module module moderate

`IndisputableMonolith.Gravity.SevenGaps.Gap2EnrichedCarrierPhase`

Defines a Fin-8 labeled tick and enriched phase on exact complexes for the Gap2 residual carrier route. Gravity workers on Wave C1 R4/R5 cite it as the live carrier after the binary-carrier draft was superseded. Packages tick descent, self-loop counting invariants, and phase extraction used by posting-cocycle and tail-fiber bridges. Mostly definitions plus invariance lemmas, not a terminal blocker proof.

claimThe module introduces a labeled eight-tick on exact path classes, an enriched phase attached to that tick, and self-loop counts invariant under global equivalence of labeled complexes. Descent sends labeled ticks to ordinary period-$8$ ticks while preserving the phase and loop data needed for Gap2 carrier attacks on exact shells.

background

Gap2 work sits in the seven-gap residual DAG for quantum-gravity Wave C. Upstream, the signature oscillatory-tail blocker route reached reduction plus Burnside mass lemmas with an honest stall: the blocker proposition is not proved, and uniform single-signature mass concentration for all large shells is refuted as an asymptotic strategy. The companion tick-phase tail blocker hardens the R4 residual after a cross-family correction: generic all-shell tick-fiber mass balance forces every exact shell amplitude to zero, so contiguous-block sums vanish.

This module supplies the enriched carrier itself: a Fin-8 tick on labeled exact complexes, not a bare binary carrier. Sibling objects include labeled ticks, descended ticks, enriched phase, self-loop counts with congruence, and self-loop ticks/phases with global-equivalence invariance. The ambient period is the RS eight-tick octave (forcing step T7).

Downstream posting-cocycle work notes that the RS eight-tick recognition-posting cocycle already exists as a period-8 transaction; a certified Fin-8 phase close wants a Fin-8 tick on exact path classes, which this carrier is built to provide.

proof idea

Definition-and-invariants module, not a terminal existence proof. It builds the labeled-tick type and constructors for descended ticks, enriched phase, self-loop counts, self-loop ticks, class ticks, and self-loop phase. Congruence and global-equivalence invariance lemmas pin that self-loop counts and related tick data are stable under the labeled equivalence used by later attacks. No R4/R5 blocker proposition is discharged here; the module only banks carrier data imported by audit, bridge, and cocycle modules.

why it matters in Recognition Science

Live carrier surface for the enriched-carrier phase route in Wave C1 Gap2. Four importers depend on it: the enriched-carrier phase axiom audit (headline theorems must print inside propext, Classical.choice, Quot.sound); the exact-class carrier attack, a superseded binary-carrier stub that re-exports this module so stale targets stay green; the posting-cocycle carrier, which implements the carrier half of the Gap2 posting-cocycle residual and needs a Fin-8 tick on exact path classes; and the tail-fiber shift bridge, the conditional TailFiberShift bankable piece on residual R4 with this module as carrier. Sits after the R4 signature and tick-phase blocker work and feeds the R5 enriched-carrier phase terminal.

scope and limits

Does not prove the SignatureFin8 oscillatory tail blocker proposition.
Does not discharge TailFiberShift unconditionally.
Does not certify full Gap2 Fin-8 phase close or the posting cocycle.
Does not restore uniform single-signature mass concentration on large shells.
Does not replace upstream tick-phase tail blocker arguments.

used by (4)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Gravity.SevenGaps.Gap2EnrichedCarrierPhaseAudit module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2ExactClassCarrierAttack module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2PostingCocycleCarrier module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2TailFiberShiftBridge module_import

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Gravity.SevenGaps.Gap2SignatureBlockerAttack module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2TickPhaseTailBlocker module_import

declarations in this module (37)

abbrev LabeledTick L54
def GlobalEquivalentInvariant L57
def descendedTick L62
theorem descendedTick_mk L69
def enrichedPhase L77
def selfLoopCount L85
theorem selfLoopCount_congr L90
theorem selfLoopCount_ge_invariant L131
def selfLoopTick L138
theorem selfLoopTick_invariant L142
def selfLoopClassTick L149
def selfLoopPhase L152
def twoLoopsComplex L158
def twoBridgesComplex L163
theorem selfLoopCount_twoLoops L167
theorem selfLoopCount_twoBridges L181
theorem not_ge_twoLoops_twoBridges L195
def doubleEdgeSig L203
def twoLoopsClass L208
def twoBridgesClass L211
theorem selfLoopClassTick_twoLoops L214
theorem selfLoopClassTick_twoBridges L219
theorem selfLoopClassTick_not_ShellSigTick L226
theorem oscillatoryTail_of_enriched_eventual_balance L242
theorem oscillatoryTail_of_enriched_identically_zero L252
def TypedResidual_enriched_carrier_oscillatoryTail L274
def TypedResidual_continuum_substrate_oscillatoryTail L280
theorem bare_r5_of_enriched_carrier_oscillatoryTail L285
theorem typedResidual_continuum_substrate_oscillatoryTail_of_enriched L292
theorem typedResidual_continuum_substrate_oscillatoryTail_of_enriched_eventual_balance L298
structure EnrichedCarrierPhaseSubstrate L306
def selfLoopEnrichedSubstrate L311
theorem enrichedCarrierPhaseSubstrate_nonempty L316
theorem signatureBlocker_iff_no_shellSig_oscillatoryTail L320
structure Gap2EnrichedCarrierPhaseStatus L328
def gap2EnrichedCarrierPhaseStatus L338
theorem gap2EnrichedCarrierPhaseStatus_flags L348