Integrated current route, forty-first refinement #
Route41 preserves Route40's proof skeleton while swapping in the four Route41 sidecar providers:
- candidate scalar/Frattini coordinates;
- target
K/Rquotient-action bridge; - Section 7 kernel/head provenance;
- Section 7 determinant pushout packets.
theorem
Q2Presentation.Induction.minimalBlock_groupTowerData_from_currentIntegrated41
{p : FramedPair}
(chief : NonScalarChiefFactor p)
:
Nonempty (MinimalBlockGroupTowerData p chief)
theorem
Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated41
{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_recursive_branch_from_fourier_currentIntegrated41
(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_currentIntegrated41
(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.finite_surjection_counts_equal_currentIntegrated41
(G : Type)
[Group G]
[Finite G]
[Nonempty G]
: