Integrated current route, one-hundred-first refinement #
Route101 is a semantic attack route integrating:
- candidate Route100 actual §8 packets;
- target Route101 projection-semantic split;
- kernel Route98 compact two-packet split;
- pushout Route98 Route82 determinant split.
This is a work route, not the promoted public route.
theorem
Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated101
{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_currentIntegrated101
(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_currentIntegrated101
(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_currentIntegrated101
(G : Type)
[Group G]
[Finite G]
[Nonempty G]
: