IndisputableMonolith.Gravity.SevenGaps.DynamicStructureContinuumSmearingAudit
Audit module for Wave C2 R3 dynamic structure-function continuum smearing in the Seven Gaps gravity stack. It checks that the continuum reach extends from fixed-background weighted sums to profiles induced by a continuum field q via G(x)=1+(q x)^2, matching the dynamic lattice bracket. Gravity continuum and structure-sum workers cite the audited statements. The module is organizational: import-and-review of the banked smearing development, not a new theorem engine.
claimAudit of the dynamic continuum-smearing package in which the structure-function profile is $G(x)=1+(q x)^2$ for a continuum field profile $q$, extending fixed-background weighted continuum reach ($\mathrm{BackgroundWeightedContinuumReach}$ / weighted structure-sum convergence) to the dynamic lattice law.
background
Seven Gaps gravity work builds continuum limits for structure-weighted sums that appear in effective gravitational response. An earlier banked layer treats fixed-background continuum reach: weighted structure sums converge under a static profile. Wave C2 R3 lifts that to a dynamic setting.
The upstream module induces the structure-function profile from a continuum field $q$ by the same algebraic law used on the dynamic lattice bracket, namely $G(x)=1+(q x)^2$. That keeps the continuum object aligned with the discrete dynamic structure rather than introducing a second ad hoc kernel.
This audit module sits one import above that development. It does not redefine $G$ or the reach predicates; it packages review surface for the dynamic smearing claims against the fixed-background baseline.
proof idea
Definition and audit shell, not a proof engine. It imports DynamicStructureContinuumSmearing and exposes the Wave C2 R3 dynamic extension for checklist-style review: continuum field $q$, induced $G(x)=1+(q x)^2$, and comparison to banked BackgroundWeightedContinuumReach / weightedStructureSum_tendsto. No independent tactic scripts or new lemmas are the point; the argument lives upstream.
why it matters in Recognition Science
Keeps the Seven Gaps gravity continuum path honest when structure functions become dynamic. Upstream Wave C2 R3 extends fixed-background continuum reach so the profile is induced by $q$ through the lattice bracket law $G(x)=1+(q x)^2$. Without an audit layer, that extension can drift from the banked weighted-sum convergence statements.
No downstream Lean consumers are wired yet (used_by empty). The module still matters as the named review gate before dynamic smearing is treated as load-bearing in broader gravity continuum or effective-$G$ arguments. It touches the continuum half of the discrete-to-continuum bridge for structure-weighted gravitational response, not the T0–T8 forcing chain directly.
scope and limits
- Does not prove weighted structure-sum convergence; that lives upstream.
- Does not derive $G(x)=1+(q x)^2$ from first principles; it audits use of that law.
- Does not treat fixed-background reach except as the baseline being extended.
- Does not supply downstream gravity theorems; no used_by edges yet.
- Does not address mass-ladder, alpha-band, or T5–T8 forcing claims.