"""v246 -- the HONEST data cross-check for the spectral-action prediction (CONTRACT.QFT4D.01 / v244/v245): does the boundary condition g1=g2=g3, sin^2 th_W = 3/8 at the unification scale survive the MEASURED Standard-Model couplings, run at ONE AND TWO loops? Answer: NO -- and there is no rescue in the current theory. CRUCIAL HONEST POINT (the framing that matters): TFPT's gauge-charged content IS exactly the Standard Model (v159: the carrier reproduces the SM beta coefficients) and the theory adds NO new states (tfpt_3: 'Dark matter = no new state'). The 'E8 cascade' of the current theory is an arithmetic even-integer SPINE (D_n = 60 - 2n, v5), NOT a particle/threshold tower. So a 'TFPT-adapted' RGE run IS the Standard-Model run, by construction -- and the SM does not unify. This is a falsifiable TENSION / likely kill-test, NOT a confirmation; the (arithmetic) spine supplies NO admissible gauge thresholds. Inputs (measured, GUT-normalised, at M_Z; PyR@TE-cross-checked, v159): alpha_i^-1 = (59.01, 29.59, 8.47); 1-loop b = (41/10, -19/6, -7); 2-loop SM gauge matrix b_ij (Machacek-Vaughn / Jones, gauge-only). sin^2 th_W(M_Z) = 0.23122. [E] 1. TFPT GAUGE CONTENT = SM, NO NEW STATES. The carrier reproduces the SM betas (v159) and the theory adds no gauge-charged states (tfpt_3); the E8 cascade is an arithmetic spine (v5), not a threshold tower. So the TFPT RGE run IS the SM run. [E] 2. THE PREDICTION. The spectral action predicts at Lambda: g1 = g2 = g3 and sin^2 th_W = 3/8 (v245). [X] 3. ONE-LOOP MISSES. Pairwise crossings spread ~10^13 - 10^17 GeV; residual at 2e16 GeV ~ 9. No common point. [X] 4. TWO-LOOP ALSO MISSES. RK4 2-loop run: the minimal spread is Delta(alpha^-1) ~ 3.2 at mu ~ 1.7e14 GeV -- the three couplings never meet (the textbook non-SUSY result); at 2e16 the spread is ~8.7. [X] 5. sin^2 th_W TENSION. 3/8 = 0.375 predicted vs 0.23122 measured. [O] 6. NO RESCUE IN THE CURRENT THEORY. With 'no new state' there is NO admissible threshold source; closing the spread would require EITHER new gauge-charged matter (a new postulate, contradicting 'no new state') OR a non-GUT / boundary reading of the spectral-action cutoff. The spectral- action 4d-GUT unification route is in genuine tension -- the SAME status as the Connes-Chamseddine NCG Standard Model -- and is likely falsified unless the theory is extended. Typed [X]/[O], NEVER [E]-as-success; the AQFT skeleton, DHR structure and SM rep-core survive regardless as an emergent boundary QFT. Python-only (1- and 2-loop RK4 running; numpy). A data-confrontation kill-test in the spirit of v62/v159 -- never [E]-as-success. """ import numpy as np from tfpt_constants import check, summary, reset M_Z = 91.1876 AINV = np.array([59.01, 29.59, 8.47]) # alpha_i^-1(M_Z), GUT-normalised (PDG-derived) B1 = np.array([41 / 10, -19 / 6, -7.0]) # SM 1-loop b_i (v159 PyR@TE) # SM 2-loop gauge matrix (GUT-norm U(1)); Machacek-Vaughn / Jones, gauge-only B2 = np.array([[199 / 50, 27 / 10, 44 / 5], [9 / 10, 35 / 6, 12.0], [11 / 10, 9 / 2, -26.0]]) SIN2_MEAS = 0.23122 def ainv_1loop(mu): return AINV - B1 / (2 * np.pi) * np.log(mu / M_Z) def crossing_1loop(i, j): L = 2 * np.pi * (AINV[i] - AINV[j]) / (B1[i] - B1[j]) return M_Z * np.exp(L) def run_2loop(t_end, dt=0.01): """RK4 integrate alpha_i^-1 from M_Z (t=0) to t_end=ln(mu_end/M_Z); return (min spread, scale of min spread, spread at end).""" def deriv(ai): a = 1.0 / ai return -B1 / (2 * np.pi) - (B2 @ a) / (8 * np.pi**2) t, ai = 0.0, AINV.copy() best, best_mu = 1e9, M_Z while t < t_end: k1 = deriv(ai); k2 = deriv(ai + 0.5 * dt * k1) k3 = deriv(ai + 0.5 * dt * k2); k4 = deriv(ai + dt * k3) ai = ai + dt / 6 * (k1 + 2 * k2 + 2 * k3 + k4); t += dt spread = float(ai.max() - ai.min()) if spread < best: best, best_mu = spread, M_Z * np.exp(t) return best, best_mu, float(ai.max() - ai.min()) def run(): reset() print("v246 unification data cross-check (1+2-loop): SM=TFPT gauge content does NOT unify -- a tension") # 1. TFPT gauge content = SM, no new states check("TFPT GAUGE CONTENT = SM, NO NEW STATES [E]: the carrier reproduces the " "SM betas b=(41/10,-19/6,-7) (v159) and the theory adds NO gauge-charged " "states (tfpt_3 'Dark matter = no new state'); the E8 cascade is an " "arithmetic spine (v5), not a threshold tower. So the TFPT RGE run IS the " "SM run", tuple(B1) == (41 / 10, -19 / 6, -7.0)) # 2. the prediction check("THE PREDICTION [E]: the spectral action predicts at Lambda g1=g2=g3 and " "sin^2 th_W = 3/8 = %.3f (v245)" % (3 / 8), abs(3 / 8 - 0.375) < 1e-12) # 3. one-loop misses m12, m13, m23 = crossing_1loop(0, 1), crossing_1loop(0, 2), crossing_1loop(1, 2) mus = sorted([m12, m13, m23]) decades = float(np.log10(mus[-1] / mus[0])) spread1_2e16 = float(np.ptp(ainv_1loop(2e16))) check("ONE-LOOP MISSES [X]: pairwise crossings a1=a2 %.2e, a1=a3 %.2e, a2=a3 " "%.2e GeV (%.1f decades); residual at 2e16 = Delta(alpha^-1) %.1f -- no " "common point" % (m12, m13, m23, decades, spread1_2e16), decades > 2.0 and spread1_2e16 > 3.0) # 4. two-loop also misses (the real run) best, best_mu, spread2_2e16 = run_2loop(np.log(2e16 / M_Z)) check("TWO-LOOP ALSO MISSES [X]: RK4 2-loop run -- the minimal spread is " "Delta(alpha^-1) = %.2f at mu = %.2e GeV (the three NEVER meet; textbook " "non-SUSY result); at 2e16 GeV the spread is %.2f. 2-loop narrows but does " "NOT close" % (best, best_mu, spread2_2e16), 1.0 < best < 6.0 and spread2_2e16 > 5.0) # 5. sin^2 thetaW tension check("sin^2 th_W TENSION [X]: predicted 3/8 = %.3f vs measured %.5f (the known " "few-percent non-SUSY shortfall)" % (3 / 8, SIN2_MEAS), abs(3 / 8 - SIN2_MEAS) > 0.1) # 6. no rescue in the current theory check("NO RESCUE IN THE CURRENT THEORY [O]: with 'no new state' there is NO " "admissible gauge-threshold source (the E8 spine is arithmetic, v5, not a " "particle spectrum); closing the spread needs EITHER new gauge-charged " "matter (a new postulate vs 'no new state') OR a non-GUT/boundary reading " "of the cutoff. The spectral-action 4d-GUT route is in genuine tension -- " "same status as NCG-SM -- likely falsified unless extended; the AQFT " "skeleton + DHR + SM rep-core survive as an emergent boundary QFT. " "Typed [X]/[O], NEVER [E]-as-success", True) return summary("v246 unification data cross-check (1+2-loop): SM=TFPT content does not unify; no rescue") if __name__ == "__main__": raise SystemExit(1 if run() else 0)