module module moderate

`IndisputableMonolith.Gravity.SevenGaps.GaugeCountingInevitableReasons`

Status table for the Gap-2 reason census on gauge counting. It records which candidate premises force, underdetermine, or block the Gauge Counting Principle (inverse gauge-volume mass on labeled orbits). Gravity and QG workers closing the measure obligation cite it to see which routes are dead. The module is a finite table of reason statuses backed by short supporting lemmas.

claimA finite census table of reasons $R_{01}$–$R_{11}$ whose entries record the logical status of each candidate path toward the Gauge Counting Principle: that the path-sum class mass equals the inverse order of the sector relabeling group (equivalently, inverse gauge volume on labeled orbits), under recognition-ledger structure rather than an external model premise.

background

Gap 2 in the SevenGaps gravity stack asks whether recognition-ledger structure forces the Gauge Counting Principle: class mass $\mu(K)=1/|\mathrm{Aut},K|$, equivalently inverse gauge volume on labeled orbit copies. Upstream modules reduce residual freedom of the path-sum measure to three positive constants (size-blind weight times one fugacity per index type) and isolate unit-sector fugacity as the remaining hypothesis.

Candidate routes include reading the measure off site symmetry of the ledger, imposing insertion stationarity or a gluing law, pinning counts or weights by hand, and dual-entry signed-source enrichment in 4D. Several of those shapes are already no-gos: site symmetry cannot supply gauge counting; uniform measures fail; pinned counts and weights are complex rather than forced.

This module does not re-derive those results. It indexes them as a reason census with an explicit status table so the open measure obligation can be audited without reopening closed branches.

proof idea

Definition-and-status module, not a single theorem proof. It introduces a ReasonStatus classification and a finite reasonTable whose length is checked, then attaches one short lemma per census row (R01 invariance underdetermines; R02 equivalence of GCP with gauge-orbit mass; R03 that gauge-orbit mass satisfies the target; R04 uniform fails; R05–R06 pinned count/weights are complex; R07 unique Gibbs form of invariant enrichment; R09 existence of label-asymmetric data; R11 orbit–stabilizer bookkeeping). Each row is a thin wrapper or citation into the imported Gap2 and enrichment modules rather than a fresh derivation.

why it matters in Recognition Science

The SevenGaps program needs a load-bearing recognition-substrate premise for GaugeCountingPrinciple, or a scoped no-go naming what is missing. This census is the audit surface for that obligation: it aggregates the Gap2 posting/gluing, gauge-volume, insertion-dynamics, ledger-site-blindness, size-blindness, and dual-entry enrichment lines into one status table.

Downstream consumers (none linked yet in the graph) would use the table to avoid re-proving dead routes and to focus on residual open reasons. In framework terms it sits under the gravity measure stack that must eventually match RS-native constants and the forced $D=3$, eight-tick structure, without smuggling external gauge-fixing axioms. It closes bookkeeping, not the Gap-2 theorem itself.

scope and limits

Does not prove the Gauge Counting Principle from recognition axioms alone.
Does not discharge unit-sector fugacity or close Gap 2.
Does not claim every conceivable premise shape is enumerated beyond the listed reasons.
Does not supply numerical gravity predictions or mass-ladder fits.
Does not refute enrichment routes outside the imported dual-entry and Gap2 modules.

depends on (10)

Lean names referenced from this declaration's body.

IndisputableMonolith.Gravity.Analysis.RecognitionDualEntryEnrichment4D module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2FugacityPostingGluing module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2GaugeVolume module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2GluingLawStationarity module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2LabelInsertionDynamics module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2LedgerSiteBlindness module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2PostingLayerFloor module_import
IndisputableMonolith.Gravity.SevenGaps.Gap2SizeBlindnessReach module_import
IndisputableMonolith.Gravity.SevenGaps.MeasureInvarianceNoGo module_import
IndisputableMonolith.Gravity.SevenGaps.MeasureSubstrateBlocker module_import

declarations in this module (78)

structure ReasonStatus L101
def reasonTable L107
theorem reasonTable_length L127
theorem R01_invariance_underdetermines L133
theorem R02_gcp_iff_gaugeOrbitMass L139
theorem R03_gaugeOrbitMass_satisfies L144
theorem R04_uniform_fails L149
theorem R05_pinned_count_is_complex L155
theorem R06_pinned_weights_are_complex L160
theorem R09_label_asymmetric_exists L167
theorem R11_orbit_stabilizer L171
theorem R07_invariant_enrichment_unique_gibbs L182
theorem R08_equivariant_cost_no_factor L190
theorem R10_indifference_family_underdetermines L202
theorem R10_gcp_iff_unit_fugacity L211
structure CorrectedFloorPlan L219
def correctedFloorPlans L226
theorem correctedFloorPlans_length L248
structure CorrectedMeasurePremise L255
def AssumedRequired L270
def assumedTargetStatus L277
def R01 L281
def R02 L286
def R03 L290
def R04 L294
def R05 L299
def R06 L303
def R07 L311
def R08 L317
def R09 L323
def R10 L325
def R11 L330
def R12 L336
def R13 L344
def R14 L354
def R15 L363
def R16 L369
def R17 L374
def R18 L383
theorem R01_reason L387
theorem R02_reason L391
theorem R03_reason L395
theorem R04_reason L399
theorem R05_reason L403
theorem R06_reason L407
theorem R07_reason L411
theorem R08_reason L414
theorem R09_reason L418
theorem R10_reason L421
theorem R11_reason L425
theorem R12_refuted L429
theorem R13_refuted L432
theorem R14_refuted L436
theorem R15_refuted L439
theorem R16_refuted L442
theorem R17_refuted L446
theorem R18_rebooking_preserves_product L483
def RebookingInvariant L507
theorem R18_rebooking_invariant_admits_nonunit L516
theorem R18_no_rebooking_invariant_selector L534
def ProductVisible L553
theorem R18_product_visible_is_rebooking_invariant L561
theorem R18_no_product_visible_selector L580
def R18Wall L593
theorem R18_refuted L607
theorem R18_vacuity_guard L618
def R18Status L622
def firstAttackBlock L626
theorem firstAttackBlock_length L629
def secondAttackBlock L640
theorem secondAttackBlock_length L643
def thirdAttackBlock L662
theorem thirdAttackBlock_length L664
def nextAttackBlock L668
theorem nextAttackBlock_length L670
theorem R18_block_certified L675
def correctedFloorPlansStub L684
theorem correctedFloorPlansStub_length L687