Integrated current route, twelfth refinement

Route12 extends route11 with two more completed sidecars:

• the target same-tower projection/action sidecar replaces the route10 target projection residual quartet by the canonical quotient/action bridge;
• the actual central-extension sidecar replaces the seven route10 P5 packets by one actual square/polar central-pushout provider.

theorem Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated12 {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))

Cover realization through route11, but with the target decoration-kernel provider routed through the projection/action route10 sidecar.

theorem Q2Presentation.Induction.boundaryFramed_nonterminal_fourier_branch_currentIntegrated12 (p : FramedPair) : ¬ScalarTerminal p → Nonempty (FourierBranchData p)

Route12 nonterminal branch.

theorem Q2Presentation.Induction.boundaryFramed_recursive_branch_from_fourier_currentIntegrated12 (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_currentIntegrated12 (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_currentIntegrated12 (p : FramedPair) : framedCountA p = framedCountQ p

theorem Q2Presentation.Induction.finite_surjection_counts_equal_currentIntegrated12 (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)))

Route12 finite-surjection equality.