Route212 determinant/pushout closers

Route212 currently imports the Route199 determinant provider, whose closure contains the two aggregate Section 7 determinant/pushout residuals

• minimalBlock_preheadCentralPushoutSemanticData;
• minimalBlock_preheadCentralPushoutSimpleHeadDeterminantActualData.

This sidecar leaves the routed file untouched. It gives a Route212-owned drop-in determinant provider whose closure reconstructs those two aggregate packets from the stricter manuscript-shaped surface already available in the project: one coherent scalar square/polar central-pushout packet and the four semantic simple-head determinant pieces.

Route212 lower determinant/pushout surface

theorem Q2Presentation.Induction.MinimalBlockPushoutRoute212Closers.minimalBlock_preheadRoute212LowerManuscriptSurface {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : ∃ (x : MinimalBlockPreheadCentralPushoutSquarePolarData D) (S : MinimalBlockPreheadCentralPushoutSemanticData D), Nonempty (MinimalBlockPreheadCentralPushoutNaturalitySemanticData S) ∧ Nonempty (MinimalBlockPreheadCentralPushoutDiagonalZeroSemanticData S) ∧ Nonempty (MinimalBlockPreheadCentralPushoutPolarZeroSemanticData S) ∧ Nonempty (MinimalBlockPreheadCentralPushoutRadicalContainmentSemanticData S)

Route212 audit surface for the lowered Section 7 determinant/pushout frontier.

The first field is the coherent scalar pushout square/polar packet attached to the actual central pushout. The remaining four fields are the semantic prop:simpleheaddet pieces for the semantic central-pushout family reconstructed from that scalar packet. The theorem does not use either Route199 aggregate residual atom as an axiom.

theorem Q2Presentation.Induction.MinimalBlockPushoutRoute212Closers.minimalBlock_preheadRoute199ResidualShape_from_route212Closers {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : ∃ (S : MinimalBlockPreheadCentralPushoutSemanticData D), Nonempty (MinimalBlockPreheadCentralPushoutSimpleHeadDeterminantActualData S)

Route199-shaped residual reconstruction from the Route212 lowered surface.

The conclusion has the same aggregate shape currently visible in Route212 audits, but the proof obtains the semantic scalar-pushout family from the coherent square/polar packet and obtains the actual determinant packet from the four semantic simple-head determinant atoms.

theorem Q2Presentation.Induction.MinimalBlockPushoutRoute212Closers.minimalBlock_preheadPushoutRouteLowerData_from_route212Closers {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : Nonempty (MinimalBlockPreheadPushoutRouteLowerData D)

Route212 lower pushout packet from the lowered determinant/pushout surface.

theorem Q2Presentation.Induction.MinimalBlockPushoutRoute212Closers.minimalBlock_preheadDeterminantPackets_from_route212Closers {p : FramedPair} {chief : NonScalarChiefFactor p} (D : MinimalBlockPreheadTowerData p chief) : ∃ (F : MinimalBlockPreheadExtraspecialEquivariantFamilyData D), Nonempty (MinimalBlockPreheadExtraspecialAnnihilationData F) ∧ Nonempty (MinimalBlockPreheadExtraspecialRadicalData F)

Route212 drop-in determinant provider.

This has the same target type as the Route199 determinant provider consumed by the current Route212 Fourier branch, but its axiom closure replaces the two aggregate residual atom names by the lowered square/polar plus simple-head semantic determinant atoms.