Alphabeta Math
RemarkRemark: Literature-sourcedProof: Not suppliedaudited 2026-09-05‡ sources checked 2026-09-05‡ not proved here
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.

‡ Recorded, not proved here. This statement is included so the library can refer to it honestly, with a citation to the literature. It is not proved anywhere in this library: the track that would prove it has not been developed here yet.

Nonabelian extension obstruction in H^3

Remark

The classification theorem on this page is specific to abelian kernels. Once the kernel is nonabelian, the extension problem is no longer classified by an honest group of degree-two classes.

The earlier remark Nonabelian extension obstructions live in H^3 and realized classes form an H^2-torsor ‡ records the right replacement: a prescribed outer action carries an obstruction in H3, and when that obstruction vanishes the realized extension classes form a torsor under an H2 built from the center. That is the next boundary, not a consequence of the present page.

Depends on

Used by

Dependency tree · two levels

5 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources