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146 lines
4.7 KiB
Text
146 lines
4.7 KiB
Text
import Mathlib.Data.Nat.Basic
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namespace Semantics.ProjectableGeometryCanonical
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/-!
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# Projectable Geometry Canonical Representation
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This module records the current canonical representation for the projectable
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geometry compressor:
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* signed 16-axis envelope,
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* 12D source/residual plane,
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* 4D primitive keel,
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* genus-3 residual boat,
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* 0D closure witness.
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It is an accounting gate for reversible compression representations, not a
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physics claim.
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-/
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/-- The canonical dimensional axis counts for the current representation. -/
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def signedEnvelopeAxes : Nat := 16
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def sourcePlaneAxes : Nat := 12
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def primitiveKeelAxes : Nat := 4
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def genusHandles : Nat := 3
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def closurePointAxes : Nat := 0
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/--
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The decision-diagram shell mass is represented in twelfths to avoid Float or
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open-ended rational parsing in the core.
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-/
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structure DimensionalShell where
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visible4d : Nat
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shadow3d : Nat
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closure0d : Nat
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lawbound : Nat
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unresolved : Nat
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total : Nat
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deriving Repr, DecidableEq
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/-- Canonical dimensional shell: 4/12 visible, 3/12 shadow, 1/12 closure, 4/12 lawbound. -/
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def canonicalShell : DimensionalShell :=
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{ visible4d := 4
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shadow3d := 3
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closure0d := 1
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lawbound := 4
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unresolved := 0
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total := 12 }
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/-- The shell closes when all named mass accounts sum to the declared total with no unresolved debt. -/
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def shellCloses (s : DimensionalShell) : Bool :=
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s.visible4d + s.shadow3d + s.closure0d + s.lawbound + s.unresolved == s.total &&
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s.unresolved == 0
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/-- Three-handle genus-3 carrier for a 12D residual lane. -/
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structure Genus3ResidualBoat where
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packetLocal : Nat
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shearTorsion : Nat
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spectralField : Nat
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residual12d : Nat
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deriving Repr, DecidableEq
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/-- The residual boat closes when its three handles exactly reconstruct the residual lane. -/
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def residualBoatCloses (boat : Genus3ResidualBoat) : Bool :=
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boat.packetLocal + boat.shearTorsion + boat.spectralField == boat.residual12d
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/-- Canonical projectable geometry representation packet. -/
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structure CanonicalProjectableRep where
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signedAxes : Nat
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sourceAxes : Nat
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primitiveAxes : Nat
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genusHandleCount : Nat
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closureAxes : Nat
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source12dMass : Nat
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lifted4dMass : Nat
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residual12dMass : Nat
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shell : DimensionalShell
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boat : Genus3ResidualBoat
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sourceHashPresent : Bool
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receiptHashPresent : Bool
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deriving Repr, DecidableEq
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/-- Source rehydration law: lifted 4D projection plus residual lane equals source mass. -/
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def sourceRehydrates (rep : CanonicalProjectableRep) : Bool :=
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rep.lifted4dMass + rep.residual12dMass == rep.source12dMass
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/-- Axis counts match the 16D -> 12D -> 4D -> genus-3 -> 0D canonical representation. -/
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def axesCanonical (rep : CanonicalProjectableRep) : Bool :=
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rep.signedAxes == signedEnvelopeAxes &&
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rep.sourceAxes == sourcePlaneAxes &&
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rep.primitiveAxes == primitiveKeelAxes &&
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rep.genusHandleCount == genusHandles &&
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rep.closureAxes == closurePointAxes
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/-- Full promotion gate for the canonical representation. -/
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def canonicalRepAdmissible (rep : CanonicalProjectableRep) : Bool :=
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axesCanonical rep &&
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shellCloses rep.shell &&
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residualBoatCloses rep.boat &&
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sourceRehydrates rep &&
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rep.boat.residual12d == rep.residual12dMass &&
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rep.sourceHashPresent &&
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rep.receiptHashPresent
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/-- A small closed witness: source mass 12, lifted mass 7, residual mass 5. -/
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def sampleClosedRep : CanonicalProjectableRep :=
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{ signedAxes := 16
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sourceAxes := 12
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primitiveAxes := 4
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genusHandleCount := 3
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closureAxes := 0
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source12dMass := 12
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lifted4dMass := 7
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residual12dMass := 5
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shell := canonicalShell
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boat := { packetLocal := 2, shearTorsion := 2, spectralField := 1, residual12d := 5 }
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sourceHashPresent := true
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receiptHashPresent := true }
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/-- Negative witness: residual handles do not reconstruct the 12D residual lane. -/
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def brokenResidualRep : CanonicalProjectableRep :=
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{ sampleClosedRep with
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boat := { packetLocal := 2, shearTorsion := 2, spectralField := 0, residual12d := 5 } }
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/-- Negative witness: an unresolved shell debt prevents closure. -/
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def unresolvedShellRep : CanonicalProjectableRep :=
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{ sampleClosedRep with
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shell := { canonicalShell with unresolved := 1, total := 13 } }
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theorem canonicalShellCloses : shellCloses canonicalShell = true := by
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rfl
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theorem sampleClosedRepAdmissible : canonicalRepAdmissible sampleClosedRep = true := by
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rfl
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theorem brokenResidualRepNotAdmissible : canonicalRepAdmissible brokenResidualRep = false := by
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rfl
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theorem unresolvedShellRepNotAdmissible : canonicalRepAdmissible unresolvedShellRep = false := by
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rfl
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#eval canonicalRepAdmissible sampleClosedRep
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#eval canonicalRepAdmissible brokenResidualRep
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#eval canonicalRepAdmissible unresolvedShellRep
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end Semantics.ProjectableGeometryCanonical
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