Alphabeta Math
PostulateStatement: AI-adaptedProof: Not applicablePipeline-generated‡ sources checked 2026-10-15
How 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.

Optional adopted classical spinning-orbit model

Physical scope

Adopt specified KKS phase orbit, primitive m,s, chosen H=cP0; no quantum spectrum/unitary Wigner/spin-supplementary or force law inferred.

Postulate

Adopted model postulate (optional): Under ACω for the referenced KKS orbit, and for fixed primitive parameters m>0 (kg) and s>0 (angular momentum units), use the coadjoint orbit and KKS symplectic form of Positive classical spin Poincare orbit and stabilizer jump as the phase space of a classical spinning particle. In a selected inertial frame choose the Hamiltonian H=cP0 (joules). This premise chooses a mathematical model; it is not inferred from the spinless action, an experiment, or the existence of the orbit alone. It does not assert a quantum spin spectrum, a Wigner unitary representation, a spin supplementary condition, a charged-spin force law, or radiation dynamics.

Facts & Assumptions

Given: The optional adoption and primitive parameters stated above.

[A1]

Positive classical spin Poincare orbit and stabilizer jump: for m,s>0 the specified rest charge point has an eight-dimensional KKS coadjoint orbit; this mathematical result does not select a physical particle model or Hamiltonian.

[A2]

The Axiom of Countable Choice (ACω): assume countable choice ACω only; no full axiom of choice is used.

Adopted premise

This item records [A1] as a model choice with the extra Hamiltonian H=cP0. No proof of nature's adoption of this model is claimed. The postulate carries no observational or statistical premise.

Depends on

Dependency tree · 2 levels

Sources