Integrated current route, eighth refinement

Route8 keeps route7's scalar/Frattini candidate refinement and switches the minimal-block group tower to the refined Section 7 kernel/Frattini/raw route. This proves Frattini normality and exposes smaller concrete quotient/action packets instead of the older broad raw-object, raw-action, semantic bridge, and head-nontriviality packets.

theorem Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated8 {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 route7's candidate P2 route and the refined P3 kernel/Frattini/raw minimal-block tower.

theorem Q2Presentation.Induction.boundaryFramed_nonterminal_fourier_branch_currentIntegrated8 (p : FramedPair) : ¬ScalarTerminal p → Nonempty (FourierBranchData p)

Route8 nonterminal branch.

theorem Q2Presentation.Induction.boundaryFramed_recursive_branch_from_fourier_currentIntegrated8 (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_currentIntegrated8 (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_currentIntegrated8 (p : FramedPair) : framedCountA p = framedCountQ p

theorem Q2Presentation.Induction.finite_surjection_counts_equal_currentIntegrated8 (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)))

Route8 finite-surjection equality.