Integrated current route, thirtieth refinement #
Route30 keeps the route28 candidate scalar/Frattini sidecar and route29 target K/R bridge, and integrates the route29 minimal-block kernel/head refinement. The kernel route replaces the broad invariant packet by four sharper Section 7 head/lower-layer packets on the selected raw quotient tower.
theorem
Q2Presentation.Induction.minimalBlock_groupTowerData_from_currentIntegrated30
{p : FramedPair}
(chief : NonScalarChiefFactor p)
:
Nonempty (MinimalBlockGroupTowerData p chief)
theorem
Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated30
{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_currentIntegrated30
(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_currentIntegrated30
(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_currentIntegrated30
(G : Type)
[Group G]
[Finite G]
[Nonempty G]
: