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. NEW IN VERSION 3: a correction to our code/Theta_numeric.sage, which set three matrix entries with '=' where Bar-Natan–van der Veen's Theta.m adds them; the two differ only on a crossing row [s, i, j] with i = j + 1, and none of the diagrams behind the reported results (all 313,230 census diagrams, their mirror images, reversed orientations and reversed mirror images, and the 59,937 knots.sage diagrams) has one, so every reported value stands (scans and logs in the archive).