Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)
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.

The ABS Clifford cokernel and symbol map

Definition

For C_n=Cl(ℝ^n,−‖·‖²), a finite-dimensional graded real module M=M^0⊕M^1 determines the ABS symbol triple (π^*M^0,π^*M^1,c(v)) on the disk/sphere pair of ℝ^n: over a nonzero vector v, Clifford multiplication c(v) is an isomorphism because c(v)^2=−‖v‖²I. Its relative KO class is the candidate symbol. The separate theorem proves that the symbol vanishes on restrictions from C_(n+1), descends to A_n, and is an isomorphism.

The symbol is a relative class on the disk/sphere pair; since c(v) is invertible for v≠0, the triple is admissible. This definition alone does not claim factorization through A_n.

Depends on

Used by

Dependency tree · two levels

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Sources