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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 curated research declarations and 119,070 complete package declarations. Search 10,000 more complete Mathlib declarations.

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Showing 709 to 714 of 2,569 results.

Project-declaredLean 4.31.0

DE₄ qexp

DE₄_qexp

Mathematical statement

D E₄ q-expansion via termwise differentiation. D E₄ = 240 * ∑ n * σ₃(n) * qⁿ from differentiating E₄ = 1 + 240 * ∑ σ₃(n) * qⁿ.

sphere packingFourier analysismodular forms

Source project: Sphere Packing in Dimension 8

Person-level attribution pending.

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Project-declaredLean 4.31.0

DE₄ term re pos

DE₄_term_re_pos

Mathematical statement

Each term n*σ₃(n)*exp(-2πnt) in D E₄ q-expansion has positive real part on imaginary axis.

sphere packingFourier analysismodular forms

Source project: Sphere Packing in Dimension 8

Person-level attribution pending.

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Project-declaredLean 4.8.0

Debate eq transposed

debate_eq_transposed

Mathematical statement

The transposed formulation of debate is the same

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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Project-declaredLean 4.32.0

Decrypt uses At Most One Query

decrypt_usesAtMostOneQuery

Mathematical statement

T-transform decryption makes at most one hash-oracle query under unit-cost instrumentation.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

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Project-declaredLean 4.29.0-rc6

Abs ball Average sub six Ball Average le

DeGiorgi.abs_ballAverage_sub_sixBallAverage_le

Mathematical statement

The average shift estimate: |(u)_B - (u)_{6B}| ≤ 6^d * M.

partial differential equationsregularity theoryanalysis

Source project: DeGiorgi

Person-level attribution pending.

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Project-declaredLean 4.29.0-rc6

Abs sub const bmo le two

DeGiorgi.abs_sub_const_bmo_le_two

Mathematical statement

The absolute value function |u - c| has BMO seminorm at most 2M whenever u has BMO seminorm at most M. Uses the reverse triangle inequality ||a| - |b|| ≤ |a - b|.

partial differential equationsregularity theoryanalysis

Source project: DeGiorgi

Person-level attribution pending.

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