Route188 Section 7 kernel/provenance closers

Route188 is the compact kernel replay for the current Route187 candidate/target semantic route. It gives named replacements for the seven Route187 kernel leaves:

• the five Route78 selected least/Frattini packets are routed through the Route184 Lemma 7.2 split;
• the two Route167 raw quotient/simple-head packets are routed through the Route183/Route180 Route43 raw-object and simple-head split.

No Route187 file is modified by this sidecar.

Route78-selected Frattini packets lowered through Route184

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.leastKernelSelectedData_from_route188Kernel {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockKernelRoute78FrattiniClosers.LeastKernelSelectedData chief)

Route188 replacement for the compact Route78 least-kernel packet.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.leastOverChiefData_from_route188Kernel {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockKernelLeastOverChiefData chief)

Route-ready least-over-chief packet for Route188.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.frattiniInternalSelectedData_from_route188Kernel {p : FramedPair} {chief : NonScalarChiefFactor p} (K : MinimalBlockKernelLeastOverChiefData chief) : Nonempty (MinimalBlockKernelRoute78FrattiniClosers.FrattiniInternalSelectedData K)

Route188 replacement for the compact Route78 internal Frattini witness.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.frattiniCentralizerSelectedData_from_route188Kernel {p : FramedPair} {chief : NonScalarChiefFactor p} (K : MinimalBlockKernelLeastOverChiefData chief) : Nonempty (MinimalBlockKernelRoute78FrattiniClosers.FrattiniCentralizerSelectedData K)

Route188 replacement for the compact Route78 Frattini-centralizer packet.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.fourthPowerKernelSelectedData_from_route188Kernel {p : FramedPair} {chief : NonScalarChiefFactor p} (K : MinimalBlockKernelLeastOverChiefData chief) : Nonempty (MinimalBlockKernelRoute78FrattiniClosers.FourthPowerKernelSelectedData K)

Route188 replacement for the compact Route78 fourth-power packet.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.frattiniSquareCommutatorLiteralExponentData_from_route188Kernel {p : FramedPair} {chief : NonScalarChiefFactor p} (K : MinimalBlockKernelLeastOverChiefData chief) : Nonempty (MinimalBlockKernelRoute78FrattiniClosers.FrattiniSquareCommutatorLiteralExponentData K)

Route188 replacement for the compact Route78 literal exponent packet.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.frattiniData_from_route188Kernel {p : FramedPair} {chief : NonScalarChiefFactor p} (K : MinimalBlockKernelLeastOverChiefData chief) : Nonempty (MinimalBlockKernelModuleConcreteFrattiniData K)

Concrete Frattini packet for the Route188 kernel provider.

Route167 raw packets lowered through Route183/Route180

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.rawQuotientTowerData_from_route188Kernel {p : FramedPair} {chief : NonScalarChiefFactor p} (K : MinimalBlockKernelLeastOverChiefData chief) (F : MinimalBlockKernelModuleConcreteFrattiniData K) : Nonempty (MinimalBlockKernelRawQuotientTowerData K F)

Route188 replacement for Section7KernelRoute167Closers.rawQuotientTowerData.

The residual dependencies are the Route43 literal raw-object/action/head packets exposed by Route180, not the compact Route167 raw atom.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.rawSimpleHeadSemanticData_from_route188Kernel {p : FramedPair} {chief : NonScalarChiefFactor p} {K : MinimalBlockKernelLeastOverChiefData chief} {F : MinimalBlockKernelModuleConcreteFrattiniData K} (Q : MinimalBlockKernelRawQuotientTowerData K F) : Nonempty (MinimalBlockKernelConcreteRoute44.RawSimpleHeadSemanticData Q.rawData.rawTowerData)

Route188 replacement for Section7KernelRoute167Closers.rawSimpleHeadSemanticData.

The same raw tower is interpreted through the Route43 simple-head pieces opened by Route180.

Drop-in kernel provider

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.kernelRoute188ModuleLayerData_from_section7KernelRoute188Closers {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (Section7KernelRoute183Closers.KernelRoute183ModuleLayerData chief)

Route188 module-layer packet with Route184 Frattini data and Route183 raw Route43 tower data.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.minimalBlock_kernelModuleConcreteProvenanceData_from_section7KernelRoute188Closers {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockKernelModuleConcreteProvenanceData chief)

Concrete kernel/module provenance through Route188.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.minimalBlock_lowerGroupModuleData_from_section7KernelRoute188Closers {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockLowerGroupModuleData chief)

Lower group/module data through Route188.

theorem Q2Presentation.Induction.Section7KernelRoute188Closers.minimalBlock_groupTowerData_from_section7KernelRoute188Closers {p : FramedPair} (chief : NonScalarChiefFactor p) : Nonempty (MinimalBlockGroupTowerData p chief)

Drop-in Route188 Section 7 kernel provider.