Source-pinned research
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This index contains 2,569 curated research declarations and 119,070 complete package declarations. Search 10,000 more complete Mathlib declarations.
Showing 1,351 to 1,356 of 2,569 results.
I₃_eq
Mathematical statement
A symmetry identity in the -minimizer endgame. Let be independent copies of , and set , , , and . Then the conditional mutual informations agree: .
Source project: Polynomial Freiman-Ruzsa project
Person-level attribution pending.
Ideal.principal_is_maximal_iff_irred
Project documentation
A principal ideal is an ideal generated by a single element. -/ def principalIdeal {F : Type} [Semiring F] (f : F) : Ideal F := Ideal.span {f} /- A principal ideal in a polynomial ring is maximal if and only if its generator is an irreducble polynomial.
Source project: ArkLib
Person-level attribution pending.
IdealGas.partitionZ_eq
Mathematical statement
The partition function Z for an ideal gas.
Source project: Physlib
Person-level attribution pending.
IdealGas.PartitionZ_eq
Mathematical statement
The partition function Z for an ideal gas.
Source project: quantumInfo
Person-level attribution pending.
immersion_antipodal_sphere
Mathematical statement
The antipodal map on 𝕊^n ⊆ ℝ^{n+1} is an immersion.
Source project: Sphere eversion
Person-level attribution pending.
InductiveMerkleTree.batch_completeness
Project documentation
Batch completeness theorem for Merkle trees: building the tree honestly, generating the batch proof for any selector opening at least one leaf, and verifying it against the tree's root succeeds with probability 1 under the random oracle. The proof reduces to functional_batch_completeness through simulateQ, exactly as the single-index completeness...
Source project: VCVio
Person-level attribution pending.