Candidate scalar/Frattini route22 proofs

Route22 keeps the route21 packet shapes but closes the two route21 residual leaves by repackaging narrower Section 8 scalar/Frattini APIs:

• scalar-pushout values, additivity, and homogeneity for the middle obstruction evaluator;
• Frattini base/fibre coordinates, realization, and the two inverse laws for the top exact-image affine fibre.

No new residual axiom is introduced here. The middle route21 structure is just the canonical-index obstruction evaluation form of the proven middle R-obstruction map, and the route21 top structure is the equivalence form of the Frattini coordinate/realization bijection for the same selected middle obstruction.

Route22 replacements for the two route21 leaves

theorem Q2Presentation.Induction.centralCover_candidateScalarFrattiniRoute22MiddleEvaluationData {p : FramedPair} (B : MinimalBlock p) (T : CentralCoverElementaryQuotientTowerData B) : Nonempty (CentralCoverCandidateScalarFrattiniRoute21MiddleEvaluationData B T)

Route22 replacement for the route21 middle evaluation residual.

The proven middle R-lift obstruction map already has the canonical middle exact-image source as its domain, so it repackages directly as the explicit route21 obstruction evaluation.

theorem Q2Presentation.Induction.centralCover_candidateScalarFrattiniRoute22TopEquivData {p : FramedPair} (B : MinimalBlock p) (T : CentralCoverElementaryQuotientTowerData B) (M : CentralCoverCandidateScalarFrattiniRoute21MiddleEvaluationData B T) : Nonempty (CentralCoverCandidateScalarFrattiniRoute21TopEquivData B T M)

Route22 replacement for the route21 top exact-image equivalence residual.

For any selected route21 middle evaluation, the existing Frattini partition theorem applies to the induced middle R-lift obstruction map. Its bijection is exactly the equivalence data required by route21.

Route-ready reassembly without the route21 residuals

theorem Q2Presentation.Induction.centralCover_candidateDirectExactImageResidualData_from_scalarFrattiniRoute22 {p : FramedPair} (B : MinimalBlock p) (T : CentralCoverElementaryQuotientTowerData B) : Nonempty (CentralCoverCandidateDirectExactImageResidualData B T)

Route22 direct exact-image residual data assembled without the route21 candidate residual axioms.

theorem Q2Presentation.Induction.centralCover_candidateExactImageFinalResidualData_from_scalarFrattiniRoute22 {p : FramedPair} (B : MinimalBlock p) (T : CentralCoverElementaryQuotientTowerData B) : Nonempty (CentralCoverCandidateExactImageFinalResidualData B T)

Route22 coherent final exact-image residual for the selected middle obstruction and matching Frattini exact-image equivalence.

theorem Q2Presentation.Induction.centralCover_candidateMiddleExactImageObstructionEvaluationData_from_scalarFrattiniRoute22 {p : FramedPair} (B : MinimalBlock p) (T : CentralCoverElementaryQuotientTowerData B) : Nonempty (CentralCoverCandidateMiddleExactImageObstructionEvaluationData B T)

Route22 middle exact-image obstruction evaluation.

theorem Q2Presentation.Induction.centralCover_candidateTopExactImageAffineFiberEquivSigma_from_scalarFrattiniRoute22 {p : FramedPair} (B : MinimalBlock p) (T : CentralCoverElementaryQuotientTowerData B) : Nonempty ((E : CentralCoverCandidateMiddleExactImageObstructionEvaluationData B T) × CentralCoverCandidateTopExactImageAffineFiberEquivData B T E)

Route22 dependent top affine-fibre packet, retaining the selected middle obstruction evaluation.

theorem Q2Presentation.Induction.centralCover_candidateRLiftSemanticData_from_scalarFrattiniRoute22 {p : FramedPair} (B : MinimalBlock p) (T : CentralCoverElementaryQuotientTowerData B) (Q : CentralCoverCandidateQuotientFrameMapData B T) : Nonempty (CentralCoverCandidateRLiftSemanticData B T)

Semantic central R-lift data from route22 and a supplied quotient-frame map.

theorem Q2Presentation.Induction.centralCover_candidateLiftPartitionData_from_scalarFrattiniRoute22 {p : FramedPair} (B : MinimalBlock p) (T : CentralCoverElementaryQuotientTowerData B) (Q : CentralCoverCandidateQuotientFrameMapData B T) : Nonempty (CentralCoverCandidateLiftPartitionData B)

Route22 candidate lift-partition provider in the same B T Q shape as the route21 candidate hook.