A first-order obstruction to Habiro's rank interpolation

The ordinary integral rank completion printed in Ohtsuki's Conjecture7.30 cannot interpolate the standard unified sl_n invariants of any integral homology sphere with nonzero Casson invariant. A representative in one finite interpolation quotient forces the first q minus1 coefficient to be affine in matrix size n. The classical coefficient formula n(n squared minus1) times the Casson invariant is cubic. For the orientation of the Poincare sphere obtained by minus1 surgery on the left-handed trefoil, sizes1,2,3 give0, minus6, minus24, whose second difference is minus12. This supplies a decisive negative answer to the literal displayed conjecture. It gives no existence criterion at Casson zero and proposes no corrected completion. The coefficient formula, theta/Casson and free-energy mechanisms are credited to Le2000, Le-Murakami-Ohtsuki1998 and Garoufalidis-Le-Marino2008; the fixed-Lie unification and Taylor identification are credited to Habiro-Le2016. The ordinary coefficient ring, common type-A parameter q=v squared=exp(h), matrix-size convention and assigned size1 invariant are explicit. Enlarged modern knot-color Newton rings are distinguished from the printed homology-sphere interpolation. No claim of novelty, first priority, present openness or exhaustive absence of earlier resolutions is made. Two independent bounded primary-source priority audits retain inaccessible bodies, selected-reading and citation-coverage gaps. Ohtsuki's volume year2002 and actual publisher release1June2004 are distinguished. The deposit contains a concise three-page research note and source-free verification archive with editable LaTeX, all33 original PR952 files unchanged, five independent mathematical/priority family reports, exact arithmetic checks and a separately scoped strict portable finite verification profile. Source-free means third-party source bodies, extracts, images, raw private corpus and credentials are excluded; authored code is included. The new finite stages were reproduced on macOS CPython3.14.6 under isolated normal and optimized execution. The original source-dependent Linux/bubblewrap whole-filesystem read-only replay was not reproduced on this host. Cited topology theorems remain mathematical inputs. Hashes and finite identities do not certify topology, historical priority or a hostile-host sandbox. The immutable submitted PR declares1/5; historical native per-turn count and total were not authenticated, and this audit adds zero substantive author proof-search responses. Extensive AI tools assisted solving, source research, computation, writing and adversarial review. This preprint is unrefereed; no independent human peer review, journal acceptance or formal proof-assistant certification is asserted.