Gravity Seven Gaps Full Theory Ledger Gap2 Metric Carrier Blocker Certified

The metric carrier blocker

The metric carrier blocker is a theorem in the Recognition Science framework's machine-checked library of formal theorems. It establishes a precise negative result: the map that forgets the metric decoration on a discrete complex is not injective. In plain terms, two different discrete geometries can be sent to the same coarse-grained continuum class, so the continuum limit cannot be defined by throwing away the metric information. The theorem is stated for a specific carrier, the MetricDecoratedComplex at a fixed refinement level, and it is proved from the definition of the map itself.

This result matters because it closes a loophole in the framework's own benchmark for a full quantum gravity theory. The benchmark requires a well-defined quantum amplitude with a derived measure and a path-sum continuum limit under metric mesh refinement. A naive approach would be to declare the continuum limit achieved by a complexity cutoff or by forgetting the metric data. The blocker theorem shows that the latter is not a valid continuum limit, because the map from decorated complexes to triangulation classes is not injective. The framework's own ledger records this as a certified blocker, meaning the theorem is kernel-checked and axiom-audited.

In Recognition Science, the result is one of several blockers that keep the benchmark honest. The full-theory ledger is a record of boolean flags, one per pillar benchmark, where a flag flips to true only when its target theorem is kernel-checked. The metric carrier blocker is a theorem that prevents a false positive: it shows that a certain kind of reduction, forgetting the metric, cannot be the continuum limit. The framework's own criterion was repaired on 2026-07-26 to require that the proved statement is the promised one, and this blocker is part of that repair. The theorem itself is a statement about the non-injectivity of a specific map, and it is a proved theorem, not a hypothesis.

The consequence is that the framework's own benchmark for a full theory remains open. The blocker does not prove that a continuum limit is impossible; it proves that one particular route is not a continuum limit. The framework's ledger records that pillars 1 and 2 are closed, but pillar 3, the discriminating prediction, remains open. The metric carrier blocker is a negative result that keeps the benchmark honest, and it is a theorem, not a prediction.

/-- **PILLAR 2 METRIC-CARRIER BLOCKER (THEOREM, P2.5).** The current
combinatorial quotient carrier forgets metric data: the forgetful map from
metric-decorated simplicial complexes is not injective (one tetrahedron
carries two admissible metrics with different edge-length and Cayley-Menger
observables).  A mesh-refinement continuum limit needs a metric-refined
carrier, which remains OPEN. -/
theorem gap2_metric_carrier_blocker_certified :
    ¬ Function.Injective
      (MetricRefinementCarrierBlocker.MetricDecoratedComplex.toClass :
        MetricRefinementCarrierBlocker.MetricDecoratedComplex 6 →
          PathSumMeasure.TriangulationClass 6) :=
  MetricRefinementCarrierBlocker.metricForget_not_injective

/-- **PILLAR 2 METRIC-CARRIER BLOCKER (THEOREM, P2.5).** The current
combinatorial quotient carrier forgets metric data: the forgetful map from
metric-decorated simplicial complexes is not injective (one tetrahedron
carries two admissible metrics with different edge-length and Cayley-Menger
observables).  A mesh-refinement continuum limit needs a metric-refined
carrier, which remains OPEN. -/
theorem gap2_metric_carrier_blocker_certified :
    ¬ Function.Injective
      (MetricRefinementCarrierBlocker.MetricDecoratedComplex.toClass :
        MetricRefinementCarrierBlocker.MetricDecoratedComplex 6 →
          PathSumMeasure.TriangulationClass 6) :=
  MetricRefinementCarrierBlocker.metricForget_not_injective

/-- **PILLAR 2 METRIC-CARRIER BLOCKER (THEOREM, P2.5).** The current
combinatorial quotient carrier forgets metric data: the forgetful map from
metric-decorated simplicial complexes is not injective (one tetrahedron
carries two admissible metrics with different edge-length and Cayley-Menger
observables).  A mesh-refinement continuum limit needs a metric-refined
carrier, which remains OPEN. -/
theorem gap2_metric_carrier_blocker_certified :
    ¬ Function.Injective
      (MetricRefinementCarrierBlocker.MetricDecoratedComplex.toClass :
        MetricRefinementCarrierBlocker.MetricDecoratedComplex 6 →
          PathSumMeasure.TriangulationClass 6) :=
  MetricRefinementCarrierBlocker.metricForget_not_injective

What this page does not claim

The blocker does not prove that a continuum limit is impossible, only that forgetting the metric is not one. The theorem does not establish any property of the framework's own cost function or the golden ratio. The result does not say anything about the physical correctness of the framework's approach to quantum gravity.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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