IndisputableMonolith.Gravity.Analysis.RecognitionMeshGeometricDeficit4DAudit
Audit companion to the 4D recognition-mesh geometric-deficit identification from QG Wave B residual R1. It records the DAG-proposition versus Lean-shape divergence for the mesh deficit (no x-ratio form) and checks that the residual is closed as stated. Gravity and QG auditors cite it when reconciling the residual DAG draft with the formal development. Structure is documentary and import-driven rather than a new proof stack.
claimAudit record for the 4D recognition-mesh geometric deficit: the mesh deficit is identified in the form without an $x$-ratio factor, matching Wave B residual R1 ($\mathtt{TypedResidual\_mesh\_geometricDeficit\_identified}$), with explicit notes on any divergence between the residual DAG proposition and the Lean encoding.
background
Recognition Science gravity analysis treats spacetime recognition on a discrete mesh whose local cost is governed by the J-cost $J(x)=(x+x^{-1})/2-1$. Geometric deficit on that mesh is the mismatch between combinatorial mesh geometry and the continuum curvature it is meant to reproduce; Wave B of the QG completion plan isolates residual R1 as the claim that this deficit is identified without an auxiliary $x$-ratio factor.
The upstream module RecognitionMeshGeometricDeficit4D is the constructive attack on that residual (plan file QG_WaveB_Gap1_Residual_DAG_Draft_20260721). Its module doc states the goal as "mesh geometricDeficit identified (no xRatio)" and already flags a recorded divergence between the DAG proposition and the Lean shape. This audit module sits one import above that work: it does not redefine the deficit, it packages the reconciliation checklist for reviewers.
proof idea
Definition and documentation module, not a theorem stack. It imports the 4D geometric-deficit development and organizes audit notes around the residual R1 claim: identification of the mesh geometric deficit without an $x$-ratio. Argument structure is comparative (DAG prop versus Lean encoding) rather than tactic-mode proof. No independent lemmas are discharged here; closure is inherited from the imported identification work.
why it matters in Recognition Science
Closes the bookkeeping gap on Wave B residual R1 in the QG full-completion session. Downstream use is empty in the current graph, so the module is a leaf audit surface: it exists so that the residual DAG draft and the Lean development stay aligned when later gravity or quantum-gravity theorems cite the 4D mesh deficit. In the broader RS forcing picture it supports the geometric side of recognition gravity (mesh cost, deficit, continuum limit) without touching T5–T8 forcing steps directly. Referees checking residual closure should start here before trusting citations of the identified deficit.
scope and limits
- Does not prove the mesh geometric deficit identity; that lives in the imported 4D module.
- Does not introduce an x-ratio form of the deficit or compare numerically to GR curvature scalars.
- Does not discharge other Wave B residuals beyond R1 bookkeeping.
- Does not claim continuum Einstein equations or fix G, c, or phi-ladder mass formulae.
- Does not supply used-by theorems; the current dependency graph treats this as a leaf audit.