Alphabeta MathTuring-Machine Configuration Boundary Interface: Examples
About this page
Pipeline-generated
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.
✓ 2 results · all verified · 2 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs; all 2 also cleared it.
1 · Prerequisites
- Construction of the Natural Numbers
- Countability and Uncountability
- Finite Counting, Factorials and Binomial Coefficients
- Formal Languages, Encodings, and Decision Problems
- Linear Recurrences and Rational Generating Functions
- Relations, Functions, and Quotients
- The ZFC Axioms and the Basic Set Constructions
- Turing-Machine Configuration Boundary Interface
2 · Logical flowchart
3 · Items
Example
The empty-input initial configuration
Example