Alphabeta MathHow 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 incompressibility method
Definition
The incompressibility method first fixes an effective injective encoding of a finite family by binary strings (often all of one length). Since fewer than outputs can have descriptions of length below , if one may choose an encoded object whose description has length at least ; Most finite strings are incompressible is the fixed-length form of this count. One then derives structure from the impossibility of a shorter description. Conditional variants keep the auxiliary data and encoding fixed and choose large using Conditional Kolmogorov complexity.
Depends on
Used by
Nothing in the library uses this result yet.
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
- Shen, §§15,17 (standard reference, not scraped)