RobustnessHypothesis
plain-language theorem explainer
RobustnessHypothesis serves as a placeholder assumption that the D=3 signature remains stable under perturbations in the Recognition framework. A paper author working on DraftV1.tex would cite it to justify Alexander duality applications for spatial embeddings. The declaration is a one-line assignment to the trivial proposition True, pending formalization via perturbation theory or implicit function theorem continuity arguments.
Claim. Assume that the three-dimensional signature forced by the eight-tick octave is stable under small perturbations in the J-cost functional.
background
The module mirrors theorem statements from Draft_v1.tex and supplies hypothesis interfaces for results that rely on external mathematics such as Alexander duality for complements of embeddings. This approach avoids global axioms and keeps the certified surface honest. RobustnessHypothesis is one such interface for the unformalized stability claim on the D=3 signature. No upstream results are referenced.
proof idea
The declaration is a one-line definition that sets the hypothesis directly to the trivial proposition True.
why it matters
This hypothesis interface enables the downstream theorem robustness_of_D3_signature, which states that the (T) setup assumptions required for Alexander duality are satisfied in this dimension and delegates to the cohomology-based SphereAdmitsCircleLinking. It fills the placeholder for the paper proposition on robustness of the D=3 signature, linking to the T8 step that forces three spatial dimensions.
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