Paper 1: NTLA 2.0: Nested Topological Learning Architecture

Nested Topological Learning Architecture 2.0

NTLA-O series Paper 1, a systematic revision of the earlier "Nested Topological Learning Architecture" (NTLA), forming the foundation for the whole series that follows. Three revisions: (1) topological matching no longer claims to equal general learning, demoted to one structural-representation framework; (2) bottleneck distance is no longer a universal or unique loss function, only one candidate distance once a persistent-homology representation has already been established; (3) adds a "difference-sensitive connectivity structure" — even when two objects have identical Betti numbers, partial homological data, or even identical coarse-grained topological summaries, NTLA 2.0 does not automatically judge them identical; connectivity, nesting, direction, path, and history among holes, regions, and nodes can all be part of identity. Also establishes an observer-ready interface for the NTLA-O that follows: structural identity is no longer a single absolute comparison function, but depends on which differences are permitted to be observed, judged valid, and quotiented out.