matrixBridgeFactsStub
This declaration defines a noncomputable stub instance of MatrixBridgeFacts supplying trivial witnesses for its two bound fields. It is cited by developers maintaining the Relativity.NewFixtures module while replacing sorries with explicit hypothesis interfaces. The proof shape is a direct field-by-field construction using exact and trivial tactics.
claimDefine a noncomputable instance of the structure MatrixBridgeFacts such that, for control parameter $ctrl$ and error bound $ε$, the weak-field bound holds by direct appeal to the hypothesis $hbound$ and the derivative bound holds by the trivial tactic.
background
The module Relativity.NewFixtures supplies stub instances for hypothesis classes introduced to replace sorries. These fixtures sit outside production namespaces to keep the trust boundary explicit between verified theorems and temporary scaffolding. MatrixBridgeFacts encodes two concrete bounds on weak fields and their derivatives in a matrix formulation of relativistic equations.
proof idea
The definition is a direct field assignment. The weak_field_bound field is witnessed by an intro-exact sequence that returns the supplied hypothesis unchanged. The derivative_bound field is witnessed by the trivial tactic, which discharges the goal without further reduction.
why it matters in Recognition Science
The stub closes a local gap in the Relativity.NewFixtures module, allowing the instance declaration to be used immediately while the actual bounds remain to be proved. It belongs to the scaffolding layer that keeps hypothesis interfaces separate from core Recognition Science results such as the J-uniqueness and phi-ladder constructions. No downstream theorems yet depend on it.
scope and limits
- Does not derive the weak-field or derivative bounds from the J-cost or Recognition Composition Law.
- Does not supply a constructive or computable witness for either bound.
- Does not interact with the eight-tick octave, spatial dimension forcing, or alpha-band constants.
- Does not replace any theorem in the UnifiedForcingChain or mass-ladder development.
formal statement (Lean)
37noncomputable def matrixBridgeFactsStub : MatrixBridgeFacts where
38 weak_field_bound := by intro ctrl ε hbound hε hε'; exact hbound
proof body
Definition body.
39 derivative_bound := by intro ctrl ε hbound hε; trivial
40
41instance : MatrixBridgeFacts := matrixBridgeFactsStub
42