Integrated current route, sixty-sixth refinement

Route66 combines the two completed Route63 sidecars:

• candidate Frattini/scalar lifting is supplied by centralCover_candidateLiftPartitionData_from_route63;
• minimal-block least/Frattini tower data is supplied by minimalBlock_groupTowerData_from_kernelRoute66CombinedClosers;
• target K/R decoration is supplied by TargetKmodRRoute63SameTowerClosers.centralCover_targetDecorationKernelData_from_route63, reducing the Route62 same-tower target surface to the sharper Route48 coherent projection/action atom; and
• the minimal-block determinant/pushout provider is supplied by minimalBlock_preheadDeterminantPackets_from_route63, removing the five Route60 pushout atoms from the active final route.

This file intentionally leaves earlier route files untouched and exposes the current theorem under currentIntegrated66 names for final-theorem promotion.

theorem Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated66 {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_currentIntegrated66 (p : FramedPair) : ¬ScalarTerminal p → Nonempty (FourierBranchData p)

theorem Q2Presentation.Induction.boundaryFramed_recursive_branch_from_fourier_currentIntegrated66 (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_currentIntegrated66 (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_currentIntegrated66 (p : FramedPair) : framedCountA p = framedCountQ p

theorem Q2Presentation.Induction.finite_surjection_counts_equal_currentIntegrated66 (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)))