Integrated Route196: candidate, kernel, pushout, and target lowerings

This route combines the currently green strict lowerings:

• Route194 candidate lowering: the two Route192 actual candidate leaves are replaced by the Frattini-coordinate and scalar-obstruction-evaluator leaves;
• Route195 Section 7 lowering: the five Route78 selected kernel/Frattini leaves are replaced by the five Route67 Lemma 7.2 leaves, and the pushout SquarePolarData leaf is replaced by ActualScalarCentralPushoutData;
• Fulcrum Route193 target lowering: the two Route28 target leaves are replaced by the concrete Route164 projection/action surface.

theorem Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated196CandidateKernelPushoutTarget164 {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_currentIntegrated196CandidateKernelPushoutTarget164 (p : FramedPair) : ¬ScalarTerminal p → Nonempty (FourierBranchData p)

theorem Q2Presentation.Induction.boundaryFramed_recursive_branch_from_fourier_currentIntegrated196CandidateKernelPushoutTarget164 (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_currentIntegrated196CandidateKernelPushoutTarget164 (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_currentIntegrated196CandidateKernelPushoutTarget164 (p : FramedPair) : framedCountA p = framedCountQ p

theorem Q2Presentation.Induction.finite_surjection_counts_equal_currentIntegrated196CandidateKernelPushoutTarget164 (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)))