Spin(2,3) Open-Letter Answer Programme

Date: 21 October 2026 Status: revised after eight standalone AI answers; no expert endorsement inferred Evidence: answer packet and adjudication ledger

The supplied answers convert eight broad questions into four executable packets. They improve the mathematical and kinematic baseline, but they do not close the programme's physical-selection chain. In particular, algebra is not promoted to dynamics, an incidence relation is not promoted to a quantum reconstruction, and a possible product spectral triple is not promoted to a viable action.

P1 — carrier certificate (OL-001, OL-002)

Machine-check the Peirce decomposition, TKK brackets, real-form conventions and neighboring closures on the carrier actually generated by the recursion. Stop if a larger triple closure is forced. Success establishes the algebraic carrier only; the physical choice still needs a dynamical selector.

P2 — joint module and action (OL-003, OL-008)

Represent the Furey/internal generators and Spin(2,3) generators on one declared real Hilbert/Krein module. Compute the commutant, grading, reality and first-order conditions. Then carry one fluctuated Dirac operator through its covariant action, stationary vacuum, residue/Hessian spectrum and RG matching. This is the highest-leverage physics packet.

P3 — operational laboratory (OL-004, OL-005)

Declare whether composites use the real-Hilbert tensor product (interactions with bilocal rather than local tomography) or a locally tomographic disk rule (with the continuous-interaction obstruction). Use the exact metaplectic quadratic representation to calculate preparations, effects, channels and invariants. Do not infer 3+1 locality from that finite-mode laboratory.

P4 — twistor scalar benchmark (OL-006, OL-007)

Fix the cover, orientation, Hermitian reality condition, field equation and boundary condition. For a conformally coupled scalar, prove the admissible boundary trace range, an inverse modulo homogeneous data, the causal commutator and positivity/wavefront conditions. Only then extend to spin or claim a physical chirality preference.

Priority and non-promotion rules

Execute P1 and P2 first: P1 is the finite integrity check and P2 is the shortest route to a falsifiable physical model. P3 is a controlled laboratory; P4 is a reconstruction benchmark. A packet may promote a claim only when its stated deliverable is reproduced. None of the eight source answers counts as a reply from a named addressee, peer review, or closure of a physical gate.