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263 lines
8.7 KiB
Text
263 lines
8.7 KiB
Text
import Semantics.RRCLogogramProjection
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/-!
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# ManifoldBoundaryAtlas
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A ManifoldBoundaryAtlas is a deterministic seed-generated set of candidate
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boundary coordinates for RRC-style projection checks. It generalizes
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`HexLogogramAtlas`: the seed does not claim a tear, proof, or manifold truth;
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it generates a finite boundary candidate surface that RRC can identify against
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receipts and residual evidence.
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Promotion is byte-law gated. If the boundary seed, law, residual, and receipt
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do not beat an explicit boundary-coordinate table, the atlas remains a HOLD
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surface.
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-/
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namespace Semantics.ManifoldBoundaryAtlas
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/-- Finite laws for generating manifold boundary candidates. -/
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inductive BoundaryLaw where
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| affineCut
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| genusInversion
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| massGradient
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| rrcProjectionEdge
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deriving Repr, DecidableEq
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/-- A generated boundary candidate in a finite coordinate domain. -/
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structure BoundaryCandidate where
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index : Nat
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coordinate : Nat
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side : Nat
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confidence : Nat
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deriving Repr, DecidableEq
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/-- Seeded boundary-atlas packet. -/
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structure BoundaryAtlasPacket where
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hexSeed : Nat
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hexDigitWidth : Nat
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blockBase : Nat
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law : BoundaryLaw
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dimensionCount : Nat
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coordinateDomain : Nat
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boundaryCount : Nat
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startIndex : Nat
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length : Nat
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stride : Nat
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genus : Nat
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massBasin : Nat
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torsionClass : Nat
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phaseClass : Nat
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explicitBoundaryBytes : Nat
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seedBytes : Nat
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lawBytes : Nat
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residualBytes : Nat
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receiptBytes : Nat
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rrcShapeOk : Bool
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residualDeclared : Bool
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deriving Repr, DecidableEq
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/-- Hex block base for a fixed-width boundary seed. -/
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def expectedHexBase (p : BoundaryAtlasPacket) : Nat :=
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16 ^ p.hexDigitWidth
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/-- Structural gate before byte-law promotion. -/
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def boundaryAtlasStructurallyValid (p : BoundaryAtlasPacket) : Bool :=
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p.hexDigitWidth > 0 &&
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p.blockBase == expectedHexBase p &&
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p.dimensionCount > 0 &&
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p.coordinateDomain > 0 &&
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p.boundaryCount > 0 &&
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p.length > 0 &&
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p.stride > 0 &&
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p.explicitBoundaryBytes > 0 &&
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p.rrcShapeOk &&
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p.residualDeclared
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/-- Raw deterministic boundary value before projection into finite domains. -/
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def boundaryRawValueAt (p : BoundaryAtlasPacket) (i : Nat) : Nat :=
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let j := p.startIndex + i
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match p.law with
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| BoundaryLaw.affineCut =>
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p.hexSeed + (j * p.stride) + p.phaseClass
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| BoundaryLaw.genusInversion =>
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p.hexSeed + (p.genus * p.dimensionCount) + (j * p.stride) + p.phaseClass
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| BoundaryLaw.massGradient =>
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p.hexSeed + (p.massBasin * p.stride) + j + p.torsionClass
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| BoundaryLaw.rrcProjectionEdge =>
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p.hexSeed + (j * p.stride) + p.massBasin + p.torsionClass + p.phaseClass
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/-- Generate the i-th RRC boundary candidate. -/
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def boundaryCandidateAt (p : BoundaryAtlasPacket) (i : Nat) : BoundaryCandidate :=
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let raw := boundaryRawValueAt p i
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{ index := i
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coordinate := raw % p.coordinateDomain
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side := raw % p.boundaryCount
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confidence := (raw / p.boundaryCount) % p.dimensionCount }
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/-- Replay the finite boundary atlas. -/
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def replayBoundaryAtlas (p : BoundaryAtlasPacket) : List BoundaryCandidate :=
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(List.range p.length).map (boundaryCandidateAt p)
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/-- Explicit table cost for boundary candidates. -/
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def explicitBoundaryTableBytes (p : BoundaryAtlasPacket) : Nat :=
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p.length * p.explicitBoundaryBytes
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/-- Encoded boundary-atlas cost with residual and receipt accounting. -/
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def boundaryAtlasEncodedBytes (p : BoundaryAtlasPacket) : Nat :=
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p.seedBytes + p.lawBytes + p.residualBytes + p.receiptBytes
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/-- The byte law: generated boundary candidates must beat explicit candidates. -/
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def boundaryAtlasByteLawHolds (p : BoundaryAtlasPacket) : Bool :=
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boundaryAtlasEncodedBytes p < explicitBoundaryTableBytes p
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/-- Promotion gate for a deterministic boundary atlas. -/
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def boundaryAtlasPromotable (p : BoundaryAtlasPacket) : Bool :=
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boundaryAtlasStructurallyValid p && boundaryAtlasByteLawHolds p
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/--
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Boundary atlases feed RRC identification, not merge admission. A promoted
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boundary atlas gives candidate boundary evidence; actual tear projection still
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needs the RRC receipt fields.
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-/
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def rrcBoundaryReceiptFromAtlas (p : BoundaryAtlasPacket) : Semantics.RRCLogogramProjection.LogogramReceipt :=
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{ shape := Semantics.RRCLogogramProjection.RRCShape.logogramProjection
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status := Semantics.RRCLogogramProjection.WitnessStatus.candidate
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regime := Semantics.RRCLogogramProjection.SemanticRegime.horribleManifoldTearing
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payloadBound := p.rrcShapeOk
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contradictionWitness := false
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tearBoundary := boundaryAtlasPromotable p
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detachedMass := false
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residualLane := p.residualDeclared }
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/-! ## Canonical witnesses -/
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/-- Small hand-checkable boundary atlas. -/
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def smallBoundaryAtlas : BoundaryAtlasPacket :=
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{ hexSeed := 3
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hexDigitWidth := 2
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blockBase := 256
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law := BoundaryLaw.affineCut
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dimensionCount := 4
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coordinateDomain := 16
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boundaryCount := 4
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startIndex := 0
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length := 4
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stride := 2
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genus := 3
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massBasin := 1
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torsionClass := 0
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phaseClass := 1
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explicitBoundaryBytes := 2
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seedBytes := 1
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lawBytes := 1
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residualBytes := 0
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receiptBytes := 1
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rrcShapeOk := true
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residualDeclared := true }
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/-- Compression-sized witness for an inverted-genus boundary surface. -/
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def canonicalBoundaryAtlas : BoundaryAtlasPacket :=
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{ hexSeed := 0xC0FFEE
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hexDigitWidth := 6
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blockBase := 16777216
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law := BoundaryLaw.genusInversion
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dimensionCount := 16
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coordinateDomain := 4096
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boundaryCount := 12
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startIndex := 0
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length := 96
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stride := 7
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genus := 3
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massBasin := 5
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torsionClass := 2
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phaseClass := 4
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explicitBoundaryBytes := 3
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seedBytes := 3
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lawBytes := 1
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residualBytes := 4
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receiptBytes := 2
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rrcShapeOk := true
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residualDeclared := true }
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/-- Too short to beat explicit boundary coordinates. -/
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def tinyBoundaryAtlas : BoundaryAtlasPacket :=
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{ canonicalBoundaryAtlas with length := 2 }
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/-- Bad coordinate domain: no finite manifold address space. -/
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def badBoundaryDomainAtlas : BoundaryAtlasPacket :=
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{ canonicalBoundaryAtlas with coordinateDomain := 0 }
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/-- Missing residual declaration: cannot promote to RRC identification. -/
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def missingResidualBoundaryAtlas : BoundaryAtlasPacket :=
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{ canonicalBoundaryAtlas with residualDeclared := false }
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theorem smallBoundaryReplay :
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replayBoundaryAtlas smallBoundaryAtlas =
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[{ index := 0, coordinate := 4, side := 0, confidence := 1 },
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{ index := 1, coordinate := 6, side := 2, confidence := 1 },
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{ index := 2, coordinate := 8, side := 0, confidence := 2 },
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{ index := 3, coordinate := 10, side := 2, confidence := 2 }] := by
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native_decide
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theorem canonicalBoundaryAtlasPromotable :
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boundaryAtlasPromotable canonicalBoundaryAtlas = true := by
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native_decide
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theorem tinyBoundaryAtlasNotPromotable :
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boundaryAtlasPromotable tinyBoundaryAtlas = false := by
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native_decide
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theorem badBoundaryDomainAtlasNotPromotable :
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boundaryAtlasPromotable badBoundaryDomainAtlas = false := by
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native_decide
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theorem missingResidualBoundaryAtlasNotPromotable :
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boundaryAtlasPromotable missingResidualBoundaryAtlas = false := by
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native_decide
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theorem promotedBoundaryAtlasStructurallyValid (p : BoundaryAtlasPacket) :
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boundaryAtlasPromotable p = true -> boundaryAtlasStructurallyValid p = true := by
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unfold boundaryAtlasPromotable
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intro h
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cases hStruct : boundaryAtlasStructurallyValid p
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· simp [hStruct] at h
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· simp
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theorem promotedBoundaryAtlasSatisfiesByteLaw (p : BoundaryAtlasPacket) :
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boundaryAtlasPromotable p = true -> boundaryAtlasByteLawHolds p = true := by
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unfold boundaryAtlasPromotable
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intro h
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cases hStruct : boundaryAtlasStructurallyValid p
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· simp [hStruct] at h
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cases hBytes : boundaryAtlasByteLawHolds p
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· simp [hStruct, hBytes] at h
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· simp
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/-- A promoted atlas contributes tear-boundary evidence to the RRC receipt. -/
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theorem promotedBoundaryAtlasSetsRrcTearBoundary (p : BoundaryAtlasPacket) :
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boundaryAtlasPromotable p = true ->
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(rrcBoundaryReceiptFromAtlas p).tearBoundary = true := by
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intro h
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unfold rrcBoundaryReceiptFromAtlas
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simp [h]
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/--
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Boundary evidence alone is intentionally insufficient for projection admission:
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contradiction and detached-mass evidence must still be supplied by later RRC
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checks.
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-/
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theorem boundaryAtlasAloneDoesNotProject :
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Semantics.RRCLogogramProjection.projectionAdmissible
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(rrcBoundaryReceiptFromAtlas canonicalBoundaryAtlas) = false := by
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native_decide
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#eval replayBoundaryAtlas smallBoundaryAtlas
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#eval boundaryAtlasPromotable canonicalBoundaryAtlas
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#eval boundaryAtlasPromotable tinyBoundaryAtlas
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#eval boundaryAtlasPromotable badBoundaryDomainAtlas
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#eval boundaryAtlasPromotable missingResidualBoundaryAtlas
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#eval Semantics.RRCLogogramProjection.projectionAdmissible
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(rrcBoundaryReceiptFromAtlas canonicalBoundaryAtlas)
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end Semantics.ManifoldBoundaryAtlas
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