Phase 1 (independent of kernel/ and two_adic/, which were not read).
Functions
| module | function | returns |
|---|---|---|
checker_q.py | Q_matrix(c, N, dps) | the Weil form Q of theory s0 on the shared basis: real symmetric (2N+1) x (2N+1) mpmath matrix, index 0 is n = -N, F(f) = v^* Q v |
checker_q.py | q_parts(c, N, dps, method="gl", with_error=False) | dict with the blocks "pole", "arch", "prime", "Q" (and "quad_err") |
checker_q.py | q_of_w(w, D, c, dps, ...) | Q of a single function given its symmetrised correlation w = g(x) + g(-x) and D = w(0) - w(x) |
checker_q.py | transform_rows(c, N, dps) | rows r with r . v = int f, int f e^{-y/2}, int f e^{+y/2} (keys zero, minus, plus) |
checker_q.py | constraint_basis(rows, dim, dps), compress(M, B, dps) | orthonormal basis of {r . v = 0} and B^* M B |
checker_props.py | class_bases(c, N, dps) | bases of the reported spaces full, minus, minus_zero, plus_zero |
checker_props.py | cc611_margins(Q, T_inf, c, N, dps) | Connes-Consani Thm 6.11 margins in the mission basis |
checker_gate.py | run_gate(n_max=200) | exact (U-S) events per object; accepts_window(events, c), accepts_places(events, c) |
checker_glue.py | T_inf, T_S, T_S_places, T_S_with_data | the seam to kernel/ and two_adic/; raise NotRouted in phase 1 |
c may be given as a decimal string ("2.9"); it is parsed at the working precision. A float c is rounded to 53 bits first, which moves Q by about 1e-15 (observed while testing, so pass strings).
Conventions
- Q is theory s0 (Zhu arXiv:2608.24827 eq. (2)-(3)) with f the window function and g = f * f~ its autocorrelation. Only n = 2 is an atom on c in [2, 3); the prime block is -(log 2 / sqrt 2) K(log 2), which is -sqrt(2) log 2 g(log 2) for real f.
- The reported function classes.
minus: g-hat(-i/2) = 0 in Connes-Consani's convention (their (22), F(g)(s) = int g(v) v^{-is} d*v), which in the mission basis is int_0^L f(y) e^{-y/2} dy = 0.minus_zero: that and g-hat(0) = 0, i.e. v_0 = 0.plus_zero: the reflected class (int f e^{+y/2} = 0 and v_0 = 0). - A discrepancy in the source. Connes-Consani arXiv:2006.13771 Thm 6.11 (p. 48) imposes g-hat(-i/2) = 0 and carries the remainder c |g-hat(0)|^2, c = 4 gamma / log 2, gamma ~ 2.94355 (Lemma 6.10). Their Theorem 1 in the introduction (p. 2) states vanishing at +i/2 and 0. The reflection y -> L - y exchanges the two classes and leaves Q invariant. It leaves T_inf invariant if the Fourier transform preserves Sonin's space and turns theta(g) into theta(g(1/.)); that was not verified from the source here, so both
minus_zeroandplus_zeroare reported.
JSON: checker_q_cells.json
cells[c] for c in {1.5, 1.9, 2.2, 2.5, 2.9}: full_N{N}_dps{dps} (three lowest eigenvalues of Q), minus_N{N}_dps40, minus_zero_N{N}_dps40, quad_err_dps40, galerkin_maxdev_N32_dps40, drift_40_60_N32, atoms. gate: the output of run_gate(). Numbers are decimal strings (25 significant digits).