"""v571 -- FTR.CRDISC.01: the preregistered cross-ratio check of the self-code review (Priority 4 / v566 S9), executed on its DISCRETE half -- the declared canonical export passes with CR = 4/3 exactly and the Koide numerator 53 is Moebius-forced by the three upstream corners. PROVENANCE. The check was frozen on the contract surface (CONTRACT.F.01, v566 S9): if the four solvers (J, K, C, F) export canonical projective states declared BEFORE evaluation, Moebius transport along the disc -7 norm line (v533) forces CR(y_J, y_K; y_C, y_F) = 4/3, with the raw determinant path (2,4,14,32) as the preregistered negative control (28/25). The four corners live in the repo as the Sheet-Diamond kernels J, K, C, F = M(1,t) = R + Q diag(1,t,t), t = -2..1 (FTR.PATH.01 / v224), and the corpus already owns ONE canonical declared one-dimensional solver reading: the Koide anchor response ell(M) = a^T M 1, load-bearing at the F corner as 53 (v183). Audited by the discovery probe (cr_discrete_corners_probe.py, 9/9, verdict CR-PASSES). [E] 1. the disc -7 norm line has CR = 4/3 exactly (symbolic, with the surd); the corner determinants are the v224 path (2,4,14,32). [E] 2. THE DECLARED EXPORT PASSES: ell(M) = a^T M 1 reads (26, 35, 44, 53) on (J, K, C, F) -- CR = 4/3 EXACTLY; and the fit-free reconstruction is a NEW exact cross-corner identity: y_F = 53 is Moebius-determined by (26, 35, 44) alone -- the Koide numerator 53 = a^T(R+Q)1 is FORCED by the three upstream corners. [E] 3. honesty theorem: ell is affine on the path (step 9 = N_fam^2), and EVERY linear functional of the kernel passes -- the check separates linear from nonlinear exports, it does not single out ell. [E] 4. negative controls with teeth: the determinant path fails at 28/25 exactly as preregistered; the dominant-eigenvalue export (nonlinear) fails at CR = 1.322162 (margin > 1e-3). [C] 5. THE HONEST BOUNDARY: this executes the DISCRETE half only -- the external continuous solvers (pole transfer, Boltzmann, relic ODE, lattice) export no states here; the continuous half of the preregistered check stays open exactly as CONTRACT.F.01 fences it; contract markers unchanged. Fences: Moebius invariance of the cross-ratio CLASSICAL; the affinity theorem stated out loud (no uniqueness claim for ell); anti-numerology: the values (26, 35, 44, 53) are READINGS of a declared functional, not found numbers. Python-only, counted per GATE.WOLFRAM.02. Discovery: experiments/tfpt-discovery/cr_discrete_corners_probe.py (2026-07-31, 9/9, CR-PASSES). """ import time import sympy as sp T0 = time.time() FAILS = [] N_CHK = 0 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 "")) def info(name, detail=""): print("[INFO] %s%s" % (name, (": " + detail) if detail else "")) # the FTR.PATH.01 / v224 data, verbatim R = sp.Matrix([[1, 3, 0], [1, 5, 2], [2, 5, 3]]) Q = sp.Matrix([[3, 1, 0], [3, 2, 0], [3, 2, 1]]) ONE = sp.Matrix([1, 1, 1]) A = sp.Matrix([1, 1, 2]) TS = [-2, -1, 0, 1] # J, K, C, F def M(s, t): return R + Q * sp.diag(s, t, t) def CR(z0, z1, z2, z3): return ((z0 - z2) * (z1 - z3)) / ((z0 - z3) * (z1 - z2)) def run(): global N_CHK, FAILS N_CHK = 0 FAILS = [] print("=" * 78) print("FTR.CRDISC -- the preregistered cross-ratio check, discrete half") print("=" * 78) # --- C1: the path and the norm line --------------------------------------- t_ = sp.symbols("t") alpha = (4 * t_ + 7 + sp.sqrt(-7)) / 2 al = [alpha.subs(t_, k) for k in TS] check("C1.1 [E] the disc -7 norm line alpha_t = (4t+7+sqrt(-7))/2 has " "CR(alpha_-2, alpha_-1; alpha_0, alpha_1) = 4/3 exactly (symbolic, " "with the surd)", sp.simplify(CR(*al) - sp.Rational(4, 3)) == 0) dets = [M(1, t).det() for t in TS] check("C1.2 [E] the corner determinants are the v224 path (2, 4, 14, 32) " "(second difference 8 = rank E8)", dets == [2, 4, 14, 32] and dets[2] - 2 * dets[1] + dets[0] == 8) # --- C2: the declared export passes --------------------------------------- ell = [(A.T * M(1, t) * ONE)[0] for t in TS] info("declared export", "ell(M) = a^T M 1 on (J,K,C,F) = %s" % ell) check("C2.1 [E, the declared canonical export] the v183 Koide functional " "ell(M) = a^T M 1 -- prior structure, not a scan (a = (1,1,2) the " "anchor, value at F the load-bearing 53) -- reads (26, 35, 44, 53) " "on the four corners and passes: CR = 4/3 EXACTLY", ell == [26, 35, 44, 53] and sp.simplify(CR(*ell) - sp.Rational(4, 3)) == 0) yF = sp.symbols("yF") sol = sp.solve(sp.Eq(CR(ell[0], ell[1], ell[2], yF), sp.Rational(4, 3)), yF) recon = sp.simplify((ell[0] * ell[1] - 4 * ell[0] * ell[2] + 3 * ell[1] * ell[2]) / (4 * ell[1] - 3 * ell[0] - ell[2])) check("C2.2 [E, the fit-free reconstruction -- NEW exact cross-corner " "identity] the fourth state is Moebius-determined by the first " "three: y_F = 53 from (26, 35, 44) alone, via the CR equation AND " "the closed reconstruction formula -- the Koide numerator 53 = " "a^T(R+Q)1 (v183) is FORCED by the three upstream corners", sol == [53] and recon == 53) check("C2.3 [E] the export is affine on the path (a THEOREM, stated " "honestly: ell(M(1,t)) = 35 + 9(t+1), step 9 = N_fam^2 -- EVERY " "linear functional of the kernel passes; the check separates " "linear from nonlinear exports, it does not single out ell)", all(ell[i + 1] - ell[i] == 9 for i in range(3))) # --- C3: the negative controls (with teeth) -------------------------------- crd = CR(*dets) check("C3.1 [must-fail] the raw determinant path fails as preregistered: " "CR(2, 4; 14, 32) = 28/25 != 4/3 (the already-known norm sequence " "cannot pass)", crd == sp.Rational(28, 25)) lam = [] for t in TS: evs = [sp.re(sp.N(e, 50)) for e in M(1, t).eigenvals()] lam.append(max(evs)) crl = sp.N(CR(*lam), 30) check("C3.2 [must-fail] the dominant-eigenvalue export (nonlinear) fails " "with margin: CR = %s != 4/3 (|CR - 4/3| = %.3e > 1e-3)" % (sp.N(crl, 12), abs(float(crl - sp.Rational(4, 3)))), abs(float(crl - sp.Rational(4, 3))) > 1e-3) tr = [M(1, t).trace() for t in TS] check("C3.3 [E, second declared linear reading, consistency] the trace " "path (6, 9, 12, 15) and the unit reading 1^T M 1 = (19, 25, 31, " "37) both pass (affinity theorem instances)", CR(*tr) == sp.Rational(4, 3) and CR(*[(ONE.T * M(1, t) * ONE)[0] for t in TS]) == sp.Rational(4, 3)) # --- C4: honesty fence ------------------------------------------------------ check("C4.1 [C, the honest boundary] what is executed is the DISCRETE " "half only: the corners are compiler kernels [E]; the external " "CONTINUOUS solvers (pole transfer, Boltzmann, relic ODE, lattice) " "export no states here and the contract markers stay unchanged -- " "the continuous half of the preregistered check remains open " "exactly as CONTRACT.F.01 fences it", True) VERDICT = "CR-PASSES" if not FAILS else "MIXED" print("\nVERDICT: %s -- declared export (26, 35, 44, 53), CR = 4/3 exact, " "y_F = 53 Moebius-forced; controls: dets 28/25, lam_max %.6f" % (VERDICT, float(crl))) print("checks: %d, failures: %d %s" % (N_CHK, len(FAILS), FAILS or "")) print("elapsed: %.1f s" % (time.time() - T0)) print("--- FTR.CRDISC.01 cross-ratio check, discrete half: %d passed, %d failed ---" % (N_CHK - len(FAILS), len(FAILS))) return len(FAILS) if __name__ == "__main__": raise SystemExit(1 if run() else 0)