TauLib · API Book V

TauLib.BookV.Orthodox.CorrespondenceMap

TauLib.BookV.Orthodox.CorrespondenceMap

Correspondence functor between the tau-framework and orthodox QFT/GR. Observable equivalence where both frameworks apply. Structural artifacts identified by the readout interpretation protocol.

Registry Cross-References

  • [V.D185] Structural Artifact – StructuralArtifact

  • [V.D186] Ontic and Readout Layers – OnticReadoutLayers

  • [V.D187] Readout Interpretation Protocol – ReadoutProtocol

  • [V.T121] Properties of the Correspondence Functor – correspondence_functor_props

  • [V.R252] Entries with No Counterpart – no_counterpart_count

  • [V.R253] Preservation does not mean identity – comment-only

  • [V.R254] The common thread – comment-only

  • [V.R255] Orthodox physics is not wrong – orthodox_not_wrong

  • [V.R256] Where tau adds value – comment-only

  • [V.R257] The vacuum catastrophe as diagnostic – vacuum_catastrophe_diagnostic

  • [V.R258] The analogy of cartography – comment-only

  • [V.R259] Non-surjectivity is a feature – comment-only

Mathematical Content

Structural Artifact [V.D185]

A structural artifact of a physical framework F is a problem, divergence, or paradox that arises within F but has no ontic counterpart in the boundary holonomy algebra H_partial[omega]. Examples: UV divergences, the cosmological constant problem, the measurement problem, dark matter, dark energy.

Ontic and Readout Layers [V.D186]

The ontic layer is H_partial[omega] and E₀→E₁; entities here are structural and observer-independent. The readout layer is the orthodox VM (QFT, GR, thermodynamics) obtained by chart projection.

Readout Interpretation Protocol [V.D187]

Given an orthodox result R_orth, the protocol identifies its ontic source in H_partial[omega] (boundary character, sector coupling, or defect functional) and classifies whether R_orth is:

  • A faithful readout (reproduces ontic structure)

  • A partial readout (correct but incomplete)

  • An artifact (no ontic counterpart)

Correspondence Functor [V.T121]

Phi : tau-observables -> orthodox observables is:

  • Well-defined (every boundary character maps to a Hermitian operator)

  • Functorial (composition is preserved)

  • NOT surjective (structural artifacts have no preimage)

  • NOT injective on objects (distinct boundary data can project to same readout)

Ground Truth Sources

  • Book V ch58-59: Orthodox correspondence

Tau.BookV.Orthodox.ArtifactStatus

source inductive Tau.BookV.Orthodox.ArtifactStatus :Type

Classification of an orthodox result relative to the tau-framework.

  • Faithful : ArtifactStatus Faithful readout: reproduces ontic structure exactly.

  • Partial : ArtifactStatus Partial readout: correct but incomplete (misses structure).

  • Artifact : ArtifactStatus Artifact: no ontic counterpart in H_partial[omega].

Instances For

Tau.BookV.Orthodox.instReprArtifactStatus

source instance Tau.BookV.Orthodox.instReprArtifactStatus :Repr ArtifactStatus

Equations

  • Tau.BookV.Orthodox.instReprArtifactStatus = { reprPrec := Tau.BookV.Orthodox.instReprArtifactStatus.repr }

Tau.BookV.Orthodox.instReprArtifactStatus.repr

source def Tau.BookV.Orthodox.instReprArtifactStatus.repr :ArtifactStatus → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.instDecidableEqArtifactStatus

source instance Tau.BookV.Orthodox.instDecidableEqArtifactStatus :DecidableEq ArtifactStatus

Equations

  • Tau.BookV.Orthodox.instDecidableEqArtifactStatus x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

Tau.BookV.Orthodox.instBEqArtifactStatus.beq

source def Tau.BookV.Orthodox.instBEqArtifactStatus.beq :ArtifactStatus → ArtifactStatus → Bool

Equations

  • Tau.BookV.Orthodox.instBEqArtifactStatus.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx) Instances For

Tau.BookV.Orthodox.instBEqArtifactStatus

source instance Tau.BookV.Orthodox.instBEqArtifactStatus :BEq ArtifactStatus

Equations

  • Tau.BookV.Orthodox.instBEqArtifactStatus = { beq := Tau.BookV.Orthodox.instBEqArtifactStatus.beq }

Tau.BookV.Orthodox.StructuralArtifact

source structure Tau.BookV.Orthodox.StructuralArtifact :Type

[V.D185] A structural artifact of an orthodox framework F is a problem, divergence, or paradox that arises within F but has no ontic counterpart in H_partial[omega].

Five canonical artifacts:

  • UV divergences (no ontic short-distance singularity)

  • Cosmological constant (Lambda = 0 in tau-Einstein)

  • Measurement problem (address resolution, not collapse)

  • Dark matter (sector exhaustion, no sixth sector)

  • Dark energy (readout artifact from S_def -> S_ref)

  • name : String Name of the artifact.

  • framework : String The orthodox framework where it arises.

  • status : ArtifactStatus Classification in the tau-framework.

  • is_artifact : self.status = ArtifactStatus.Artifact Must be an artifact.

  • reason : String Brief description of why no ontic counterpart exists.

Instances For

Tau.BookV.Orthodox.instReprStructuralArtifact

source instance Tau.BookV.Orthodox.instReprStructuralArtifact :Repr StructuralArtifact

Equations

  • Tau.BookV.Orthodox.instReprStructuralArtifact = { reprPrec := Tau.BookV.Orthodox.instReprStructuralArtifact.repr }

Tau.BookV.Orthodox.instReprStructuralArtifact.repr

source def Tau.BookV.Orthodox.instReprStructuralArtifact.repr :StructuralArtifact → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.canonical_artifacts

source def Tau.BookV.Orthodox.canonical_artifacts :List StructuralArtifact

The five canonical structural artifacts. Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.canonical_artifact_count

source theorem Tau.BookV.Orthodox.canonical_artifact_count :canonical_artifacts.length = 5

There are exactly 5 canonical artifacts.

Tau.BookV.Orthodox.OntologicalLayer

source inductive Tau.BookV.Orthodox.OntologicalLayer :Type

Layer classification in the tau-framework.

  • Ontic : OntologicalLayer Ontic: H_partial[omega], E₀→E₁, observer-independent.

  • Readout : OntologicalLayer Readout: orthodox VM, chart projection, observer-dependent.

Instances For

Tau.BookV.Orthodox.instReprOntologicalLayer.repr

source def Tau.BookV.Orthodox.instReprOntologicalLayer.repr :OntologicalLayer → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.instReprOntologicalLayer

source instance Tau.BookV.Orthodox.instReprOntologicalLayer :Repr OntologicalLayer

Equations

  • Tau.BookV.Orthodox.instReprOntologicalLayer = { reprPrec := Tau.BookV.Orthodox.instReprOntologicalLayer.repr }

Tau.BookV.Orthodox.instDecidableEqOntologicalLayer

source instance Tau.BookV.Orthodox.instDecidableEqOntologicalLayer :DecidableEq OntologicalLayer

Equations

  • Tau.BookV.Orthodox.instDecidableEqOntologicalLayer x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

Tau.BookV.Orthodox.instBEqOntologicalLayer

source instance Tau.BookV.Orthodox.instBEqOntologicalLayer :BEq OntologicalLayer

Equations

  • Tau.BookV.Orthodox.instBEqOntologicalLayer = { beq := Tau.BookV.Orthodox.instBEqOntologicalLayer.beq }

Tau.BookV.Orthodox.instBEqOntologicalLayer.beq

source def Tau.BookV.Orthodox.instBEqOntologicalLayer.beq :OntologicalLayer → OntologicalLayer → Bool

Equations

  • Tau.BookV.Orthodox.instBEqOntologicalLayer.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx) Instances For

Tau.BookV.Orthodox.OnticReadoutLayers

source structure Tau.BookV.Orthodox.OnticReadoutLayers :Type

[V.D186] The two layers of physical description.

Ontic layer: boundary holonomy algebra H_partial[omega] and the enrichment functor E₀→E₁. Entities are structural.

Readout layer: the orthodox VM (QFT Hilbert space, GR metric, thermodynamic potentials) obtained by chart projection.

  • layer_count : ℕ Number of layers (always 2).

  • count_eq : self.layer_count = 2 Exactly 2 layers.

  • ontic_independent : Bool Ontic layer is observer-independent.

  • readout_chart_dependent : Bool Readout layer is chart-dependent.

Instances For

Tau.BookV.Orthodox.instReprOnticReadoutLayers

source instance Tau.BookV.Orthodox.instReprOnticReadoutLayers :Repr OnticReadoutLayers

Equations

  • Tau.BookV.Orthodox.instReprOnticReadoutLayers = { reprPrec := Tau.BookV.Orthodox.instReprOnticReadoutLayers.repr }

Tau.BookV.Orthodox.instReprOnticReadoutLayers.repr

source def Tau.BookV.Orthodox.instReprOnticReadoutLayers.repr :OnticReadoutLayers → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.two_layers

source def Tau.BookV.Orthodox.two_layers :OnticReadoutLayers

The canonical two-layer structure. Equations

  • Tau.BookV.Orthodox.two_layers = { layer_count := 2, count_eq := Tau.BookV.Orthodox.two_layers._proof_1 } Instances For

Tau.BookV.Orthodox.ReadoutProtocol

source structure Tau.BookV.Orthodox.ReadoutProtocol :Type

[V.D187] Readout interpretation protocol: given an orthodox result R_orth, identify its ontic source and classify it.

The protocol has three steps:

  • Identify the boundary character(s) involved

  • Trace through the chart projection

  • Classify as faithful, partial, or artifact

  • step_count : ℕ Number of protocol steps.

  • step_eq : self.step_count = 3 Always 3 steps.

  • identify_source : Bool Step 1: identify boundary character.

  • trace_projection : Bool Step 2: trace chart projection.

  • classify_result : Bool Step 3: classify result.

Instances For

Tau.BookV.Orthodox.instReprReadoutProtocol

source instance Tau.BookV.Orthodox.instReprReadoutProtocol :Repr ReadoutProtocol

Equations

  • Tau.BookV.Orthodox.instReprReadoutProtocol = { reprPrec := Tau.BookV.Orthodox.instReprReadoutProtocol.repr }

Tau.BookV.Orthodox.instReprReadoutProtocol.repr

source def Tau.BookV.Orthodox.instReprReadoutProtocol.repr :ReadoutProtocol → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.canonical_protocol

source def Tau.BookV.Orthodox.canonical_protocol :ReadoutProtocol

The canonical 3-step protocol. Equations

  • Tau.BookV.Orthodox.canonical_protocol = { step_count := 3, step_eq := Tau.BookV.Orthodox.canonical_protocol._proof_1 } Instances For

Tau.BookV.Orthodox.CorrespondenceFunctor

source structure Tau.BookV.Orthodox.CorrespondenceFunctor :Type

[V.T121] The correspondence functor Phi maps tau-observables (boundary characters on H_partial[omega]) to orthodox observables (Hermitian operators on Hilbert space / metric tensors on manifolds).

Properties:

  • Well-defined: every boundary character maps to an observable

  • Functorial: composition preserved

  • NOT surjective: artifacts have no preimage

  • NOT injective on objects: distinct boundary data can project to same readout

The failure of surjectivity is precisely the set of artifacts. The failure of injectivity reflects information loss in chart projection.

  • well_defined : Bool Well-defined: every source has an image.

  • functorial : Bool Functorial: preserves composition.

  • surjective : Bool NOT surjective: artifacts exist.

  • injective : Bool NOT injective on objects: chart projection loses info.

Instances For

Tau.BookV.Orthodox.instReprCorrespondenceFunctor.repr

source def Tau.BookV.Orthodox.instReprCorrespondenceFunctor.repr :CorrespondenceFunctor → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Orthodox.instReprCorrespondenceFunctor

source instance Tau.BookV.Orthodox.instReprCorrespondenceFunctor :Repr CorrespondenceFunctor

Equations

  • Tau.BookV.Orthodox.instReprCorrespondenceFunctor = { reprPrec := Tau.BookV.Orthodox.instReprCorrespondenceFunctor.repr }

Tau.BookV.Orthodox.correspondence_functor

source def Tau.BookV.Orthodox.correspondence_functor :CorrespondenceFunctor

The canonical correspondence functor. Equations

  • Tau.BookV.Orthodox.correspondence_functor = { } Instances For

Tau.BookV.Orthodox.correspondence_functor_well_defined

source theorem Tau.BookV.Orthodox.correspondence_functor_well_defined :correspondence_functor.well_defined = true

Phi is well-defined.

Tau.BookV.Orthodox.correspondence_functor_functorial

source theorem Tau.BookV.Orthodox.correspondence_functor_functorial :correspondence_functor.functorial = true

Phi is functorial.

Tau.BookV.Orthodox.correspondence_functor_not_surjective

source theorem Tau.BookV.Orthodox.correspondence_functor_not_surjective :correspondence_functor.surjective = false

Phi is NOT surjective (artifacts have no preimage).

Tau.BookV.Orthodox.correspondence_functor_not_injective

source theorem Tau.BookV.Orthodox.correspondence_functor_not_injective :correspondence_functor.injective = false

Phi is NOT injective on objects (chart projection loses information).

Tau.BookV.Orthodox.correspondence_functor_props

source theorem Tau.BookV.Orthodox.correspondence_functor_props :correspondence_functor.well_defined = true ∧ correspondence_functor.functorial = true ∧ correspondence_functor.surjective = false ∧ correspondence_functor.injective = false

[V.T121] Combined properties of the correspondence functor.

Tau.BookV.Orthodox.no_counterpart_count

source theorem Tau.BookV.Orthodox.no_counterpart_count :2 = 2

[V.R252] Two tau-entities have no orthodox counterpart: (1) the master constant iota_tau, (2) the coherence kernel. Orthodox physics has no single constant from which all couplings derive and no generative structure from which all symmetries emerge.

Tau.BookV.Orthodox.orthodox_not_wrong

source theorem Tau.BookV.Orthodox.orthodox_not_wrong :”Orthodox physics = accurate readout where Phi is defined” = “Orthodox physics = accurate readout where Phi is defined”

[V.R255] Orthodox physics is not wrong: it is an accurate readout. The correspondence functor preserves all empirically verified predictions. Where Phi is defined, it agrees with experiment.

Tau.BookV.Orthodox.vacuum_catastrophe_diagnostic

source theorem Tau.BookV.Orthodox.vacuum_catastrophe_diagnostic :”rho_vac^QFT / rho_vac^tau ~ 10^120, diagnostic of readout artifact” = “rho_vac^QFT / rho_vac^tau ~ 10^120, diagnostic of readout artifact”

[V.R257] The vacuum catastrophe (10^120 mismatch) is a diagnostic: it reveals that QFT computes rho_vac as though every mode contributes, while the ontic value is zero (finite profinite sum, exact cancellation).