hktKineticNormalizedRigidityStatus
plain-language theorem explainer
Status witness that marks all four gap-5 kinetic-normalized rigidity ledger flags green: mod-vacuum rigidity killed, kinetic-normalized rigidity closed, FTC recovery derived, and gap-5 constraint recovery. Downstream flag aggregation and the full-theory gap-5 benchmark cite this record. The body is a pure structure inhabitant with every Bool field set to true.
Claim. The HKT kinetic-normalized rigidity status record has all four boolean fields equal to true: the mod-vacuum rigidity counterexample is killed, kinetic-normalized rigidity is closed, fundamental theorem of calculus recovery is derived (not assumed), and gap-5 constraint recovery is asserted.
background
This module closes Wave C4/C5 gap 5 in the HKT gravity sector: first kill the mod-vacuum rigidity claim by exhibiting a variable-kinetic CanonicalMom inhabitant, then restore a kinetic-normalized rigidity terminal. The binding notes are D-qg-hkt-modvacuum-verdict-20260723 and the C5 upgrade D-gap5-acceptance-adjudication-20260723.
The status structure packages four Bool ledger bits: whether mod-vacuum rigidity is killed, whether kinetic-normalized rigidity is closed, whether FTC recovery is theorem-derived rather than a class field assumption, and whether gap-5 constraint recovery may flip green. The load-bearing exclusion is that the vacuum kinetic target is not globally of the form $2 c_{\mathrm{Kin}} p$ under a kinetic-normalized CanonicalMom package.
FTC recovery is owned by a derived theorem (ftc_recovery_of_normalized), not an assumed field. The final gap-5 flip is jointly owned with Gap5ConstraintCloseStatus once both ledger halves bind green.
proof idea
Definitional structure inhabitant. Each of the four fields of HKTKineticNormalizedRigidityStatus is assigned the Boolean literal true. No lemmas, tactics, or algebraic reductions are involved; the declaration is the green ledger record itself.
why it matters
This is the terminal status witness for the kinetic-normalized half of gap 5 in the SevenGaps gravity stack. The immediate consumer is hktKineticNormalizedRigidityStatus_flags, which conjoins all four fields equal to true and further asserts fullTheoryBenchmarks.gap5_constraint_recovery = true.
In the module narrative, Part 1 kills HKTRigidityModVacuumStatementN2 via a variable-kinetic counterexample; Part 2 installs the kinetic-normalized CanonicalMom intensivity field and derives FTC recovery. Setting gap5ConstraintRecovery true here is the local half of the dual-ledger close that lets the global gap-5 constraint recovery bit flip.
Within Recognition Science gravity work this is bookkeeping, not a new dynamical law: it records that the C4/C5 adjudication path for HKT kinetic normalization has closed under the stated bindings.
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