IndisputableMonolith.Gravity.SevenGaps.DynamicStructureContinuumSmearingAudit
Audit layer for dynamic structure-function continuum smearing in the Seven Gaps gravity stack. It checks that a continuum field profile q induces the structure weight G(x)=1+(q x)^2 and that the resulting weighted continuum reach still converges as in the fixed-background case. Gravity workers cite it when verifying Wave C2 R3 bookkeeping. The module is organizational: import-and-audit, not a new existence proof.
claimAudit of dynamic continuum smearing: for a continuum field profile $q$, the induced structure weight is $G(x)=1+(q x)^2$, and the weighted structure sum still tends to the continuum reach previously established for fixed backgrounds.
background
Recognition Science gravity work packages the continuum limit of discrete structure sums under weighted profiles. The banked fixed-background result (BackgroundWeightedContinuumReach / weightedStructureSum_tendsto) already shows that a static weight yields a well-defined continuum reach.
Wave C2 R3 lifts that to a dynamic setting: the structure-function profile is no longer an external fixed weight. It is induced by a continuum field profile $q$ through the same algebraic law that appears in the dynamic lattice bracket, namely $G(x)=1+(q x)^2$.
This audit module sits one layer above that construction. It does not redefine $G$ or the reach; it packages checks that the dynamic induction of $G$ from $q$ is wired consistently with the fixed-background continuum theorems it extends.
proof idea
Definition and audit module, not a single theorem proof. It imports DynamicStructureContinuumSmearing and organizes verification that the $q$-induced weight $G(x)=1+(q x)^2$ plugs into the existing weighted continuum-reach machinery without breaking the tendsto statement. Expect thin wrappers, type-class or Prop audits, and re-exports rather than a long tactic script.
why it matters in Recognition Science
Closes the bookkeeping gap between fixed-background continuum smearing and the dynamic lattice bracket used in the Seven Gaps gravity program. Downstream gravity arguments that need a continuum limit for structure sums under a live field profile $q$ depend on this audit having a clean status. It is the Wave C2 R3 checkpoint: same $G$ law as the dynamic bracket, same continuum reach as the banked static case. No further parent theorems are listed in the graph yet (used_by is empty), so its role is presently as a verified intermediate in the gravity continuum stack.
scope and limits
- Does not prove a new continuum-reach theorem from scratch.
- Does not derive $G(x)=1+(q x)^2$ from first principles; it audits that law as given.
- Does not address discrete lattice dynamics beyond the continuum smearing interface.
- Does not fix numerical constants ($c$, $\hbar$, $G_N$, $\alpha$) or mass-ladder claims.
- Does not supply downstream consumers; the use graph is currently empty.