A Robinson counterexample to ideal-only tangency certificates

The classical Robinson sextic is globally nonnegative, but adding any nonnegative constant does not make it a finite sum of real polynomial squares modulo even the full ideal of polynomials vanishing on its real tangency variety. This refutes both the exact ordinary-radical certificate and the every-positive-epsilon original-ideal certificate proposed in the unrestricted tangency-minor formulation of Schweighofer's 2007 question. The same zero-line and coordinate-axis obstruction refutes the separate-cross-product reading printed in the report. Arbitrarily many summands of arbitrary degree are allowed. The attained example is within the unrestricted question; a separate nonattaining diagnostic concerns only the literal-product reading and uses a constant shift of the standard example in Schweighofer (2006), Section 1.6, equation (6). The standard sphere-minimization mechanism retains its attribution to Laurent's updated manuscript dated 6 February 2010, Section 7.2.3, Lemma 7.21, manuscript pages 117-118 (https://homepages.cwi.nl/~monique/files/moment-ima-update-new.pdf). The earlier 2009 published chapter has a different Lemma 7.21; its DOI is bibliographic context, not the tangency locator. Robinson's form and classical zero-set ingredients retain their attribution. The identical ten-zero cubic obstruction is explicitly credited to Reznick (2000), Section 4(b), printed page 259, authenticated in the author-hosted publisher reprint. Complete 2008 and 2009 Ha-Pham article texts were not obtained; truncated-certificate comparisons rely on later primary statements and the access gaps remain disclosed. The 66-record citation graph is a metadata screen with marked primary-text follow-ups. No author-approved formula correction, first bibliographic priority or continued open status through 2026 is asserted. This unrefereed research note is accompanied by its unchanged historical candidate, reproducible exact-algebra checks, fresh independent adversarial proof/computational/source reviews, and a bounded priority audit. AI tools were used extensively in development, verification, adversarial review and writing. Independent AI-assisted review is not independent human or journal peer review; the note has received neither. Finite controls supplement the universal mathematical proof and are not formal proof-assistant certification or numerical SOS-degree-cutoff evidence.