Integrated current route, one-hundred-thirtieth refinement #
Route130 lowers both the candidate exact-image leaves and the target leaf:
- candidate: two exact-image residual atoms -> two lower exact-image/obstruction packets;
- target: Route45 literal selected-action leaf -> Route102/same-tower packets;
- kernel: Route120 compact kernel trio -> one provenance-semantic kernel leaf;
- pushout: two broad determinant leaves -> one coherent central-extension leaf.
This becomes the current public route once PresentationCorrect imports it.
theorem
Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated130
{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_currentIntegrated130
(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_currentIntegrated130
(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_currentIntegrated130
(G : Type)
[Group G]
[Finite G]
[Nonempty G]
: