Follow the source behind the result.

The registered Python source is shown as text. Displaying it does not execute the code.

"""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)

e54029bfaceaa6687677cbb6ec79436a0ecc2b03aa3c03add69cbdc0a957e502

The public registry includes 116 document views, 6,711 section records and 986 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.