Pith. sign in
module module moderate

IndisputableMonolith.Gravity.Analysis.OrderSensitiveCoefficientForce4D

show as:
view Lean formalization →

Gate module for 4D order-sensitive gravity: coefficient forcing may be asserted only after continuum promotion of the residual is earned. It packages a license predicate, an empirical gate, and a negative theorem blocking forced coefficients while the continuum step is unearned. Analysts working Campaign G4/G5 cite it to keep discrete residual claims from jumping to continuum coefficients. The structure is definitional predicates plus one blocking lemma, not a long derivation.

claimCoefficient forcing in the 4D order-sensitive residual setting is licensed only when continuum promotion has been earned. Write $L$ for the license predicate, $G$ for the empirical gate, and $F$ for a forced-coefficient claim. The module asserts that $F$ is inadmissible whenever continuum promotion remains unearned, i.e. $\neg L \Rightarrow \neg F$, together with equality lemmas identifying $L$ and $G$ with their defining propositions.

background

Recognition Science gravity analysis promotes discrete, order-sensitive residuals on metric edge images to continuum statements under a shape-regular refinement family. The upstream module ContinuumOrderSensitiveResidual4D (Campaign G4/G5) replaces finite Boolean non-membership in the metric edge image by a normalized-separation trichotomy. That continuum step is a prerequisite, not an automatic rewrite.

This module sits immediately downstream of that promotion. Its local contract is licensing: one may speak of a forced continuum coefficient only after the residual has earned continuum status. Sibling names mark the pieces: a license predicate and its characterizing equality, an empirical gate and its equality, a forced-coefficient type or proposition, and a negative result that no forced coefficient holds while the continuum step is unearned.

Notation is RS-native gravity analysis in 4D (three spatial dimensions plus the discrete tick structure). No new physical constants are introduced here; the module only polices the logical order of claims.

proof idea

Definition-and-gate module rather than a long proof development. License and empirical-gate objects are introduced as propositions (or defs of Prop) with equality lemmas pinning them to their intended meaning. The substantive claim is the blocking result: while continuum promotion remains unearned, no forced-coefficient assertion is admitted. That lemma is the enforcement edge tying this file to ContinuumOrderSensitiveResidual4D. Expect short term-mode or one-line wrappers once the predicates are unfolded, not a multi-step analytic argument inside this file.

why it matters in Recognition Science

Without this gate, Campaign G4/G5 continuum promotion could be skipped and discrete order-sensitive residuals treated as if they already forced continuum coefficients. The module encodes the discipline that coefficient forcing is licensed only when continuum promotion is earned, matching the module doc-comment exactly.

No downstream consumers are recorded in the current graph (used_by is empty), so its role is prophylactic: it is the named place where unearned forcing is refused. In the broader gravity stack it protects later coefficient and phenomenology claims from resting on a missing continuum step. It does not itself derive $G$, $\phi$-ladder masses, or the T0–T8 forcing chain; it only sequences residual analysis before coefficient claims.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (6)