Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17
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.

FALSE: a countably infinite sigma-algebra exists

Statement

There exists a countably infinite sigma-algebra.

Facts & Assumptions

Given: A putative countably infinite sigma-algebra.

[L1]

No sigma-algebra is countably infinite (No sigma-algebra is countably infinite).

Refutation

technique · contradiction
1.1

Suppose, for contradiction, that a countably infinite sigma-algebra exists.

assume-contra
2.1

This contradicts [L1], so the asserted object does not exist.

step 1.1L1discharge-contradiction∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 15 results over 7 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.

Sources