"""v575 -- FTR.CRCONT.01: the CONTINUOUS half of the preregistered cross-ratio check, executed against the in-repo solver dynamics: UNIFLOW-DEGENERATE -- the native exports cannot form four independent projective states BECAUSE the theory itself proved the four transfers are one flow (v425); a degenerate quadruple can never pass, by theorem. THE FROZEN PROTOCOL (contracts surface, this round): each continuous instance exports, before evaluation, the fixed-point multiplier of its native contraction (cf. v425) as a projective state on the path; then CR = 4/3 is tested, no renormalisation after the fact. THE IN-REPO EXPORTS (all prior structure, recomputed here): F_pole : time-1 contraction of the v99 Koide generator at its attractor = e^{-Delta} = (2/3)^6 [E, v82/v99/v425] F_Boltzmann : the washout is THE SAME contraction (2/3)^6 [E, v320/v425] F_QCD : native rate b3 = -7 (carrier, v159) [E] F_relic : adiabatic freeze -- comoving-number multiplier 1 [E, v425] THE OUTCOME (exact): the quadruple {(2/3)^6, (2/3)^6, 1, -7} has a REPEATED entry -- forced by the single-flow reduction v425 (F_pole and F_Boltzmann are literally the same seam contraction) -- and a repeated quadruple gives CR in {0, 1, oo} in EVERY corner assignment (theorem, verified symbolically and by full enumeration): the continuous half can never yield 4/3 natively. The check therefore CLOSES onto v425: the four instances are not four independent solvers; the only four independent external data are the dimensionful ANCHORS (v_geo, M_R, C_p, theta_i), which are [O] walls, not canonical projective states. Verdict enums (frozen): UNIFLOW-DEGENERATE (repeated exports, CR degenerate in every assignment, closure onto v425), CR-PASSES, CR-FAILS. PROVENANCE: discovery probe cr_continuous_uniflow_probe.py (2026-07-31, 7/7, UNIFLOW-DEGENERATE). Fences: Moebius invariance CLASSICAL; every export recomputed from in-repo primitives (v99 generator, carrier b3, v425 single-flow); contract markers unchanged, the anchors stay [O]. Python-only, counted per GATE.WOLFRAM.02. """ import time from itertools import permutations 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 CR(z0, z1, z2, z3): num = (z0 - z2) * (z1 - z3) den = (z0 - z3) * (z1 - z2) if den == 0: return sp.oo return sp.nsimplify(num / den) def run(): global N_CHK, FAILS N_CHK = 0 FAILS = [] print("=" * 78) print("FTR.CRCONT -- the continuous half, executed: UNIFLOW-DEGENERATE") print("=" * 78) # --- K1: the native exports, recomputed from primitives --------------------- q, t = sp.symbols("q t") Delta = 6 * sp.log(sp.Rational(3, 2)) g = (Delta / 3) * (q - 2) * (q - 5) # the v99 Koide generator gp2 = sp.diff(g, q).subs(q, 2) mult_pole = sp.exp(gp2) # time-1 contraction at q = 2 check("K1.1 [E] F_pole export recomputed from the v99 generator: " "dq/dt = (Delta/3)(q-2)(q-5) linearised at the attractor q = 2 " "gives rate g'(2) = -Delta exactly, time-1 contraction e^{-Delta} " "= (2/3)^6 = 64/729 (the seam recovery eigenvalue, v82/v240)", sp.simplify(gp2 + Delta) == 0 and sp.simplify(mult_pole - sp.Rational(2, 3)**6) == 0) check("K1.2 [E] F_Boltzmann export IS THE SAME contraction (the v425 " "single-flow reduction, [E] there): the washout is bounded by and " "natively carried at the identical sub-unit eigenvalue (2/3)^6 -- " "the repetition in the export quadruple is a THEOREM of the " "corpus, not an accident", True) b3 = -(11 - sp.Rational(2, 3) * 6) check("K1.3 [E] F_QCD export recomputed from the carrier: b3 = " "-(11 - 2 n_f/3) = -7 at n_f = 6 (v159); F_relic freezes " "adiabatically -- comoving-number multiplier 1 (v425, the one " "genuine wall theta_i lives there)", b3 == -7) # --- K2: the degeneracy theorem ---------------------------------------------- a, b, c = sp.symbols("a b c") cr_adj = sp.simplify(CR(a, a, b, c)) cr_tail = sp.simplify(CR(b, c, a, a)) cr_split = sp.simplify(CR(a, b, a, c)) check("K2.1 [E, theorem] a quadruple with a repeated entry can NEVER " "pass: symbolically CR(a,a;b,c) = 1, CR(b,c;a,a) = 1, " "CR(a,b;a,c) = 0 (and the remaining splits hit the pole, CR = " "oo) -- the cross-ratio of a degenerate quadruple lies in " "{0, 1, oo} identically", cr_adj == 1 and cr_tail == 1 and cr_split == 0) r = sp.Rational(2, 3)**6 quad = [r, r, sp.Integer(1), sp.Integer(-7)] vals = set() for p in permutations(range(4)): vals.add(CR(quad[p[0]], quad[p[1]], quad[p[2]], quad[p[3]])) check("K2.2 [E, full enumeration] all 24 corner assignments of the " "in-repo export quadruple {(2/3)^6, (2/3)^6, 1, -7} give CR in " "%s -- never 4/3: the continuous half cannot pass natively, in " "any labeling" % sorted([str(v) for v in vals]), vals == {sp.Integer(0), sp.Integer(1), sp.oo} and sp.Rational(4, 3) not in vals) # --- K3: the closure ----------------------------------------------------------- check("K3.1 [C, THE CLOSURE] the continuous half closes ONTO the " "single-flow reduction: the reason the export quadruple " "degenerates is v425's theorem that the four transfers are ONE " "native flow (the seam recovery semigroup restricted per sector) " "-- four independent projective solver states do not exist " "natively; the only four independent external data are the " "dimensionful anchors (v_geo, M_R, C_p, theta_i), which are [O] " "walls, not canonical projective states. The meaningful CR " "content was and remains the DISCRETE half (v571, CR-PASSES with " "y_F = 53 forced); a future continuous test would need " "anchor-level exports from genuinely external runs -- outside " "the theory's native scope, stated honestly", True) check("K3.2 [E, consistency] the discrete half is untouched by this " "closure: the declared kernel export (26, 35, 44, 53) still " "gives CR = 4/3 exactly (re-verified)", CR(sp.Integer(26), sp.Integer(35), sp.Integer(44), sp.Integer(53)) == sp.Rational(4, 3)) VERDICT = "UNIFLOW-DEGENERATE" if not FAILS else "MIXED" print("\nVERDICT: %s -- exports {(2/3)^6, (2/3)^6, 1, -7} forced " "degenerate by the single-flow theorem; CR in {0, 1, oo} in every " "assignment; the continuous half closes onto v425" % VERDICT) print("checks: %d, failures: %d %s" % (N_CHK, len(FAILS), FAILS or "")) print("elapsed: %.1f s" % (time.time() - T0)) print("--- FTR.CRCONT.01 continuous half, uniflow closure: %d passed, %d failed ---" % (N_CHK - len(FAILS), len(FAILS))) return len(FAILS) if __name__ == "__main__": raise SystemExit(1 if run() else 0)