Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 2,569 research declarations. Search 10,000 more complete Mathlib declarations.

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2569 results

Project-declaredLean 4.8.0

Bob sound

bob_sound

Plain-language statement

Honest Bob usually rejects if Alice is off by ≥ s

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.8.0

Bob steps cost

bob_steps_cost

Plain-language statement

Bob makes few queries, regardless of Alice and Vera

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.8.0

Bobs catches

bobs_catches

Plain-language statement

If Alice lies about probabilities by more than b, Bob usually catches Alice in a lie

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.8.0

Bobs safe

bobs_safe

Plain-language statement

If Honest Bob rejects, Vera usually complains. The error probability is higher if Bob does complain, though, so we use an expectation over vera_score.

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.32.0

Chord Set subset smul arc Set

BohrSet.chordSet_subset_smul_arcSet

Plain-language statement

For a finite ambient group, the chord model of a Bohr set BB is contained in the arc model after widening BB by the factor π/2\pi/2: Bchord((π/2)B)arcB_{\mathrm{chord}}\subseteq ((\pi/2)B)_{\mathrm{arc}}.

additive combinatoricsarithmetic progressionsFourier analysis

Source project: Arithmetic Progressions Almost Periodicity

Person-level attribution pending.

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Project-declaredLean 4.32.0

Le iff width

BohrSet.le_iff_width

Plain-language statement

Characterization of the order on Bohr sets. The relation B1B2B_1\le B_2 holds exactly when every frequency of B2B_2 is also a frequency of B1B_1, and widthB1(ψ)widthB2(ψ)\operatorname{width}_{B_1}(\psi)\le \operatorname{width}_{B_2}(\psi) for each such frequency.

additive combinatoricsarithmetic progressionsFourier analysis

Source project: Arithmetic Progressions Almost Periodicity

Person-level attribution pending.

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