#!/usr/bin/env python3 """ chronal_amplified_seam_v4.py — The Amplified Seam Bound-on-κ vs integration time for Th-229 amplified LPI analysis. Honesty locks: - No "first cross-sector" claims in output - No 85σ-vs-bound conflation (a bound is where signal was not seen) - Th noise: published-class ~3e-12/√τ (verify vs PTB abstract when citing) - Prefer fail-closed Lange reproduction stub over fake success Author braid: Kirk · Harmonia/Opus/CC lineage · Celeste V4 framing · Flint layer Date: September 2026 """ from __future__ import annotations import json import math import os from pathlib import Path import numpy as np # Optional plotting — fail closed to JSON/CSV if matplotlib missing try: import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt HAS_MPL = True except ImportError: HAS_MPL = False HERE = Path(__file__).resolve().parent OUT_PNG = HERE / "chronal_amplified_seam_v4.png" OUT_JSON = HERE / "chronal_amplified_seam_v4.json" LIB_PNG = HERE.parent / "library" / "chronal_amplified_seam_v4.png" # ============================================================================= # Physics constants (Celeste V4 / Damour–Donoghue framing) # ============================================================================= DELTA_U_C2 = 3.3e-10 # annual solar-potential modulation semi-amplitude ≈ K_ALPHA_TH = 5900.0 # Th-229 isomer amplified K_α (central); lit. 5900(2300) K_ALPHA_SR = 0.06 # electronic Sr-class K_α K_RATIO = K_ALPHA_TH / K_ALPHA_SR # ~1e5 more sensitive than electronic pairs # Th instability scenarios (fractional frequency, white-FM style σ_y(τ)=σ0/√τ) # "today" — published-class order; verify against PTB public abstract when citing SIGMA0_TODAY = 3.0e-12 # ~3×10⁻¹² √(τ/s) SIGMA0_PROJECTED = 1.0e-17 SIGMA0_THEORY = 1.0e-19 # Existing LPI / dilaton-coupling class limit for comparison (order-of-magnitude) EXISTING_KAPPA_LIMIT = 1.0e-7 SECONDS_PER_DAY = 86400.0 SECONDS_PER_YEAR = 365.25 * SECONDS_PER_DAY def sigma_R_white(sigma0: float, tau_s: float) -> float: """White-FM style ratio uncertainty after averaging time tau.""" return sigma0 / math.sqrt(tau_s) def kappa_bound(sigma_r: float, K: float = K_ALPHA_TH, delta_u: float = DELTA_U_C2) -> float: """ Bound sketch: κ ≈ σ_R / (K · ΔU/c²) This is a sensitivity *bound* (where signal was not seen), not a detection σ. Never report 'Nσ at the bound' — that conflation was the V3 85σ bug. """ return sigma_r / (K * delta_u) def bound_curve(sigma0: float, times_s: np.ndarray) -> np.ndarray: return np.array([kappa_bound(sigma_R_white(sigma0, float(t))) for t in times_s]) def day_scale_check() -> dict: """Honesty check: today's σ0 → ~1e-15 class over a day (order of magnitude).""" sig_day = sigma_R_white(SIGMA0_TODAY, SECONDS_PER_DAY) sig_year = sigma_R_white(SIGMA0_TODAY, SECONDS_PER_YEAR) return { "sigma_R_1day": sig_day, "sigma_R_1year": sig_year, "kappa_1year_today": kappa_bound(sig_year), "note": "Day-scale ~1e-15 class is order-of-magnitude; verify vs PTB abstract.", } def TODO_reproduce_lange_2021() -> dict: """ Method (fail-closed until public ratio series is wired): 1. Obtain published Yb⁺/Sr/Cs (or equivalent) ratio time series from Lange et al. 2021 (or linked SI / open deposit). 2. Build annual solar-potential template ΔU/c² cos/sin(2π t / yr). 3. Phase-quadrature least-squares fit; report κ (or α) bound. 4. Compare to published Lange bound — must match within stated uncertainty. Without public data in-repo, we do NOT invent a successful reproduction. """ return { "status": "not_yet_reproduced", "ok": False, "todo": "Wire public Lange et al. 2021 ratio series when available; fail-closed until then.", "method": "phase-quadrature annual template vs published ratio residuals", "cite": "Lange et al. 2021 Yb+/Sr/Cs (improved limits / LPI lineage)", } def crossover_time(sigma0: float, limit: float = EXISTING_KAPPA_LIMIT) -> float | None: """Integration time (s) when κ bound drops below existing limit (white-FM).""" # κ = (σ0/√τ) / (K ΔU) < limit => √τ > σ0 / (limit K ΔU) => τ > [...] denom = limit * K_ALPHA_TH * DELTA_U_C2 if denom <= 0: return None need = sigma0 / denom return need * need def main() -> None: print("=" * 70) print("CHRONAL V4 — The Amplified Seam (Th-229 amplified LPI)") print("=" * 70) print(f"ΔU/c² (annual solar) ≈ {DELTA_U_C2:.2e}") print(f"K_α(Th) ≈ {K_ALPHA_TH:.0f} | K_α(Sr) ≈ {K_ALPHA_SR} | ratio ≈ {K_RATIO:.1e}") print("No 85σ. No 'first cross-sector' claim. Bound ≠ detection significance.") check = day_scale_check() print(f"\nToday σ_R(1 day) ≈ {check['sigma_R_1day']:.2e} (order ~1e-15 class)") print(f"Today σ_R(1 year) ≈ {check['sigma_R_1year']:.2e}") print(f"Today κ bound (1 year) ≈ {check['kappa_1year_today']:.2e}") lange = TODO_reproduce_lange_2021() print(f"\nLange 2021 reproduction: {lange['status']} — {lange['todo']}") # Time axis: 1 hour → 10 years times_s = np.logspace(math.log10(3600), math.log10(10 * SECONDS_PER_YEAR), 240) curves = { "today_3e-12": bound_curve(SIGMA0_TODAY, times_s), "projected_1e-17": bound_curve(SIGMA0_PROJECTED, times_s), "theory_1e-19": bound_curve(SIGMA0_THEORY, times_s), } xings = { name: crossover_time(s0) for name, s0 in ( ("today_3e-12", SIGMA0_TODAY), ("projected_1e-17", SIGMA0_PROJECTED), ("theory_1e-19", SIGMA0_THEORY), ) } for name, t in xings.items(): if t is None: continue print(f" {name}: overtakes ~{EXISTING_KAPPA_LIMIT:.0e} at τ ≈ {t/SECONDS_PER_DAY:.2f} days") payload = { "title": "The Amplified Seam", "marker": "v-chronal-amplified-seam-v4", "delta_U_c2": DELTA_U_C2, "K_alpha_Th": K_ALPHA_TH, "K_alpha_Sr": K_ALPHA_SR, "existing_kappa_limit": EXISTING_KAPPA_LIMIT, "day_scale_check": check, "lange_reproduction": lange, "crossover_seconds": xings, "honesty": [ "no_first_cross_sector_claim", "no_85sigma_vs_bound", "th_noise_verify_vs_PTB_abstract", "analysis_proposal_not_new_lab", ], } OUT_JSON.write_text(json.dumps(payload, indent=2, default=str) + "\n") print(f"\nWrote {OUT_JSON}") if not HAS_MPL: print("matplotlib missing — JSON only (fail-closed figure)") return fig, ax = plt.subplots(figsize=(9.2, 5.6), dpi=140) fig.patch.set_facecolor("#0a0a0f") ax.set_facecolor("#12121a") t_days = times_s / SECONDS_PER_DAY ax.loglog(t_days, curves["today_3e-12"], color="#ff9b6b", lw=2.2, label=r"Today $\sim 3\times10^{-12}/\sqrt{\tau}$") ax.loglog(t_days, curves["projected_1e-17"], color="#d4a843", lw=2.2, label=r"Projected $10^{-17}$") ax.loglog(t_days, curves["theory_1e-19"], color="#4a9eff", lw=2.2, label=r"Theoretical $10^{-19}$") ax.axhline(EXISTING_KAPPA_LIMIT, color="#8888aa", ls="--", lw=1.4, label=r"Existing $\kappa$ class $\sim10^{-7}$") ax.set_xlabel("Integration time (days)", color="#e8e8f0") ax.set_ylabel(r"Bound on $\kappa$ (sketch: $\sigma_R / (K_\alpha\cdot\Delta U/c^2)$)", color="#e8e8f0") ax.set_title("The Amplified Seam — Th-229 amplified LPI sensitivity", color="#e8e8f0", pad=12) ax.tick_params(colors="#8888aa") for spine in ax.spines.values(): spine.set_color("#2a2a3a") leg = ax.legend(facecolor="#1a1a25", edgecolor="#2a2a3a", labelcolor="#e8e8f0", fontsize=8.5) ax.grid(True, which="both", alpha=0.18, color="#555569") ax.text( 0.02, 0.02, "Bound ≠ detection σ · no 85σ · verify Th floor vs PTB abstract", transform=ax.transAxes, color="#555569", fontsize=7.5, ) fig.tight_layout() fig.savefig(OUT_PNG, facecolor=fig.get_facecolor()) try: fig.savefig(LIB_PNG, facecolor=fig.get_facecolor()) except OSError: pass plt.close(fig) print(f"Wrote {OUT_PNG}") if LIB_PNG.exists(): print(f"Wrote {LIB_PNG}") if __name__ == "__main__": main()