robustness_of_D3_signature
plain-language theorem explainer
The declaration asserts that the D=3 signature remains stable under the robustness hypothesis from the draft paper. Researchers tracing dimensional uniqueness in the Recognition Science forcing chain would cite this when confirming T8. The proof is a direct term reduction to the trivial proposition.
Claim. Assuming the robustness hypothesis for the three-dimensional signature holds, the statement is true.
background
The module mirrors theorem statements from Draft_v1.tex and supplies hypothesis interfaces for external mathematics such as Alexander duality. RobustnessHypothesis is defined as the placeholder proposition True, standing in for the paper proposition on robustness of the D=3 signature pending formalization of perturbation theory and continuity arguments. Upstream, SphereAdmitsCircleLinking states that the D-sphere admits nontrivial linking of disjoint embedded circles, with the linking number nonzero precisely when the reduced cohomology group is nontrivial via Alexander duality (Hatcher Thm 3.44). Additional dependencies include the period abbreviation T from Breath1024 and the required structure from DomainBootstrap.
proof idea
The proof is a one-line term that applies trivial to discharge the goal under the supplied hypothesis.
why it matters
This theorem supplies the certified surface for the paper proposition on robustness of the D=3 signature. It sits at the T8 step of the forcing chain where three spatial dimensions are forced. The hypothesis remains a placeholder until perturbation theory is added, so the result currently functions as scaffolding rather than a closed proof. No downstream uses are recorded.
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