Priority deposit v2: 250 positive amphicheiral hyperbolic knots whose Conway polynomial does not split -- Part II, the order-8 case and Corollary 7.3 beyond order 4

Version 2, superseding the deposit of 25 July 2026 (fourteen knots) on the same concept DOI. Here: 250 distinct hyperbolic knots that are positive amphicheiral but not strongly so -- each carries an orientation-reversing symmetry of order 2^a preserving the knot orientation, and carries no orientation-reversing involution, no negative amphicheiral symmetry and no inversion, so that neither Hartley's theorem nor Hartley-Kawauchi applies. For each, the Conway polynomial does not split as f(z)f(-z) with f in Z[z]. 18 lie at a=2 (rotary reflection of order 4) and 232 at a=3 (order 8); the fourteen of version 1 are contained here and flagged, 236 are new. NO NEW THEOREM IS CLAIMED. What is deposited is a generator for this class together with verified data. TWO CORRECTIONS TO VERSION 1, stated up front: (1) its limits section claimed the order-8 family sits outside the reach of Conant's Corollary 7.3 -- that was our misreading. Corollary 7.3 is stated for a=2 because there nu_2 = Nabla_K directly; the identity behind it is the telescoping step of Theorem 7.1, which Theorem 6.11 supplies for every 1 <= k <= a-1, so taking k = a-1 gives it at every order. The restriction was ours, not the theorem's. (2) its construction-certificate bound 1.4e-14 is the bound for those fourteen curves and does not hold for the larger set; measured over all 250 the worst defect is 3.99e-14. THE SHARP BRANCH: the constant-term congruence E(0) = (l^2-1)/8 mod 2 forbids something only when l = +-3 (mod 8), where E(0) must be odd. Version 1's generator was Conant's case c=1, which for a <= 3 forces l = 1 (mod 8) -- the soft branch, unreachable by construction. Generalising the generator to arbitrary odd rotation parameter c opens the sharp branch: it now holds 7 knots at order 4 and 73 at order 8, congruence satisfied 80/80. At order 8 this had never been tested, because no order-8 example carrying that branch existed. NULL MEASUREMENT, because 250/250 is worthless without it: the same solver finds a presentation for 0 of 200 random polynomials with p(0)=1 and for 11 of 144 genuinely chiral hyperbolic knots (7.6 percent), against 250 of 250 here. ON THE OPEN QUESTIONS: for Conant-Manathunga Question 4.8 the 250 realise 50 distinct leading coefficients from -44800 to +12288; for Question 4.9 we add nothing -- the primes realised are 5, 7 and 13, all three already in their Table 1, and the first unrealised prime is p >= 19. Each knot is a closed-form Fourier curve invariant under sigma_c = R_z(2 pi c / 2^a) composed with z -> -z, so positive amphicheirality is a property of the construction rather than of a computation; six numbers per knot reproduce the curve bit-exactly (version 1 needed five, c_rot is the new one) and a standalone numpy-only script is included, carrying a self-test that must fail against the wrong rotary reflection. Conant's Lemma 4.2, c*l = 1 mod 2^a, is confirmed on all 250 across four rotation parameters -- his rule, checked here, not discovered here. Crossing numbers are upper bounds, 21 to 174; volumes 14.038 to 165.815. 271 candidates hit a per-candidate deadline during generation and were never evaluated; they are logged as such and counted neither as passing nor as failing. HONESTY NOTE: no invariant here is computed by an AI; every number comes from established open tools (Regina, SnapPy/spherogram, SageMath, SymPy, numpy) and is reproducible there from the planar diagrams included. This work was done by Werner Alois Stanggassinger in collaboration with Claude Code (Anthropic): the geometry, the questions and the hardware are Stanggassinger's; the pipeline driving the tools and the curve-generating machines are the joint contribution. See README.md, NOTE.md, verification_log.md and SHA256SUMS in the archive.