gate-1: distinct-phenomenon argument and falsification scaffolds

Falsifiable argument for the README first identity gate.

Surveys five neighbour theories - Galois, quotients, IFC,
refinements, provenance - and locates distinctness in the
integration of structured loss across the named axes.

Three falsification tests with explicit retraction conditions:
  T1 Galois reduction    - attacked via meet in abstraction lattice
  T2 Quotient reduction  - attacked via equalizer construction
  T3 Informativeness collapse - open obligation

Sophisticated submodules in EchoVsQuotient.agda and
EchoVsGalois.agda formalise the 2-cell argument: natural 2-cells
in neighbour frameworks are Sigma-over-preimages-shaped.

Combined T1+T2 conclusion: the obstruction is axis-pair-specific,
not an artefact of any one neighbour theory framework.

Author: hyperpolymath