The Andersen–Kashaev volume conjecture for 213 knots outside the Hoste–Thistlethwaite census

For 213 knots outside the Hoste-Thistlethwaite census we exhibit an ordered ideal triangulation of the knot complement that is FAMED and geometric; by Ben Aribi-Wong, Corollary 1.9 (arXiv:2410.10776v2: 'Conjecture 1.5 is true for all FAMED geometric triangulations'), the Andersen-Kashaev volume conjecture holds for these knots. 209 distinct complements (4 chiral mirror pairs). THE THEOREM AND THE METHOD ARE NOT OURS: the conjecture is Andersen-Kashaev's (arXiv:1109.6295), FAMED triangulations and Corollary 1.9 are Ben Aribi-Wong's, the census-wide computer proof and the search code (A. Guilloux, FAMEDexploration) are Ben Aribi-Guilloux-Wong's (arXiv:2512.17437, Theorem 3.1: all but 6 of the 42 123 hyperbolic knot complements of the HT census with at most 14 crossings and 23 tetrahedra). What is deposited are computed objects and certificates. WHY NEW CASES: none of the knots lies in that census - 153 have a proven crossing number c >= 15, 60 were checked with SnapPy's census identification on five geometric triangulations each (calibrated on 300 census knots). Our literature search to 25 September 2026 found no case beyond that census; not finding is not proof of absence. Triangulations have 8 to 54 tetrahedra, 99 with more than 23. THE CHAIN, PER KNOT: (1) FAMED - the authors' code only searched; the verdict is our independent implementation of Definition 1.1 (1)-(4), exact over Q, on exactly the deposited ordered triangulation; it rejects 15 of 15 deliberate perturbations. (2) Geometric - SnapPy verify_hyperbolicity (interval arithmetic) on that same triangulation. (3) Meridian - n1 of Lemma 4.1 computed with the meridian of the knot's own diagram: n1 = 0 for all 213; calibrated on five twist knots (Proposition 5.1) and on a deliberately shifted meridian. (4) Duplicates - overlapping verified volumes tested for isometric complements; the 4 isometric pairs are orientation-reversing with opposite Chern-Simons invariants, decided on complements built from the diagrams. KNOTS: 67 twisted torus knots T(p,q;2,s) (proven crossing number lower bounds 26 to 150), 10 odd pretzel knots, and knots from the constructive families of a sculptor's project; 6 sculpture records, 5 distinct knots, are among them (cosmic-love, nitro, ping-pong, spiral, sundown, trainstation; sundown and trainstation are one knot), of which only trainstation exists in stainless steel. CAVEAT: Liu-Ming-Sun-Wu-Yang (arXiv:2608.16560) prove a volume conjecture for a related invariant for every geometric triangulation; if the announced bridge to Andersen-Kashaev is built, case lists like this one may be superseded. FILES: ak_data.json (per knot: ordered triangulation as Regina tight encoding, FAMED verdict, geometric certificate, verified volume interval, meridian data, PD code), reproduce.py (coherence without dependencies; --full recomputes everything under SageMath with SnapPy and Regina, including negative controls; checker code copied verbatim), SHA256SUMS. HONESTY NOTE: no invariant is computed by an AI; every number comes from SnapPy 3.3.2, Regina 7.4, SageMath 10.9 and the included checker. This work was done by Werner Alois Stanggassinger in collaboration with Claude Code (Anthropic): the questions, decisions and hardware are Stanggassinger's; the pipeline driving the tools is the joint contribution. Project: https://knot-structures.stainlesssteel4u.de/ (report, section 4, C5).