matrixNeumannStub
plain-language theorem explainer
This definition supplies a placeholder instance of MatrixNeumannFacts that asserts a trivial numerical bound on higher-order terms for small metric perturbations in matrix Neumann problems. Researchers developing linearized gravity or gauge-theory fixtures would cite it to bypass unresolved estimates during early integration. The proof reduces to introducing the parameters and verifying the inequality |0| ≤ 16 × 0.1² by norm_num followed by simpa.
Claim. The definition provides an instance of the MatrixNeumannFacts structure in which, for a background metric perturbation $g_0$, small parameter $h$, and coordinates $x,μ,ν$, the higher-order correction terms satisfy $|0| ≤ 16 × (0.1)^2$.
background
The Relativity.NewFixtures module supplies stub instances for hypothesis classes that replace sorries while keeping them outside production namespaces to preserve a clear trust boundary. MatrixNeumannFacts encodes a bound on higher-order terms appearing in matrix formulations of Neumann boundary-value problems that arise in gauge and curvature contexts. The sole upstream dependency is the has class, which states that a mineral exhibits a characteristic spectral peak at frequency $ω_k = ω_0 · φ^k$ and ranks seven classes by their rung index k while bounding the discrimination floor.
proof idea
The implementation is a one-line wrapper that introduces the parameters g0, h, h_small, x, μ, ν, asserts the numerical inequality |(0 : ℝ)| ≤ 16 × (0.1 : ℝ)^2 by norm_num, and closes the goal with simpa.
why it matters
The stub enables the suite of relativity fixtures (gaugeFactsStub, curvatureFactsStub, linearizedPDEStub, etc.) to compile without sorries while the full bounds are developed. It occupies a temporary slot in the progression toward phi-based constants and the eight-tick octave, with the trivial bound intended to be discharged once a proper higher-terms estimate is available. The module doc-comment explicitly positions such fixtures as non-production scaffolding.
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