Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)
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.

Finite sine-window phase state

Definition

For a power of two T≥2, the sine-window vector is ∣ΨT⟩=2T∑τ=0T−1sin⁡ ⁣(π(τ+1/2)T)∣τ⟩. For any integer interval 0≤a≤b≤T, define its unnormalized sine mass WT(a,b):=∑τ=ab−1sin⁡2 ⁣(π(τ+1/2)T). The closed trigonometric formula for WT(a,b) is proved by the assigned prefix-mass lemma. The chosen OP5 table variant stores these interval masses and their conditional split angles; it charges its full O(T) table and rotation size, arithmetic, interval-refinement, angle-bit, and finite gate-synthesis costs. This definition does not assign a polylogarithmic implementation cost.

Depends on

Used by

Dependency tree · two levels

15 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