic pair reduces to the kinematic pair as defined previously.
  - #B6EGJM excerpt - 3.3.3. The kinestatic connection network. The primary graph of the mechanism together with the kinematic pairs is called the kinestatic model of the mechanical system. Its associa…
  - #N4SRQY excerpt - Consider a mechanism defined by its primary graph \mathcal{G} composed of n_{RB} internal vertices (associated with the rigid bodies), n_b boundary vertices corresponding to rigid…
  - #NW6FV7 excerpt - (T^{KP}, W^{KP}, T^{RB}, W^{RB}, T^b, W^b) \in \mathcal{D}_f(\mathcal{G}).
  - #H2G4UG excerpt - Composition of \mathcal{D}_f(\mathcal{G}) with the Dirac structures \mathcal{D}_{\mathcal{CW}}(Q_{KP}) corresponding to all the kinematic pairs then results in the Dirac structure…
  - #G9HDBH excerpt - (27) \quad (T^I, W^I, T^{RB}, W^{RB}, T^b, W^b) \in \mathcal{D}_{KS}.
  - #Q2AX73 excerpt - 3.3.4. Dynamics of spatial mechanisms. The state space \mathcal{X} of the complete mechanism is the product space of the state spaces of all the rigid bodies, i.e., \mathcal{X} = …
  - #5EXEUY excerpt - 10 Or the effort-continuous graph Dirac structure in case the rigid bodies corresponding to the boundary vertices have nonzero inertia operator.
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  - #6P9MN2 excerpt - number of internal vertices of the primary graph). Recalling that the rigid body dynamics is defined as a port-Hamiltonian system with respect to the Dirac structure (23), one the…
  - #LRQVV7 excerpt - (28) \quad \left( -\frac{dx}{dt}, \frac{\partial H_M}{\partial x}(x), T^I, W^I, T^b, W^b \right) \in \mathcal{D}_M.
  - #T377KK excerpt - 3.4. Hydraulic networks. The interpretation of the flow/effort-continuous graph Dirac structures as capturing the basic conservation/balance laws of a network becomes especially t…
  - #V36FNS excerpt - A hydraulic network can be modeled as a directed graph with edges corresponding to pipes; see, e.g., [29, 12]. The vertices may correspond to either connection points with fluid r…
  - #Q94EMV excerpt - (29) \quad \dot{x} = -B\nu
  - #EC3UEB excerpt - with B denoting the incidence matrix of the graph. In the absence of fluid reservoirs this simply reduces to Kirchhoff’s current laws B\nu = 0 .
  - #STLSVN excerpt - For incompressible fluids a standard model of the fluid flow \nu_e through pipe e is
  - #HVZ7NS excerpt - (30) \quad J_e \dot{\nu}_e = P_i - P_j - \lambda_e(\nu_e),
  - #RSXKKZ excerpt - where P_i and P_j are the pressures at the tail, respectively, head, vertices of edge e . Note that this in fact captures two effects: one corresponding to energy storage and one …
  - #EEQZLT excerpt - In the case of fluid reservoirs at the vertices the pressures P_v at each vertex v are functions of x_v , and thus, being scalar functions, are always derivable from an energy fun…
  - #LWGJEH excerpt - 3.5. Port-Hamiltonian formulation of consensus algorithms. While all previous examples of port-Hamiltonian systems on graphs arise from physical modeling, the system treated in th…
  - #KCLMKA excerpt - Consider a network of N agents moving in linear space \mathcal{R} , whose interaction topology is described by an undirected graph \mathcal{G} (symmetric interaction). Denote by E…
  - #BDNP2U excerpt
  - #RF99H6 excerpt
  - #ZJE3C3 excerpt
  - #3K39K5 excerpt
  - #ZD2TL2 excerpt - Associated to each agent v is a vector x_v \in \mathcal{R} describing the motion in the linear space \mathcal{R} . In the standard consensus algorithm (see, e.g., [25]), the vecto…
  - #RZUEXY excerpt - (31) \quad \dot{x}_v(t) = - \sum_{(v,w) \in E(\mathcal{G})} g_{(v,w)}(x_v(t) - x_w(t)),
  - #J5VMWA excerpt - where g_{(v,w)} > 0 denotes a certain positive-definite weight matrix associated to each edge. For simplicity of exposition let us take the linear space \mathcal{R} to be equal to…
  - #X8T4W9 excerpt - (32) \quad \dot{x} = -B_i G B_i^T x - B_i G B_b^T u,
  - #G7VS2D excerpt - with B the incidence matrix of the graph endowed with an arbitrary orientation , 11 and G the diagonal matrix with elements g_{(v,w)} corresponding to each edge (v,w) . This defin…
  - #K4E4NK excerpt - (33) \quad \dot{x} = -B_i G B_i^T \frac{\partial H}{\partial x}(x) - B_i G B_b^T u,
  - #Q77NPV excerpt - which are the same equations as those for the mass-damper system (19), with u = e_b \in \Lambda^b . Note that the corresponding artificial output vector y = f_b \in \Lambda_b give…
  - #RRGB7U excerpt - y := B_b G B_i^T \frac{\partial H}{\partial x}(x) + B_b G B_b^T u
  - #7GUJ8S excerpt - equals minus the rate of the leader variables if the leader variables were supposed to obey the consensus algorithm with regard to the follower agents (which is not the case). Hen…
  - #QU6R8V excerpt - 3.5.1. Network clustering dynamical models. A dynamical model for network clustering, where the network splits into subnetworks which separately reach consensus, was recently prop…
  - #AQ8H4A excerpt - (34) \quad \dot{x}_i = -\frac{dJ_i}{dx_i}(x_i) + u_i, \quad i = 1, \dots, N,
  - #58YHX7 excerpt - where the functions J_i(x_i) are certain objective functions. Let the vector u with components u_i be determined as
  - #L4HRXQ excerpt - (35) \quad u = B \frac{\partial V}{\partial z}(z), \quad z = -B^T x,
  - #NZ7TQ7 excerpt - 11 It is easily seen [4] that the Laplacian matrix BGB^T is independent of the chosen orientation.
  - #MZPL7R excerpt
  - #J2KBF9 excerpt
  - #RDRKRR excerpt
  - #QPGHR7 excerpt
  - #5H2H8P excerpt - where V(z) = V_1(z_1) + \dots + V_M(z_M) for certain functions V_1, \dots, V_M . This is readily seen to result in a port-Hamiltonian system with total Hamiltonian H(x, z) = \frac…
  - #XCM7V8 excerpt - Many other models of network dynamics, of a “nonphysical” background, can be formulated as port-Hamiltonian systems on graphs. Examples include coordination control [1] and edge a…
  - #TFQ2A4 excerpt - 4. Dynamical analysis. In this section we will investigate the dynamical properties of a paradigmatic example of a port-Hamiltonian system on a graph, namely the mass-spring-dampe…
  - #BP8RHQ excerpt - Thus we will consider a mass-spring-damper system as described by a graph \mathcal{G}(\mathcal{V}, \mathcal{E}_s \cup \mathcal{E}_d) , where the vertices in \mathcal{V} correspond…
  - #J7QVPB excerpt - (36) \quad \begin{bmatrix} \dot{q} \\ \dot{p} \end{bmatrix} = \begin{bmatrix} 0 & B_s^T \\ -B_s & -B_d R B_d^T \end{bmatrix} \begin{bmatrix} \frac{\partial H}{\partial q}(q, p) \\…
  - #843TM7 excerpt - Throughout this section we make the following simplifying assumption. 13
  - #JD32RD excerpt - ASSUMPTION 4.1. The graph \mathcal{G}(\mathcal{V}, \mathcal{E}_s \cup \mathcal{E}_d) is connected or, equivalently, \ker B_s^T \cap \ker B_d^T = \text{span } \mathbb{1} .
  - #37Z7LS section: 4.1. Equilibria and Casimirs.

SECTION #TRNF2U
Document: #PB725Y Graph theoretic foundations of multibody dynamics
Context:
  #PB725Y Graph theoretic foundations of multibody dynamics
    #ZMAZUL Graph Theoretic Foundations of Multibody Dynamics Part II: Analysis and Algorithms
      #TRNF2U Abstract

Children:
  - #XZ9X34 excerpt - This second, of a two part paper, uses concepts from graph theory to obtain a deeper understanding of the mathematical foundations of multibody dynamics. The first part [7] establ…

### 30. Assistant

Good, I have enough. Now writing micro-abstracts for the three remaining documents and generating cover images for all ten, then organizing folders.

#### Tool call: `update_document_metadata`

```json
{
  "document_id": "KSLF8E",
  "micro_abstract": "Uses mereotopology and SWRL rules to represent assembly joints as ontological relations, illustrated on a fixture assembly case study."
}
```

#### Tool call: `update_document_metadata`

```json
{
  "document_id": "RT6CVD",
  "micro_abstract": "Builds port-Hamiltonian systems on open directed graphs via Dirac structures, unifying mass-spring-damper networks, spatial mechanisms, hydraulic networks, and consensus dynamics under one compositional geometric framework."
}
```

#### Tool call: `update_document_metadata`

```json
{
  "document_id": "PB725Y",
  "micro_abstract": "Second of a two-part paper deriving O(N) recursive algorithms (Newton-Euler, Lyapunov/Riccati factorizations) for multibody dynamics from the graph-theoretic spatial kernel/operator (SKO/SPO) models built in Part I."
}
```

### 31. Tool result: update_document_metadata

Updated metadata for #KSLF8E: micro_abstract

### 32. Tool result: update_document_metadata

Updated metadata for #RT6CVD: micro_abstract

### 33. Tool result: update_document_metadata

Updated metadata for #PB725Y: micro_abstract

### 34. Assistant

Now generating cover art for each of the 10 documents, grounded in their actual content/aesthetic.

#### Tool call: `generate_image`

```json
{
  "prompt": "Abstract technical illustration for a paper on geometric structures in d dimensions: a luminous lattice of interlocking simplicial cells (vertices, edges, triangular and tetrahedral faces) floating in dark space, rendered like an architect's wireframe diagram with subtle order-theoretic Hasse-diagram lines connecting cells of different dimension, cool blue and white ink on charcoal background, precise technical-diagram aesthetic, no text."
}
```

#### Tool call: `generate_image`

```json
{
  "prompt": "Technical cutaway illustration of an electro-mechanical assembly exploded into labeled UML-style class boxes: bolts, brackets, and gears connected by thin dashed relationship lines and diamond aggregation markers, isometric engineering-blueprint style, cyan lines on navy blueprint paper, precise CAD rendering, no readable text, evokes structured object-oriented modeling of machine parts."
}
```

#### Tool call: `generate_image`

```json
{
  "prompt": "Conceptual diagram artwork of open dynamical systems composed through wiring diagrams: nested translucent boxes with colored wires threading in and out, some boxes plugged into larger boxes like an operad composition tree, glowing signal-flow lines in teal, magenta and gold on a deep indigo background, clean vector-diagram aesthetic evocative of category theory and systems engineering, no text."
}
```

#### Tool call: `generate_image`

```json
{
  "prompt": "Elegant scientific diagram of a port-Hamiltonian network: a directed graph of nodes (masses, reservoirs) and edges (springs, dampers, pipes) with small flow and effort arrows at each port, energy flowing through the graph rendered as glowing golden light along the edges against a deep teal background, style of a physics textbook figure turned into fine art, geometric and precise, no text."
}
```

#### Tool call: `generate_image`

```json
{
  "prompt": "Fine-art rendering of discrete exterior calculus: a curved triangulated surface (simplicial mesh) over which discrete differential forms are visualized as small oriented arrows and shaded dual cells, primal mesh in white wireframe and dual mesh in orange overlay, floating above a dark background like a differential-geometry textbook figure elevated to art, crisp vector linework, no text."
}
```

#### Tool call: `generate_image`

```json
{
  "prompt": "Minimalist geometric artwork illustrating order and topology of cellular structures in d dimensions: a stack of translucent polytopes (points, edges, polygons, polyhedra) connected by thin order-relation lines forming a partial order lattice, rendered in monochrome ink washes with occasional deep red accent lines, evokes 1990s computational geometry diagrams, no text."
}
```

#### Tool call: `generate_image`

```json
{
  "prompt": "Elegant mathematical illustration of finite element exterior calculus: a differential form field visualized over a triangulated 2D mesh with Whitney basis functions shown as glowing gradient patches on each triangle, small Hodge-star arrows linking primal and dual elements, cool blues and warm ochre gradients on white background, precise academic-diagram style elevated to fine art, no text."
}
```

#### Tool call: `generate_image`

```json
{
  "prompt": "Playful yet precise illustration representing applied category theory's 'seven sketches': seven small interconnected diagrams arranged like constellation panels — a preorder Hasse diagram, a monoidal box-and-wire diagram, an operad tree, a profunctor bridge, a sheaf over an open cover, a database schema graph, and a Petri net — all rendered in a unified pastel color-coded ink style on cream paper, textbook-elegant, no text."
}
```

#### Tool call: `generate_image`

```json
{
  "prompt": "Technical illustration of the NIST Open Assembly Model: a formal information model of a mechanical assembly shown as a hierarchical tree of labeled boxes and connector lines describing parts, tolerances, joints, and constraints, precise government-report engineering-diagram style, muted grays and institutional blue accents, isometric machine parts fading into abstract schema boxes, no text."
}
```

#### Tool call: `generate_image`

```json
{
  "prompt": "Dynamic technical illustration of graph-theoretic multibody dynamics: an articulated tree of rigid bodies (spheres and rods) connected by hinge-joint graph edges, overlaid with recursive spatial operator equations rendered as faint glowing matrix blocks propagating up and down the tree like recursive computation waves, dark background with electric blue and amber highlights, precise robotics-textbook diagram aesthetic, no text."
}
```

### 35. Tool result: generate_image

GENERATED IMAGE #NZRH53
URL: /images/NZRH53
Model: gpt-image-2
Prompt: Abstract technical illustration for a paper on geometric structures in d dimensions: a luminous lattice of interlocking simplicial cells (vertices, edges, triangular and tetrahedral faces) floating in dark space, rendered like an architect's wireframe diagram with subtle order-theoretic Hasse-diagram lines connecting cells of different dimension, cool blue and white ink on charcoal background, precise technical-diagram aesthetic, no text.

### 36. Tool result: generate_image

GENERATED IMAGE #WA2J7X
URL: /images/WA2J7X
Model: gpt-image-2
Prompt: Technical cutaway illustration of an electro-mechanical assembly exploded into labeled UML-style class boxes: bolts, brackets, and gears connected by thin dashed relationship lines and diamond aggregation markers, isometric engineering-blueprint style, cyan lines on navy blueprint paper, precise CAD rendering, no readable text, evokes structured object-oriented modeling of machine parts.

### 37. Tool result: generate_image

GENERATED IMAGE #4PCU4X
URL: /images/4PCU4X
Model: gpt-image-2
Prompt: Conceptual diagram artwork of open dynamical systems composed through wiring diagrams: nested translucent boxes with colored wires threading in and out, some boxes plugged into larger boxes like an operad composition tree, glowing signal-flow lines in teal, magenta and gold on a deep indigo background, clean vector-diagram aesthetic evocative of category theory and systems engineering, no text.

### 38. Tool result: generate_image

GENERATED IMAGE #SP65TH
URL: /images/SP65TH
Model: gpt-image-2
Prompt: Elegant scientific diagram of a port-Hamiltonian network: a directed graph of nodes (masses, reservoirs) and edges (springs, dampers, pipes) with small flow and effort arrows at each port, energy flowing through the graph rendered as glowing golden light along the edges against a deep teal background, style of a physics textbook figure turned into fine art, geometric and precise, no text.

### 39. Tool result: generate_image

GENERATED IMAGE #JQHYCT
URL: /images/JQHYCT
Model: gpt-image-2
Prompt: Fine-art rendering of discrete exterior calculus: a curved triangulated surface (simplicial mesh) over which discrete differential forms are visualized as small oriented arrows and shaded dual cells, primal mesh in white wireframe and dual mesh in orange overlay, floating above a dark background like a differential-geometry textbook figure elevated to art, crisp vector linework, no text.

### 40. Tool result: generate_image

GENERATED IMAGE #QSLDKV
URL: /images/QSLDKV
Model: gpt-image-2
Prompt: Minimalist geometric artwork illustrating order and topology of cellular structures in d dimensions: a stack of translucent polytopes (points, edges, polygons, polyhedra) connected by thin order-relation lines forming a partial order lattice, rendered in monochrome ink washes with occasional deep red accent lines, evokes 1990s computational geometry diagrams, no text.

### 41. Tool result: generate_image

GENERATED IMAGE #SGRSV3
URL: /images/SGRSV3
Model: gpt-image-2
Prompt: Elegant mathematical illustration of finite element exterior calculus: a differential form field visualized over a triangulated 2D mesh with Whitney basis functions shown as glowing gradient patches on each triangle, small Hodge-star arrows linking primal and dual elements, cool blues and warm ochre gradients on white background, precise academic-diagram style elevated to fine art, no text.

### 42. Tool result: generate_image

GENERATED IMAGE #JKKRJZ
URL: /images/JKKRJZ
Model: gpt-image-2
Prompt: Playful yet precise illustration representing applied category theory's 'seven sketches': seven small interconnected diagrams arranged like constellation panels — a preorder Hasse diagram, a monoidal box-and-wire diagram, an operad tree, a profunctor bridge, a sheaf over an open cover, a database schema graph, and a Petri net — all rendered in a unified pastel color-coded ink style on cream paper, textbook-elegant, no text.

### 43. Tool result: generate_image

GENERATED IMAGE #BG6ZXM
URL: /images/BG6ZXM
Model: gpt-image-2
Prompt: Technical illustration of the NIST Open Assembly Model: a formal information model of a mechanical assembly shown as a hierarchical tree of labeled boxes and connector lines describing parts, tolerances, joints, and constraints, precise government-report engineering-diagram style, muted grays and institutional blue accents, isometric machine parts fading into abstract schema boxes, no text.

### 44. Tool result: generate_image

GENERATED IMAGE #YVUBFB
URL: /images/YVUBFB
Model: gpt-image-2
Prompt: Dynamic technical illustration of graph-theoretic multibody dynamics: an articulated tree of rigid bodies (spheres and rods) connected by hinge-joint graph edges, overlaid with recursive spatial operator equations rendered as faint glowing matrix blocks propagating up and down the tree like recursive computation waves, dark background with electric blue and amber highlights, precise robotics-textbook diagram aesthetic, no text.

### 45. Assistant tool calls

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "NZRH53",
  "document_id": "NHJEJG",
  "folder": "Assembly & Mechanism Ontology"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "BG6ZXM",
  "document_id": "6PYNP3",
  "folder": "Assembly & Mechanism Ontology"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "QSLDKV",
  "document_id": "KSLF8E",
  "folder": "Assembly & Mechanism Ontology"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "WA2J7X",
  "document_id": "KT87MS",
  "folder": "Assembly & Mechanism Ontology"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "4PCU4X",
  "document_id": "TA7A6Y",
  "folder": "Graph-Theoretic & Compositional Systems Theory"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "SP65TH",
  "document_id": "RT6CVD",
  "folder": "Graph-Theoretic & Compositional Systems Theory"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "YVUBFB",
  "document_id": "PB725Y",
  "folder": "Graph-Theoretic & Compositional Systems Theory"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "JKKRJZ",
  "document_id": "A6DBK8",
  "folder": "Graph-Theoretic & Compositional Systems Theory"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "JQHYCT",
  "document_id": "AX2VJD",
  "folder": "Discrete & Finite Element Exterior Calculus"
}
```

#### Tool call: `update_document_metadata`

```json
{
  "cover_image_id": "SGRSV3",
  "document_id": "LTESUF",
  "folder": "Discrete & Finite Element Exterior Calculus"
}
```

### 46. Tool result: update_document_metadata

Updated metadata for #NHJEJG: cover_image_id, folder

### 47. Tool result: update_document_metadata

Updated metadata for #6PYNP3: cover_image_id, folder

### 48. Tool result: update_document_metadata

Updated metadata for #KSLF8E: cover_image_id, folder

### 49. Tool result: update_document_metadata

Updated metadata for #KT87MS: cover_image_id, folder

### 50. Tool result: update_document_metadata

Updated metadata for #TA7A6Y: cover_image_id, folder

### 51. Tool result: update_document_metadata

Updated metadata for #RT6CVD: cover_image_id, folder

### 52. Tool result: update_document_metadata

Updated metadata for #PB725Y: cover_image_id, folder

### 53. Tool result: update_document_metadata

Updated metadata for #A6DBK8: cover_image_id, folder

### 54. Tool result: update_document_metadata

Updated metadata for #AX2VJD: cover_image_id, folder

### 55. Tool result: update_document_metadata

Updated metadata for #LTESUF: cover_image_id, folder

### 56. Assistant

All 10 documents now have micro-abstracts, generated cover art, and folder placement:

**Assembly & Mechanism Ontology**
- #NHJEJG Brisson 1993 — geometric structures/topology & order
- #6PYNP3 Rachuri et al. 2003 — NIST Open Assembly Model (UML)
- #KSLF8E Kim 2008 — ontology & assembly joint topology
- #KT87MS Aameri, Cheong, Beck 2019 — ontology for generative design of assemblies

**Graph-Theoretic & Compositional Systems Theory**
- #TA7A6Y Vagner, Spivak, Lerman 2015 — wiring-diagram operad algebras
- #RT6CVD van der Schaft & Maschke 2013 — port-Hamiltonian systems on graphs
- #PB725Y Jain 2011 — graph-theoretic multibody dynamics, Part II
- #A6DBK8 Fong & Spivak 2018 — Seven Sketches in Compositionality

**Discrete & Finite Element Exterior Calculus**
- #AX2VJD Desbrun et al. 2005 — discrete exterior calculus
- #LTESUF Arnold, Falk, Winther 2010 — finite element exterior calculus

Each now carries a concise, content-checked micro-abstract (the three that lacked one after import — Kim, van der Schaft/Maschke, Jain — were written after reading their abstracts directly) and a bespoke cover image reflecting its subject matter (simplicial lattices, UML assembly schemas, wiring-diagram operads, port-Hamiltonian graphs, DEC/FEEC meshes, and the "seven sketches" constellation).