IndisputableMonolith.Gravity.SevenGaps.Gap2MeasureStatusBinding
Records that the posted-history gauge-counting measure is inert in its enrichment parameter: any two enrichments yield the same measure. Equates the history carrier to the plain path-sum carrier and rewrites history discharge as a prior theorem. Retracts the Gap2 measure-status flags while leaving the continuum-limit residual open. Downstream residual-DAG and axiom-audit modules import this binding.
claimThe history-enriched gauge-counting measure $\mu_{\mathrm{hist}}$ is independent of the enrichment parameter: for enrichments $e,e'$, $\mu_{\mathrm{hist}}(e)=\mu_{\mathrm{hist}}(e')$. The history carrier is equivalent to the plain path-sum carrier, and $\mu_{\mathrm{hist}}$ coincides with the earlier $1/|\mathrm{Aut}|$ measure. Gap2 measure-status flags are retracted (false); the continuum-limit residual stays open.
background
In the Seven Gaps gravity campaign, Lane 2 supplies a path-sum measure for the Recognition Science partition function. PathSumMeasure postulates the discrete-gravity symmetry factor $\mu(K)=1/|\mathrm{Aut},K|$. ExactShellGaugePreflight derives that factor from pure gauge counting, with a gauge-mass definition that never mentions $\mu$ or Aut. MeasureSubstrateBlocker proves the no-go that relabeling invariance, positivity, and normalization alone do not select a path-sum measure, and isolates uniform gauge density as a model premise.
GaugeHistoryMeasure implements the adjudicated Wave C1 design that obtains the same counting measure from a posted-history presentation (residual R5). FullTheoryLedger tracks boolean pillar benchmarks that flip only when target theorems are kernel-checked, axiom-audited, and critic-passed. This module binds those constructions into an honest status record: history enrichment is parameter-inert (forced by uniqueness of the gauge-counting solution), yet that inertness is explicitly not the continuum defect.
proof idea
Status-binding layer, not a deep new derivation. Packages carrier and measure identifications: history carrier equivalent to the plain path-sum carrier; history measure identical to the old $1/|\mathrm{Aut}|$ measure; history discharge rewritten as an application of a prior theorem. Parameter-inertness of the history measure is recorded as a theorem: uniqueness of the gauge-counting solution forces every correct derivation to be inert in the enrichment. Measure-side status Bools are set false (retraction). A separate flag records that the continuum limit remains open. A rollup closes the Gap2 package after the relevant ledger flag.
why it matters in Recognition Science
Feeds Gap2ContinuumMeasureResidualDAG, which names ordered residuals for Pillar-2 measure and continuum-limit recovery and updates the measure-half status (R1 blocker closed; R2 recorded through this binding). Also feeds Gap2MeasureStatusBindingAudit, whose axiom audit requires headline theorems inside [propext, Classical.choice, Quot.sound] and now certifies that the two measure-side status Bools are false and that the R6 witness is parameter-inert, rather than that the Bools are true.
Inside the Recognition gravity program this separates a closed, uniqueness-forced inertness fact from the still-open continuum residual, keeping FullTheoryLedger honest about what gauge counting has and has not delivered.
scope and limits
- Does not prove the continuum limit of the path-sum measure.
- Does not introduce a new measure; only binds and retracts status of existing ones.
- Does not claim history enrichment resolves the MeasureInvarianceNoGo blocker.
- Does not flip FullTheoryLedger measure flags to true; it records retraction.
- Does not address T8 dimension forcing or the eight-tick octave.