Pith. sign in
module module high

IndisputableMonolith.Gravity.SevenGaps.MeasureSubstrateBlocker

show as:
view Lean formalization →

Isolates the exact extra principle behind the gauge-counting path-sum measure: class mass times gauge-witness volume equals labeled orbit size. Cited by anyone reconciling the Lane D1 no-go (invariance alone fails) with the gauge-preflight derivation of mu = 1/|Aut|. Packages the principle, shows uniform class mass fails it, and emits a substrate-measure blocker certificate for the full-theory ledger.

claimThe gauge-counting principle asserts that for each combinatorial class $K$, class mass $m(K)$ times gauge-witness volume equals labeled-orbit size. Gauge-orbit mass satisfies the principle; uniform class mass does not. The module records a substrate-measure blocker certificate packaging that obstruction for the Seven Gaps ledger.

background

In the Seven Gaps gravity campaign, the scoped path-sum measure is the discrete-gravity symmetry factor $\mu(K)=1/|\mathrm{Aut},K|$. The module ExactShellGaugePreflight derives that factor from pure gauge counting, with a gauge-mass definition that never mentions $\mu$ or $\mathrm{Aut}$. MeasureInvarianceNoGo kills the earlier claim that relabeling invariance plus positivity and normalization alone force $\mu=1/|\mathrm{Aut}|$, supplying explicit counter-witnesses.

This module sits between those two results. It names the missing substrate input used by the gauge-counting derivation: class mass times gauge-witness volume equals labeled orbit size. That equality is the exact extra principle beyond bare invariance.

Local content includes the principle itself, the gauge-orbit mass that satisfies it, equivalences tying the principle to placing $\mu$ on representatives, the uniform class-mass alternative that fails, and the blocker certificate consumed downstream.

proof idea

Principle-plus-witness package, not a single deep proof. Defines the gauge-counting principle as the equality of class mass times gauge-witness volume with labeled-orbit size. Shows gauge-orbit mass satisfies the principle, and that the principle is equivalent both to equating the mass with gauge-orbit mass and to placing $\mu$ on representatives in the expected way. Separately exhibits uniform class mass as a counter-model that fails the principle. Packages the obstruction as the substrate-measure blocker certificate for ledger import.

why it matters in Recognition Science

Feeds FullTheoryLedger, the Phase 0c machine-checked status record of the full quantum-gravity theory campaign. That ledger flips a boolean per pillar benchmark only when the target is kernel-checked, axiom-audited, and critic-passed; this module's blocker certificate is one such status input.

It closes the conceptual gap between MeasureInvarianceNoGo (invariance is not enough) and ExactShellGaugePreflight (gauge counting derives $1/|\mathrm{Aut}|$) by naming the precise extra principle the derivation uses. Within Recognition Science gravity, this is part of the Seven Gaps program that disciplines which path-sum measure assumptions are forced versus postulated on the discrete side.

scope and limits

used by (1)

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

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (7)