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.
Möbius inversion of gives
Example
The divisor-sum theorem from the CRT development states
for every positive integer (For every positive integer , ). Apply Classical Möbius inversion over positive divisors with and . The form indexed by the complementary divisor gives
At , the values from The number-theoretic Möbius function from prime factorisation give
where the terms correspond to . Thus Möbius inversion recovers directly from the CRT divisor-sum theorem.
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: 100 results over 23 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
- P. J. Cameron, Notes on Number Theory, Theorem 7.11 (standard reference, not scraped)
- Stanford Pairing-Based Cryptography notes, Möbius inversion (standard reference, not scraped)