Integrated current route, nineteenth refinement

Route19 keeps route18's assembly shape but swaps in the newest sidecars:

• target K/R remains through TargetKmodRRoute18ProjectionProofs, because the route19 target experiment routed back to older bridge leaves;
• candidate scalar/Frattini through CandidateScalarFrattiniRoute19Proofs, replacing the five route16 candidate leaves by two direct exact-image residuals;
• Section 7 kernel/head through MinimalBlockKernelConcreteRoute19Proofs, replacing the monolithic route16 kernel package by narrower same-tower provenance leaves;
• pushout/determinant through MinimalBlockPushoutRoute19Proofs, replacing the two route16 pushout leaves by split actual central-extension packets.

theorem Q2Presentation.Induction.minimalBlock_groupTowerData_from_currentIntegrated19 {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockGroupTowerData p chief)

Route18 group tower: same-tower kernel/head provenance split.

theorem Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated19 {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))

Route18 cover realization: target route18 bridge, candidate route18 direct exact-image split, kernel route18, and route18 pushout data.

theorem Q2Presentation.Induction.boundaryFramed_nonterminal_fourier_branch_currentIntegrated19 (p : FramedPair) : ¬ScalarTerminal p → Nonempty (FourierBranchData p)

Route18 nonterminal branch.

theorem Q2Presentation.Induction.boundaryFramed_recursive_branch_from_fourier_currentIntegrated19 (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_currentIntegrated19 (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_currentIntegrated19 (p : FramedPair) : framedCountA p = framedCountQ p

theorem Q2Presentation.Induction.finite_surjection_counts_equal_currentIntegrated19 (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)))

Route18 finite-surjection equality.