Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedPipeline-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.

Two-qubit QSD CNOT upper-bound instance

Example

Substituting n=2 into the stated no-ancilla QSD count gives (23/48)·16−(3/2)·4+4/3=3 CNOTs, with one-qubit gates counted separately.

Facts & Assumptions

Given: the no-ancilla QSD CNOT bound for n=2.

[A1]

QSD CNOT Upper Bound proves the no-ancilla n≥2 CNOT upper bound. At n=2 its supplier uses the three-CNOT base case, so neither recursive optimization is needed.

Verification

1.1A1algebra

Substitute n=2 in [A1]. The bound is (23/48)⋅16−(3/2)⋅4+4/3=23/3−6+4/3=9−6=3 CNOTs.

2.1step 1.1given∎

The conclusion counts CNOTs only. One-qubit gates and classical compile time are separate resources, so this substitution supplies neither a total gate count nor a compilation-time estimate.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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