Maximal norm discontinuity for a bounded-region continuum fermion interaction

We give a self-contained explicit counterexample for the existential unregularized bounded-region fermion question on printed page 371 of Oberwolfach Report 7/2025, with pointwise operator-norm topology distinguished from strong-operator topology on page 365. In dimension three, one fixed smooth nonnegative radial compactly supported pair potential and one fixed interaction ball give a fixed smooth normalized annihilation mode whose Heisenberg norm differences tend to the maximal value 2. Explicit packed finite-particle Slaters and times pi/(2N+1-kappa) witness the same vector-norm limit, a stronger vector asymptotic, and changing normal-state values tending to 4. Both diagonal-density and normal-ordered interactions are covered with ordered-pair coefficient 1 and no ultraviolet smearing. A fixed smooth-cutoff commutator, Slater second moment and two-sector Duhamel comparison give error O(N^(-1/6)+N^(-1/3)). The kinetic energy acts on all of R³. Continuity on every fixed vector and in every fixed normal state remains valid. Siebert's arXiv:2609.34402v1, submitted 28 September 2026 before the original 7 October candidate, supplies the earlier high-density cluster and localized phase mechanism. Its stated theorem concerns full-space difference potentials, but its proof directly adapts to this bounded symmetric cutoff kernel and yields the qualitative existential conclusion. Its Proposition 2.6 explicitly gives maximal norm 2 for the full-space constant-number reference. The present note gives an explicit free-Slater transfer to the fixed spatial cutoff. A separately checked audit-time energy bootstrap also recovers the cutoff maximal limit through the earlier localized phase mechanism. These cutoff implications are deductions made in the audit, not literal cutoff theorems attributed to the prior paper. No first solution, first quantitative refinement, historically certified novelty, or continued open status through October 2026 is claimed. The bounded primary-source priority audit records access and indexing limitations. This five-page unrefereed research note is accompanied by its identical authored PDF/LaTeX source, unchanged 26-file historical candidate and independently authored analytic, operator-algebra, computational, source/model, priority and priority-mapping audits. The fresh computational family has 2,668 exact finite predicates and 558 floating diagnostics; finite tests supplement the universal written proof, and numerical diagnostics are not rigorous interval enclosures or formal proof certificates. Historical optimized-assertion and inventory weaknesses are repaired by externally pinned closed regular-file validation and isolated nonoptimized checker execution, while all original bytes and the original 1/5 candidate count are preserved. Historical result outputs are not claimed byte-identical to current replays, and runtime source-byte checks are explicitly omitted. AI tools were used extensively in development, verification, adversarial review and writing. Independent AI-assisted review is not human or journal peer review; neither is claimed. No copied third-party source bodies are distributed. No all-potential, all-region, dimension-one/two, fixed-density/energy, thermodynamic, fixed-state-discontinuity or CAR-invariance result is asserted.