Paper 2: NTLA-O I: Main, Internal, and External Observers

Main / Internal / External Observers, Legality, Judgment Domain, and the Observation-Difference Kernel

NTLA-O series Paper 2 (the filename retains its original unnumbered title; Paper 9's Section 1 series table confirms it as "NTLA-O I"). The core contribution splits the "observer," relative to a nested carrier domain, into three roles — Main (M), Internal (I), External (E) — and proves a single-crossing theorem for the role chain: moving from small to large along a strictly nested chain, the same observer's role must cross External→Main→Internal in that order, irreversibly and without skipping — so role is not an intrinsic property of the observer, but a relative quantity jointly determined by "observer × reference domain." Section 6 presents the paper's most important counterexample: unbounded structure does not equal unbounded observation — even with infinite internal nesting depth, as long as the indistinguishability kernel is the same at every layer, the number of observational differences can still be just one, proving that "infinite nesting alone does not automatically produce new cognitive content." Later sections build an observation-refinement partial order, coarsening decomposition, an inverse system, and a limit-separation theorem (injective but not necessarily surjective), and convert the original NTLA's assumption "different hole connectivity means different" into a provable separating-feature-family proposition.