Integrated Route150 compact attack route

Route150 combines candidate Route147 compact provider, target Route147 compact provider, compact kernel, and pushout Route147 central-extension closer:

• candidate Section 8 via CandidateRoute147PointwiseClosers;
• target Section 8 via TargetKmodRRoute147SameTowerPointwiseClosers;
• kernel least/Frattini and raw/head via the compact Section7KernelRoute147CombinedClosers invariant-package provider;
• pushout/determinant via Section7PushoutRoute147CentralExtensionClosers.

This is an attack route, not a public promotion. It lowers Route145's manuscript-shaped atoms further into selected quotient/action, Frattini, raw-object, and central-extension atoms.

Route150 compact kernel provider

theorem Q2Presentation.Induction.minimalBlock_kernelModuleConcreteProvenanceData_currentIntegrated150Compact {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockKernelModuleConcreteProvenanceData chief)

Route148 kernel provenance: use the Route147 compact invariant-package provider, which replaces four split raw/head/lower atoms by the coherent same-tower invariant package.

theorem Q2Presentation.Induction.minimalBlock_lowerGroupModuleData_currentIntegrated150Compact {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockLowerGroupModuleData chief)

theorem Q2Presentation.Induction.minimalBlock_groupTowerData_currentIntegrated150Compact {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockGroupTowerData p chief)

Route150 central-cover realization

theorem Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated150Compact {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))

Integrated Route150

theorem Q2Presentation.Induction.boundaryFramed_nonterminal_fourier_branch_currentIntegrated150Compact (p : FramedPair) : ¬ScalarTerminal p → Nonempty (FourierBranchData p)

theorem Q2Presentation.Induction.boundaryFramed_recursive_branch_from_fourier_currentIntegrated150Compact (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_currentIntegrated150Compact (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_currentIntegrated150Compact (p : FramedPair) : framedCountA p = framedCountQ p

theorem Q2Presentation.Induction.finite_surjection_counts_equal_currentIntegrated150Compact (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)))