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 591 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.32.0

Mean Energy eq ratio of integrals

CanonicalEnsemble.meanEnergy_eq_ratio_of_integrals

Plain-language statement

The mean energy can be expressed as a ratio of integrals.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Thermodynamic Entropy eq shannon Entropy

CanonicalEnsemble.thermodynamicEntropy_eq_shannonEntropy

Plain-language statement

In the finite, nonempty case the thermodynamic and Shannon entropies coincide. All semi-classical correction factors vanish (dof = 0, phaseSpaceUnit = 1), so the absolute thermodynamic entropy reduces to the discrete Shannon form.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Two State probability fst

CanonicalEnsemble.twoState_probability_fst

Plain-language statement

Probability of the first state (energy E₀) in closed form.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Two State probability snd

CanonicalEnsemble.twoState_probability_snd

Plain-language statement

Probability of the second state (energy E₁) in closed form.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Rows linearly independent

CKMMatrix.rows_linearly_independent

Plain-language statement

The rows of a CKM matrix are linearly independent.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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