Peak sanctuaries as an inhabited dual of drainage basins

Peatfield’s evidence supports a precise version of the “dual of basins” intuition. Hydrologically, a watershed collects terrain cells toward a common outlet: watersheds are upstream-connected cells associated with an outlet #WL3SCW and FastFlow defines a basin by a shared stream-tree root #A6G5PJ The terrain-generation paper explicitly constructs a dual graph on the crests between watershed cells #U7AJ7K A sanctuary can be modeled as a culturally selected point on or just inside that crest system: not necessarily the highest summit, but the point that most directly overlooks—and is visible from—a particular inhabited plain #QPEZUU #N7XTK3 Its relation reverses downstream collection: settlement paths, attention, and offerings converge uphill, while sight, fire, and divine protection project back down #RBPN5L The local service regions suggested by Peatfield #F2VBJL are therefore analogous to catchments, while intervisible sanctuaries form a second, crest-level network #GDV37F #JAHVNN Formally, assigning each inhabited cell to one shrine would induce a partition analogous to the inverse-image partition of a function #BLF82B but raw viewsheds overlap, so without a unique service assignment the better object is a cover, bipartite graph, or weighted field rather than a strict partition. Alexander’s language adds a complementary reading: each shrine is a strong center supported by its surrounding settlements and landscape #GHEACQ while dominant sanctuaries create a recursive hierarchy of centers #25Z8H8 Movement closes the loop: visibility affects trail attraction #MZP8G3 and slope-constrained walkers generate mountain paths #2QALPN This suggests a generative model coupling hydrological basin labels, one-sided viewsheds, accessibility/trail evolution, and shrine-to-shrine intervisibility.