Route199 determinant-semantic closer for the Route198 pushout atoms

Route198 exposes seven determinant-semantic atoms:

• minimalBlock_preheadCentralPushoutQuadraticFamilyData;
• minimalBlock_preheadCentralPushoutSquareDiagonalData;
• minimalBlock_preheadCentralPushoutPolarSymmData;
• minimalBlock_preheadCentralPushoutNaturalitySemanticData;
• minimalBlock_preheadCentralPushoutDiagonalZeroSemanticData;
• minimalBlock_preheadCentralPushoutPolarZeroSemanticData;
• minimalBlock_preheadCentralPushoutRadicalContainmentSemanticData.

This sidecar keeps the same downstream determinant-provider shape, but ties the seven fields to one semantic central-pushout family S and one actual simple-head determinant packet for that same S. The square/diagonal/polar fields are definitional projections of S, and the four prop:simpleheaddet semantic fields are theorem-level projections of the actual determinant packet.

The resulting integrated route removes the seven Route198 atom names from the finite theorem closure and replaces them by the smaller same-family surface:

• minimalBlock_preheadCentralPushoutSemanticData;
• minimalBlock_preheadCentralPushoutSimpleHeadDeterminantActualData.

Same-family Route199 determinant-semantic packet

structure Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.MinimalBlockPreheadPushoutRoute199DeterminantSemanticData {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : Type

Route199 same-family determinant packet for one pre-head tower.

• semantic : MinimalBlockPreheadCentralPushoutSemanticData D
• determinant : MinimalBlockPreheadCentralPushoutSimpleHeadDeterminantActualData self.semantic

def Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.MinimalBlockPreheadPushoutRoute199DeterminantSemanticData.quadraticFamily {p : FramedPair} {chief : NonScalarChiefFactor p} {D : MinimalBlockPreheadTowerData p chief} (P : MinimalBlockPreheadPushoutRoute199DeterminantSemanticData D) : MinimalBlockPreheadCentralPushoutQuadraticFamilyData D

The split quadratic-family packet induced by the same semantic pushout.

Equations

• P.quadraticFamily = P.semantic.toQuadraticFamily

def Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.MinimalBlockPreheadPushoutRoute199DeterminantSemanticData.squareDiagonal {p : FramedPair} {chief : NonScalarChiefFactor p} {D : MinimalBlockPreheadTowerData p chief} (P : MinimalBlockPreheadPushoutRoute199DeterminantSemanticData D) : MinimalBlockPreheadCentralPushoutSquareDiagonalData P.quadraticFamily

The square-diagonal identity for that induced quadratic family.

Equations

• ⋯ = ⋯

def Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.MinimalBlockPreheadPushoutRoute199DeterminantSemanticData.polarSymm {p : FramedPair} {chief : NonScalarChiefFactor p} {D : MinimalBlockPreheadTowerData p chief} (P : MinimalBlockPreheadPushoutRoute199DeterminantSemanticData D) : MinimalBlockPreheadCentralPushoutPolarSymmData P.quadraticFamily

The polar-symmetry identity for that induced quadratic family.

Equations

• ⋯ = ⋯

def Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.MinimalBlockPreheadPushoutRoute199DeterminantSemanticData.naturality {p : FramedPair} {chief : NonScalarChiefFactor p} {D : MinimalBlockPreheadTowerData p chief} (P : MinimalBlockPreheadPushoutRoute199DeterminantSemanticData D) : MinimalBlockPreheadCentralPushoutNaturalitySemanticData P.semantic

Naturality of the same central-pushout family, projected from the actual simple-head determinant packet.

Equations

• ⋯ = ⋯

def Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.MinimalBlockPreheadPushoutRoute199DeterminantSemanticData.diagonalZero {p : FramedPair} {chief : NonScalarChiefFactor p} {D : MinimalBlockPreheadTowerData p chief} (P : MinimalBlockPreheadPushoutRoute199DeterminantSemanticData D) : MinimalBlockPreheadCentralPushoutDiagonalZeroSemanticData P.semantic

Diagonal vanishing on T, projected from annihilation of the actual square map for the same central-pushout family.

Equations

• ⋯ = ⋯

def Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.MinimalBlockPreheadPushoutRoute199DeterminantSemanticData.polarZero {p : FramedPair} {chief : NonScalarChiefFactor p} {D : MinimalBlockPreheadTowerData p chief} (P : MinimalBlockPreheadPushoutRoute199DeterminantSemanticData D) : MinimalBlockPreheadCentralPushoutPolarZeroSemanticData P.semantic

Polar vanishing on T x M, projected from annihilation of the actual square map for the same central-pushout family.

Equations

• ⋯ = ⋯

def Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.MinimalBlockPreheadPushoutRoute199DeterminantSemanticData.radicalContainment {p : FramedPair} {chief : NonScalarChiefFactor p} {D : MinimalBlockPreheadTowerData p chief} (P : MinimalBlockPreheadPushoutRoute199DeterminantSemanticData D) : MinimalBlockPreheadCentralPushoutRadicalContainmentSemanticData P.semantic

Polar-radical containment, projected from the actual determinant packet for the same central-pushout family.

Equations

• ⋯ = ⋯

def Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.MinimalBlockPreheadPushoutRoute199DeterminantSemanticData.toPushoutRouteLower {p : FramedPair} {chief : NonScalarChiefFactor p} {D : MinimalBlockPreheadTowerData p chief} (P : MinimalBlockPreheadPushoutRoute199DeterminantSemanticData D) : MinimalBlockPreheadPushoutRouteLowerData D

Convert the Route199 packet to the lower pushout-route packet consumed by the integrated Fourier branch.

Equations

• P.toPushoutRouteLower = { selfDuality := P.semantic.toSelfDuality, simpleHeadDeterminant := ⋯ }

Route-ready lowerers

theorem Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.minimalBlock_preheadPushoutRoute199DeterminantSemanticData {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : Nonempty (MinimalBlockPreheadPushoutRoute199DeterminantSemanticData D)

Build the Route199 same-family determinant packet from the smaller semantic central-pushout family and actual simple-head determinant residuals.

theorem Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.minimalBlock_preheadRoute199DeterminantSemanticSurface {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : ∃ (S : MinimalBlockPreheadCentralPushoutSemanticData D), Nonempty (MinimalBlockPreheadCentralPushoutSimpleHeadDeterminantActualData S)

Audit-facing Route199 lower surface.

theorem Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.minimalBlock_preheadRoute198DeterminantAtoms_from_route199DeterminantSemanticClosers {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : ∃ (Q : MinimalBlockPreheadCentralPushoutQuadraticFamilyData D), Nonempty (MinimalBlockPreheadCentralPushoutSquareDiagonalData Q) ∧ Nonempty (MinimalBlockPreheadCentralPushoutPolarSymmData Q) ∧ ∃ (S : MinimalBlockPreheadCentralPushoutSemanticData D), Nonempty (MinimalBlockPreheadCentralPushoutNaturalitySemanticData S) ∧ Nonempty (MinimalBlockPreheadCentralPushoutDiagonalZeroSemanticData S) ∧ Nonempty (MinimalBlockPreheadCentralPushoutPolarZeroSemanticData S) ∧ Nonempty (MinimalBlockPreheadCentralPushoutRadicalContainmentSemanticData S)

Audit-facing reconstruction of the seven Route198 determinant-semantic packets from the smaller same-family Route199 surface.

The closure of this theorem should contain the two Route199 residuals listed in the module header, not the seven Route198 atom names.

theorem Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.minimalBlock_preheadPushoutRouteLowerData_from_route199DeterminantSemanticClosers {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : Nonempty (MinimalBlockPreheadPushoutRouteLowerData D)

Route199 lower pushout packet.

theorem Q2Presentation.Induction.MinimalBlockPushoutRoute199DeterminantSemanticClosers.minimalBlock_preheadDeterminantPackets_from_route199DeterminantSemanticClosers {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : ∃ (F : MinimalBlockPreheadExtraspecialEquivariantFamilyData D), Nonempty (MinimalBlockPreheadExtraspecialAnnihilationData F) ∧ Nonempty (MinimalBlockPreheadExtraspecialRadicalData F)

Drop-in determinant provider for Route198-compatible integrated routes, with the seven determinant-semantic Route198 atom names strictly lowered to the Route199 same-family surface.