recognition /
NumberTheory /
NumberTheory.HilbertPolyaCandidate /
explainer
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formal statement (Lean)
171 theorem involutionOp_diagOp_comm :
172 involutionOp ∘ₗ diagOp = diagOp ∘ₗ involutionOp := by
proof body
Term-mode proof.
173 ext v
174 simp [costAt_neg_eq]
175
176 /-- The reciprocal involution intertwines the prime-shift with its
177 inverse: `U ∘ V_p = V_p^{-1} ∘ U`.
178
179 This is the operator-level analog of the zeta functional equation's
180 involution `s ↔ 1-s`. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (17)
Lean names referenced from this declaration's body.
reciprocal
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
U
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
reciprocal
in IndisputableMonolith.Foundation.LedgerForcing
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
costAt_neg_eq
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
diagOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
involutionOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
zeta
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use
U
in IndisputableMonolith.Recognition
decl_use