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def definition def or abbrev moderate

matrixBridgeFactsStub

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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

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