recognition /
NumberTheory /
NumberTheory.HilbertPolyaCandidate /
explainer
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formal statement (Lean)
110 abbrev StateSpace : Type := MultIndex →₀ ℝ
proof body
Definition body.
111
112 /-! ## The three operators
113
114 We use `Finsupp.lsum` and similar mathlib constructions to define
115 linear endomorphisms of `StateSpace`. The "basis vector" `e_v` is
116 `Finsupp.single v 1`. -/
117
118 /-- The diagonal cost operator `D`: maps `e_v` to `J(toRat v) · e_v`.
119
120 Defined as the linear map sending each basis element `e_v` to
121 `costAt v • e_v`. -/
used by (9)
From the project-wide theorem graph. These declarations reference this one in their body.
cost_operator_regularity_certificate
in IndisputableMonolith.NumberTheory.CostOperatorRegularity
decl_use
denseDomain
in IndisputableMonolith.NumberTheory.CostOperatorRegularity
decl_use
denseDomain_mem
in IndisputableMonolith.NumberTheory.CostOperatorRegularity
decl_use
candidateOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
diagOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
involutionOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
primeHop
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
shiftInvOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
shiftOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
depends on (18)
Lean names referenced from this declaration's body.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
decl_use
cost
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
toRat
in IndisputableMonolith.Foundation.RationalsFromLogic
decl_use
as
in IndisputableMonolith.Foundation.SimplicialLedger.ContinuumBridge
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
map
in IndisputableMonolith.Measurement.RSNative.Core
decl_use
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use
costAt
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
MultIndex
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
toRat
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use