Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Adopted finite two-group gauging model
The adopted finite three-dimensional vertex-spin regulator with G = Z/2 and trivial A, including its unit background response and relative state-sum convention; no continuum or empirical claim.
Postulate
Adopt as the finite physical model the three-dimensional vertex-spin regulator with , trivial -form group , zero Postnikov cocycle, zero action, and the normalized uniform measure on spins. Its global symmetry flips every spin, its background response is the unit weight for every flat background, and its selected boundary state space and relative amplitudes are those specified by the model definition. The finite background gauging and sewing prescription is part of this adopted model. This postulate says nothing about a continuum limit, an empirical realization, or the truth of any more general quantum field theory.