Integrated current route, thirty-seventh refinement

Route37 keeps the Route36 Section 8 candidate and target providers, and swaps in the new Section 7 refinements:

• candidate scalar/Frattini through CandidateScalarFrattiniRoute37Proofs;
• target K/R through TargetKmodRRoute37BridgeProofs;
• kernel/head through MinimalBlockKernelConcreteRoute37Proofs;
• pushout/determinant through MinimalBlockPushoutRoute37Proofs.

This is an honest lowering route, not a final closure route: the broad Route36 kernel and pushout packets are replaced by finer manuscript-shaped packets.

theorem Q2Presentation.Induction.minimalBlock_groupTowerData_from_currentIntegrated37 {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockGroupTowerData p chief)

theorem Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated37 {p : FramedPair} {chief : NonScalarChiefFactor p} (G : MinimalBlockGroupTowerData p chief) (h : ¬ScalarTerminal p) (Fdet : MinimalBlockPreheadExtraspecialEquivariantFamilyData G.preheadTowerData) (A : MinimalBlockPreheadExtraspecialAnnihilationData Fdet) (Rdet : MinimalBlockPreheadExtraspecialRadicalData Fdet) : Nonempty (CoverRealization (G.toMinimalBlock h Fdet A Rdet))

theorem Q2Presentation.Induction.boundaryFramed_nonterminal_fourier_branch_currentIntegrated37 (p : FramedPair) : ¬ScalarTerminal p → Nonempty (FourierBranchData p)

theorem Q2Presentation.Induction.boundaryFramed_recursive_branch_from_fourier_currentIntegrated37 (p : FramedPair) (h : ¬ScalarTerminal p) : ∃ (children : List FramedPair) (combine : List Cardinal.{0} → Cardinal.{0}), (∀ c ∈ children, framedMeasure c < framedMeasure p) ∧ framedCountA p = combine (List.map framedCountA children) ∧ framedCountQ p = combine (List.map framedCountQ children)

theorem Q2Presentation.Induction.boundaryFramed_recursion_step_currentIntegrated37 (p : FramedPair) : framedCountA p = framedCountQ p ∨ ∃ (children : List FramedPair) (combine : List Cardinal.{0} → Cardinal.{0}), (∀ c ∈ children, framedMeasure c < framedMeasure p) ∧ framedCountA p = combine (List.map framedCountA children) ∧ framedCountQ p = combine (List.map framedCountQ children)

theorem Q2Presentation.Induction.boundaryFramed_counts_equal_currentIntegrated37 (p : FramedPair) : framedCountA p = framedCountQ p

theorem Q2Presentation.Induction.finite_surjection_counts_equal_currentIntegrated37 (G : Type) [Group G] [Finite G] [Nonempty G] : Cardinal.mk (Profinite.SurjContHom GammaA (ProfiniteGrp.ofFiniteGrp (FiniteGrp.of G))) = Cardinal.mk (Profinite.SurjContHom GQ2Profinite (ProfiniteGrp.ofFiniteGrp (FiniteGrp.of G)))