IndisputableMonolith.Gravity.SevenGaps.Gap2MeasureDerivationHostileProbe
Hostile probe module checking that Gap 2's closing GaugeCountingPrinciple is definitionally identical to the substrate blocker's, not a parallel copy. It also records that the Gibbs class-mass equals the orbit measure only after the load-bearing composition, not by reflexivity, and that wrong labeled weights fail gauge counting. Gravity auditors cite it when auditing whether the measure-derivation assembly actually lands on mu. Structure is a battery of definitional and counterexample lemmas against the two imported assemblies.
claimThe Gap-2 closing form of the gauge-counting principle is definitionally the same proposition as the measure-substrate blocker. The Gibbs class mass equals the orbit measure $\mu = 1/|\mathrm{Aut}|$ only through the assembled composition (C4 Jacobian, C17 fugacity elimination, C16 LIFO), not by reflexivity of definitions. Among invariant weights, only the Gibbs weight satisfies gauge counting; mis-labeled weights fail it.
background
Gap 2 (A27) is the typed obligation to derive the path-sum measure on the gravity side. The upstream assembly module builds GaugeCountingPrinciple for the class mass of the Gibbs weight from the C4 erasure Jacobian and C17 fugacity elimination, naming the C16 LIFO process as the process-side discrimination premise, without importing the full theory ledger.
The companion no-go module kills the earlier claim that relabeling invariance plus positivity and normalization alone force $\mu = 1/|\mathrm{Aut}|$ on the scoped path sum: invariance is necessary but not sufficient. The Gibbs weight is the Boltzmann-type weight on orbit classes; class mass is the summed weight of a gauge orbit; gauge counting is the principle that the physical measure counts each orbit once with the correct symmetry factor.
This probe module sits between those two: it does not re-derive the measure, it stress-tests definitional identity and discrimination claims so the closing certificate cannot silently point at a different proposition than the blocker.
proof idea
Not a single theorem: a hostile battery. One family of lemmas asserts definitional equality (or iff) between the closing gauge-counting principle and the blocker's certificate, and that the closing lands on $\mu$ with no extra premises. Another family shows the Gibbs class-mass identity is not rfl, records orbit-cardinality facts for two-point configurations, and exhibits wrong labeled weights that fail gauge counting. A third strand isolates that only the Gibbs weight among invariant candidates survives, and that the composition has the expected load-bearing shape. Imports supply the assembly and the invariance no-go; the probe only compares and witnesses.
why it matters in Recognition Science
In the Seven Gaps gravity lane, flag-8 style obligations are easy to close with a look-alike proposition. This module exists so the Gap-2 measure derivation cannot claim success unless its closing GaugeCountingPrinciple is literally the substrate blocker's. That ties the assembly (C4/C17/C16 route to Gibbs class mass) to the D1 no-go: invariance alone is dead, and the constructive path must hit $\mu$ for the right reason.
No downstream modules currently import it (used_by is empty); it is an audit and certificate layer for the Gap-2 assembly rather than a lemma in a longer proof chain. Framework-wise it protects the gravity measure step that later feeds RS-native constants and the phi-ladder mass story, by keeping the path-sum measure honest about gauge orbits.
scope and limits
- Does not flip the Gap-2 flag or finish the full measure-derivation obligation.
- Does not re-prove the C4 Jacobian, C17 fugacity, or C16 LIFO steps.
- Does not claim invariance alone determines mu; that route is already killed upstream.
- Does not import or constrain FullTheoryLedger.
- Does not supply new downstream gravity dynamics; currently unused by other modules.
depends on (2)
declarations in this module (13)
-
theorem
gcp_closing_is_blocker_gcp -
theorem
gibbsWeight_def_no_aut -
theorem
classMass_gibbs_eq_mu_is_not_rfl -
theorem
classMass_one_eq_orbit -
theorem
twoPoint_orbitCard -
theorem
wrong_labeled_weight_fails_gaugeCounting -
theorem
only_gibbs_among_invariant -
theorem
closing_has_no_premises_arg -
theorem
composition_load_bearing_shape -
theorem
closing_via_blocker_iff -
theorem
closing_lands_on_mu -
theorem
blocker_certificate_available -
theorem
flag_moved