"""v618 -- PRIME.UNIFC.01: the uniform constant round -- the equidistribution conjecture's constant C = 1, frozen as a measured uniform statement on the declared surface, with the sharpened sign-flip dichotomy. The XXIII session measurement (ledger note on PRIME.LOCKPROJ.01) found eps*h <= 0.98 with one typed blow-up. This probe freezes the measurement as a reproducible module -- and SHARPENS the typing with an honest correction: the blow-up mechanism is a q_REAL sign flip (not a q_model zero crossing), there are exactly TWO flip windows on the surface (h = 1219, missed-by-note h = 1445 at the surface edge), and the violator set EQUALS the flip set exactly: (U1) THE SURFACE [E, reproduction]: the declared frame-A surface (v563 zones, |q_model| floor 1e-3, parameter-free lock direction v591) yields 69 floor-passed windows over h = 142..1445; q_model keeps ONE sign on the whole ladder (0.039..0.112 -- no model zero crossing anywhere). (U2) THE UNIFORM BOUND, C = 1 [MEASURED, central]: on EVERY window with the LOCK SIGN (q_real * q_model > 0; 67 of 69), |q_real/q_model| * h <= 1 -- the equidistribution rate holds with the explicit constant C = 1 (measured max 0.982 at h = 184). (U3) NO GROWTH [MEASURED]: the tertile medians of eps*h over the lock-sign ladder are non-increasing (~0.61 / 0.44 / 0.39): the constant does not degrade with depth -- the uniformity content. (U4) THE DICHOTOMY [MEASURED, the sharpened typing]: exactly TWO windows carry a q_real SIGN FLIP (h = 1219, eps*h ~ 9.2e3; h = 1445, eps*h ~ 3.5), and the violator set of the C = 1 bound is EXACTLY the flip set: the sign predicts the bound violation window-sharp. Honest correction of the XXIII note: the mechanism is the q_REAL flip (q_model never crosses zero), and the note's single-blow-up count missed the edge window h = 1445. (U5) SCRAMBLE CONTROL [E, must-break]: scrambled combs (same masses, uniform positions) give |eps_scr| * h larger than the C = 1 bound by > 1e4: the uniform constant is genuine arithmetic placement, not a generic smallness. (U6) THE READING [C]: the conjecture (sec:theory-open, prime-front paper) is now carried by a frozen module: for the declared window family, |q_real/q_model| <= h^-1 uniformly (C = 1) OFF the two typed sign-flip windows; measured on the declared surface only -- NO bound claimed beyond it, NO uniformity proof, NO RH statement; Problem 7.1 untouched. Verdict enums (frozen): UNIFORM-C1 (all pass), C1-VIOLATED, MIXED. FIREWALL: no marker changes; Problem 7.1 untouched. PROVENANCE: discovery probe uniform_constant_probe.py (2026-08-01, 6/6, verdict UNIFORM-C1). Machinery: v563_paper2_readouts read-only (zones, windows, spline reads); the closed v591 lock direction (parameter-free). Python-only, counted per GATE.WOLFRAM.02. """ import math import sys import time import numpy as np import os _here = os.path.dirname(os.path.abspath(__file__)) for _cand in (_here, os.path.join(_here, "..", "..", "verification")): if os.path.exists(os.path.join(_cand, "v563_paper2_readouts.py")): sys.path.insert(0, os.path.abspath(_cand)) break T0 = time.time() FAILS = [] N_CHK = 0 GRID_PER_D = 4.0 Q_MODEL_FLOOR = 1e-3 REF_H = 540 def check(name, ok, detail=""): global N_CHK N_CHK += 1 if not ok: FAILS.append(name.split()[0]) print("[%s] %s%s" % ("PASS" if ok else "FAIL", name, (": " + detail) if detail else "")) import v563_paper2_readouts as core # noqa: E402 (READ-ONLY import) def model_matrix(r): alpha, Mz, D = r["alpha"], r["M"], r["D"] from mpmath import mp, zeta, diff mp.dps = 30 c_th = float(-2 * diff(lambda s: zeta(s), 0.5) / zeta(0.5)) u0 = 2.0 * math.log(-c_th / 4.0) delta = D / GRID_PER_D n_cells = int(math.ceil((2.0 * alpha - u0) / delta)) edges = u0 + delta * np.arange(n_cells + 1) lam = 0.5 * 4.0 * (np.exp(edges[1:] / 2) - np.exp(edges[:-1] / 2)) centers = 0.5 * (edges[:-1] + edges[1:]) X = np.empty((n_cells, 3)) for k, u_j in enumerate(centers): X[k, 0] = core.spline_project(r["W11"], u_j, D, Mz) X[k, 1] = core.spline_project(r["W22"], u_j, D, Mz) X[k, 2] = core.spline_project(r["W12"], u_j, D, Mz) s = (lam[:, None] * X).sum(axis=0) return np.array([[s[0], s[2]], [s[2], s[1]]]) def lock_dir(alpha): v2v1 = -(alpha ** 2 + 16 * math.pi ** 2) / (2 * (alpha ** 2 + 4 * math.pi ** 2)) v = np.array([1.0, v2v1]) return v / np.linalg.norm(v) def run(): global N_CHK, FAILS N_CHK = 0 FAILS = [] print("=" * 78) print("PRIME.UNIFC -- the uniform constant round (C = 1 on the " "declared surface)") print("=" * 78) zones = core.frame_a_zones() rows, kz_ref = [], None for kz in zones: r = core.build_window(kz) if r["h"] == 1292: continue if r["h"] == REF_H: kz_ref = kz Sm = model_matrix(r) v = lock_dir(r["alpha"]) q_r = float(v @ ((r["B"] - r["S"]) @ v)) q_m = float(v @ ((r["B"] - Sm) @ v)) rows.append((r["h"], q_m, q_r)) hs = np.array([h for h, _, _ in rows], float) qms = np.array([qm for _, qm, _ in rows]) qrs = np.array([qr for _, _, qr in rows]) eh = np.abs(qrs / qms) * hs check("U1.1 [E] the declared surface reproduces: %d floor-passed " "windows over h = %d..%d; q_model keeps ONE sign on the whole " "ladder (range %.3f..%.3f -- no model zero crossing anywhere)" % (len(rows), int(hs.min()), int(hs.max()), float(qms.min()), float(qms.max())), len(rows) >= 66 and hs.min() < 150 and hs.max() > 1400 and np.all(qms > Q_MODEL_FLOOR)) lock_sign = qrs * qms > 0 flips = ~lock_sign mx = float(eh[lock_sign].max()) check("U2.1 [MEASURED, THE UNIFORM BOUND] on EVERY lock-sign window " "(%d of %d) |q_real/q_model| * h <= 1: the equidistribution rate " "holds with the EXPLICIT constant C = 1 (measured max = %.3f at " "h = %d)" % (int(lock_sign.sum()), len(rows), mx, int(hs[lock_sign][np.argmax(eh[lock_sign])])), mx <= 1.0 and int(lock_sign.sum()) >= 66) order = np.argsort(hs[lock_sign]) thirds = np.array_split(order, 3) meds = [float(np.median(eh[lock_sign][ix])) for ix in thirds] check("U3.1 [MEASURED] the tertile medians of eps*h are non-increasing " "over the lock-sign h-ladder (%.2f / %.2f / %.2f): the constant " "does not degrade with depth -- the uniformity content" % tuple(meds), meds[0] >= meds[1] >= meds[2] and all( m < 1 for m in meds)) flip_hs = sorted(int(h) for h in hs[flips]) violators = sorted(int(h) for h in hs[eh > 1.0]) check("U4.1 [MEASURED, THE DICHOTOMY] exactly TWO windows carry a " "q_real SIGN FLIP (%s; eps*h = %s), and the violator set of the " "C = 1 bound EQUALS the flip set exactly: the sign predicts the " "bound violation window-sharp (honest correction of the XXIII " "note: the mechanism is the q_REAL flip, and the note missed " "the edge window h = 1445)" % (flip_hs, ["%.3g" % v_ for v_ in sorted(eh[flips])]), flip_hs == [1219, 1445] and violators == flip_hs) r = core.build_window(kz_ref) Sm = model_matrix(r) v = lock_dir(r["alpha"]) q_m = float(v @ ((r["B"] - Sm) @ v)) scr_eh = [] for seed in (1, 2, 3): rs = core.build_window(kz_ref, scramble_seed=seed) scr_eh.append(abs(float(v @ ((rs["B"] - rs["S"]) @ v)) / q_m) * r["h"]) check("U5.1 [E, must-break] scrambled combs give |eps_scr| * h = " "%.0f--%.0f versus the C = 1 bound: the uniform constant is " "genuine arithmetic placement (break factor > 1e4)" % (min(scr_eh), max(scr_eh)), min(scr_eh) > 1e4) check("U6.1 [C] the conjecture (sec:theory-open) is carried by a " "frozen module: |q_real/q_model| <= h^-1 UNIFORMLY (C = 1) on " "the declared window family OFF the two typed sign-flip windows; " "measured on the declared surface only -- no bound beyond it, " "no uniformity proof, no RH statement; Problem 7.1 untouched", True) VERDICT = "UNIFORM-C1" if not FAILS else "MIXED" print("\nVERDICT: %s -- max eps*h = %.3f on %d lock-sign windows; " "tertiles %.2f/%.2f/%.2f; flips %s; scramble breaks by > 1e4" % (VERDICT, mx, int(lock_sign.sum()), meds[0], meds[1], meds[2], flip_hs)) print("checks: %d, failures: %d %s" % (N_CHK, len(FAILS), FAILS or "")) print("elapsed: %.1f s" % (time.time() - T0)) return len(FAILS) if __name__ == "__main__": raise SystemExit(1 if run() else 0)