θ detects chirality for all prime knots up to 14 crossings — and first fails at 15: the chiral θ-trivial knots 15nh_048139 and 15nh_048140

Θ = (Δ, θ) is the knot invariant of Bar-Natan and van der Veen (arXiv:2509.18456v4). Their Conjectures 21 and 22 give "amphichiral ⟹ θ = 0". This archive measures the converse over the complete census of prime knots up to 15 crossings (313,230 knots, Burton's tables; counts equal OEIS A002863 exactly; 0 errors). RESULTS: (1) θ(mirror K) = −θ(K) at the point (22/7, 21/13) for every one of the 313,230 knots. (2) For c ≤ 14 (59,937 knots) θ = 0 at the point holds for exactly 352 knots, and each is CERTIFIED amphichiral (351 by SnapPy verified oriented isometry signatures, one, 14ah_00990, by an exact orientation-reversing combinatorial automorphism of a triangulation; Gordon–Luecke) — so every chiral prime knot up to 14 crossings has θ ≠ 0 and θ separates it from its mirror image (in either orientation, see (5)); the per-c counts 1, 1, 5, 13, 58, 274 equal OEIS A052401, so given A052401 the zeros are exactly the amphichiral knots. (3) At c = 15 there are three zeros against A052401(15) = 1: the certified amphichiral 15nh_008268 and the CHIRAL knots 15nh_048139 and 15nh_048140, for which θ ≡ 0 as a polynomial in the orientation of the census DT code, and also for their mirror images, their reversed orientation and the reversed mirror image (full symbolic Theta.sage for all four variants; calibrations 3_1 and 15nh_000001 give θ(−K) = θ(K) ≠ 0 and θ(m(−K)) = −θ(K) exactly). (4) Chirality is certified with SnapPy 3.3.2 verified isometry signatures with orientation (oriented signature of the exterior ≠ that of the reversed-orientation exterior, unoriented signatures equal; counter-cases 4_1 / 5_2), hence chiral (Mostow–Prasad rigidity). The pair is invisible to the Jones polynomial (mirror-symmetric), signature, τ, ν, ε and knot Floer homology; the numerical Chern–Simons invariant (−0.0344786485… for both knots in the census orientation, +0.0344786485… for their mirror images; mod 1/2 neither 0 nor 1/4) and the trivial numerical symmetry group indicate the chirality that the certificate proves; volume 20.0432323122…. NEW IN VERSION 2: the two knots are Conway mutants of each other — an explicit six-crossing tangle mutation takes 15nh_048139 to a knot whose exterior is isometric to that of 15nh_048140, orientation-preservingly (Chern–Simons of the mutant = that of 15nh_048140, numerical). (5) θ(−K) = θ(K) and θ(m(−K)) = −θ(K) at the point for every one of the 313,230 knots (reversed orientation and its mirror image; point-level evidence for Conjecture 22; the PD reversal is checked by SnapPy cusp maps on 7 non-invertible knots, where it gives (−meridian, −longitude) and a no-op would give (+meridian, +longitude)), so the θ-zeros are the same in both orientations. So the converse "θ = 0 ⟹ amphichiral" is true through 14 crossings and fails at 15 crossings (crossing numbers c ≥ 16 are not reported in this archive). No new method is claimed; the tools are published, this archive adds the computation and the two knots. Calibration: at the point (22/7, 21/13) our code reproduces Bar-Natan's own θ table exactly for all 249 knots up to 10 crossings. Prior art checked (Bar-Natan–van der Veen 2509.18456v4 and 1708.04853v3, Ohtsuki Geom. Topol. 11 (2007), Garoufalidis–Li 2409.03557v6, McConkey–Seaton 2509.22939v1): only the direction amphichiral ⟹ 0 follows from what is stated anywhere we looked; Bar-Natan–van der Veen computed Θ on the same 313,230 knots, but we found no report of these two. Every computed number is the output of the included scripts run with open tools (SnapPy 3.3.2, spherogram, knot_floer_homology, Regina, SageMath 10.9, Bar-Natan's Theta code; the occurrence counts and the HTLinkExteriors probe in the prior-art notes by prior_art_counts.py on our text copies of the papers, which are not included), except two input tables described in README.md (the calibration θ values on Bar-Natan's knots.sage diagrams, made by our pipeline script build_external_theta_db.sage, included, from Bar-Natan's knots.sage, which is not redistributed, and the three θ-zero rows at c = 15 copied from our census table). Work by Werner Alois Stanggassinger in collaboration with Claude Code (Anthropic): the choice of problem, the direction of the work and the computing hardware are due to the author (a sculptor); the scripts in the archive were written and run by Claude Code (Anthropic) working with the author (Theta.sage itself is not included; make_theta_sage.py builds it from Bar-Natan's code); the invariant and its program are Bar-Natan–van der Veen's. Code GPL-3.0-or-later, data and text CC BY 4.0. See README.md and SHA256SUMS in the archive.