canonicalDefectSampledFamily_excess_bounded
plain-language theorem explainer
The theorem shows that for any defect sensor with nonzero charge the canonical sampled family has annular excess bounded by some constant K independent of refinement depth N. Recognition Science workers refining Axiom 2 cite it to separate the topological floor from the regular error term in the zeta-defect construction. The proof is a direct one-line application of the ring-regular error bound theorem to the canonical family.
Claim. Let $s$ be a defect sensor with nonzero charge. Then there exists $K$ such that for every natural number $N$ the annular excess of the mesh at depth $N$ in the canonical sampled family attached to $s$ satisfies annularExcess(mesh $N$) $≤ K$.
background
The Defect Sampled Trace module constructs realized annular meshes from phase sampling of a hypothetical zeta defect. Central definitions are DefectSampledFamily (a full refinement family of realized meshes) and canonicalDefectSampledFamily (the specific family chosen for a given sensor). RealizedDefectAnnularExcessBounded asserts that after subtracting the topological floor the remaining regular-part error stays uniformly bounded across all depths $N$ (see the sibling definition at line 125).
proof idea
The proof is a one-line wrapper that applies realizedDefectAnnularExcessBounded_of_ringRegularErrorBound to the canonical family, supplying the ring-regular error bound already established for that family by canonicalDefectSampledFamily_ringRegularErrorBound.
why it matters
This supplies the bounded-excess half of the refined Axiom 2 statement in the module, ensuring the regular remainder requires only analytic control while total cost diverges with nonzero charge. It forms the key bridge to annular coercivity: any uniform upper bound on the sampled family would contradict the charge-driven unboundedness. The result sits inside the Recognition Science chain after elimination of Axiom 1 and uses the J-cost and multiplicative-recognizer cost structures from upstream.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.