# Verification and scope report

Title: Finite Adjoint-Transform Orbits for Funcoids and Reloids

- Eight-page English manuscript; author alone at top, company and contact in a footnote.
- Complete written proof and detailed originating-researcher self-audit.
- 7392 exact finite-model value checks, four models, ordinary and optimized outputs identical.
- All right-transform identities and the left identities using fiber algebra are checked in those models. Four left cofinality identities and the infinite density statements are proved analytically and excluded from the finite-model claim.
- Every typed table entry and the finite/empty cases are addressed in the manuscript.
- The original source diagram and primary definitions were checked; the false RI=P arrow is explicitly refuted, not assumed.
- Trimble's prior representation theorem and standard mathematical inputs are credited.
- Desktop and source-only portable compilation succeed with identical page content streams.
- All eight pages were visually inspected: no clipped text, overlapping elements, missing symbols or unresolved references.

Accepted scope: In ZFC, for arbitrary fixed sets A and B, the missing right adjoint-transform of the outward reloid map is the join of the induced funcoid with the funcoidal product of the two Frechet filters. Its orbit under the two adjoint transforms has at most twenty typed maps when both sets are infinite and at most two when one is finite. The formula and finite transition system resolve the full missing-node and finite-or-infinite orbit question in OPG-60024. An extra arrow in the earlier diagram is disproved. Twenty is an upper bound, not a claim of pairwise distinctness or optimality.

One original-source closure. No independent review, proof-assistant certification, optimal orbit bound or absolute priority claim. AI tools assisted source retrieval, derivation, diagnostics and exposition. License: CC BY 4.0.