Integrated current route, twenty-third refinement

Route23 is an intermediate reduction route over route22. It swaps in the four route22 sidecars that have landed:

• target K/R through TargetKmodRRoute23ActualProofs;
• candidate scalar/Frattini through CandidateScalarFrattiniRoute22Proofs;
• pushout/determinant through MinimalBlockPushoutRoute23Proofs.
• kernel/head provenance through MinimalBlockKernelConcreteRoute23Proofs.

theorem Q2Presentation.Induction.minimalBlock_groupTowerData_from_currentIntegrated23 {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockGroupTowerData p chief)

Route23 group tower: the coherent route23 kernel/head branch.

theorem Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated22 {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))

Route23 cover realization: target route23 projection/action, candidate route23 Frattini partition, route23 kernel, and route23 coherent actual central-extension pushout data.

theorem Q2Presentation.Induction.boundaryFramed_nonterminal_fourier_branch_currentIntegrated23 (p : FramedPair) : ¬ScalarTerminal p → Nonempty (FourierBranchData p)

Route23 nonterminal branch.

theorem Q2Presentation.Induction.boundaryFramed_recursive_branch_from_fourier_currentIntegrated23 (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_currentIntegrated23 (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_currentIntegrated23 (p : FramedPair) : framedCountA p = framedCountQ p

theorem Q2Presentation.Induction.finite_surjection_counts_equal_currentIntegrated23 (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)))

Route23 finite-surjection equality.