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.
M2 Protected Quantization Construction Obligation
Original F4 background/charge scope retained as the physical realization objective. Specifying required data does not assert its physical existence; smooth source-model restrictions remain explicit.
Statement
HELD OBLIGATION, not an existence theorem, physical postulate, or open-problem classification: Construct the regulated physical protected sector and curve comparison for the original background/charge scope. Prove the actual vacuum/twist index class and its relation to four-dimensional chirality, and control regulator removal and additional light constituents. A net-index objective requires all local net contributions but does not require full-state equivalence or a calculation of every vectorlike multiplicity.
Facts & Assumptions
Given: The exact input contracts in M2 Regulated Protected Sector Data and M2 Curve Comparison Realization Data. The physical realization remains a separately held authoring obligation.
M2 Regulated Protected Sector Data: the required regulated physical Hilbert quotient, preserved charge, domains, and regulator removal are named as data inputs, with no physical existence assertion.
M2 Curve Comparison Realization Data: the actual curve comparison, physical bundle/twist, comparison domains, and relative zero-mode contributions are required data; no index equality or rank-one assumption is asserted.
Proof
By [F1], a physical protected-sector realization would require the actual Hilbert quotient, preserved charge, and regulator-removal data. By [F2], a curve reduction would additionally require its actual physical comparison, bundle/twist, and relative sector. These are distinct input obligations, not consequences of the mathematical definition of a data package.
The source item [F1] defines only the required data package and explicitly asserts no physical existence. Therefore the obligation in the statement records work needed to establish the physical realization and index relation; it asserts neither their existence nor their nonexistence. It is not a logical supplier for an index theorem.