Paper 12: Add Code/, trace.yaml, reproduce.py, meta.yaml, README

Full paper structure following PACSeries conventions:
- Code/trace.yaml: 10 experiments traced to source repos
- Code/experiments/: 9 experiment scripts copied from midnight/
- Code/reproduce.py: reproduction entry point with data download instructions
- Data/ directories for catalogs and results
- meta.yaml with key results and pre-registration info
- README.md with reproduction instructions

Pre-registration commit 193c87d linked in trace.yaml.
Data sources: SDSS DR16 (MgII, FeII), DR12 (CIV), XQR-30 (multi-ion).

Author: lornecodes

foundational/docs/preprints/PACSeries/v0.3/observational_contact_absorption_spectroscopy/Code/experiments/exp_03_photon_archaeology.py

@@ -0,0 +1,340 @@
+"""
+exp_03 -- Photon Archaeology: Alpha Invariance and SEC-Encoded Line Widths
+
+Midnight Initiative, Thread 1 (Photon Archaeology)
+
+Hypothesis: Ancient photons carry two independent signatures. Spectral line
+RATIOS encode PAC structure (ADE graph eigenvalues) and are epoch-invariant.
+Spectral line WIDTHS encode SEC state (disequilibrium at the current cascade
+level) and are epoch-dependent.
+
+DFT predicts alpha_EM is structurally invariant: alpha = 2/(3*phi*F_10) *
+(1 - F_10/(4*pi*F_7^2)). Every component is either a Fibonacci number
+(integer) or phi (the unique PAC fixed point). No parameter can drift.
+This contradicts Webb et al. (Delta_alpha/alpha ~ 10^{-5}).
+
+Tests:
+  T1: Alpha formula within 6 ppm, perturbation of any component breaks it
+  T2: A_8 line ratios match hydrogen <5%, identical at all z
+  T3: Line widths vary >1% across z, correlated with cascade disequilibrium
+  T4: Clean PAC/SEC separation — ratio variability = 0, width variability > 1%
+
+Sources: M1/M6/M8 (alpha), M9 (cascade clock), M-R exp_04/20/24
+"""
+
+import sys
+import numpy as np
+from pathlib import Path
+from scipy.stats import spearmanr
+
+MIDNIGHT_ROOT = Path(__file__).resolve().parent.parent
+EXPERIMENTS_ROOT = MIDNIGHT_ROOT.parent
+
+sys.path.insert(0, str(MIDNIGHT_ROOT / "core"))
+sys.path.insert(0, str(EXPERIMENTS_ROOT / "milestone-r" / "core"))
+sys.path.insert(0, str(EXPERIMENTS_ROOT / "milestone9" / "core"))
+
+from phase_rate import (
+    PHI, INV_PHI, LN_PHI, PI,
+    save_midnight_results, _convert_numpy,
+)
+from radiation_physics import (
+    ALPHA_EM_DFT, RYDBERG_EV,
+    line_width_from_disequilibrium,
+    fib,
+)
+from infodynamics import (
+    CascadeClock, z_to_lookback, B_DFT, cascade_clock,
+    cascade_clock_fit,
+)
+
+ALPHA_EM_CODATA = 7.2973525693e-3
+F3 = fib(3)   # 2
+F4 = fib(4)   # 3
+F7 = fib(7)   # 13
+F10 = fib(10) # 55
+
+
+def alpha_from_components(f3, f4, phi, f10, f7):
+    """Compute alpha from the five components."""
+    return f3 / (f4 * phi * f10) * (1.0 - f10 / (4.0 * PI * f7**2))
+
+
+# ============================================================
+# T1: Alpha invariance is structural
+# ============================================================
+
+def test_T1_alpha_invariance():
+    """T1: Alpha formula has no continuously deformable parameter."""
+    print("\n  T1: Alpha invariance is structural, not parametric")
+
+    alpha_dft = alpha_from_components(F3, F4, PHI, F10, F7)
+    ppm_base = abs(alpha_dft - ALPHA_EM_CODATA) / ALPHA_EM_CODATA * 1e6
+    within_6ppm = ppm_base < 6.0
+    print(f"    alpha_DFT = {alpha_dft:.10e}")
+    print(f"    CODATA    = {ALPHA_EM_CODATA:.10e}")
+    print(f"    Deviation: {ppm_base:.1f} ppm (<6: {within_6ppm})")
+
+    perturbation = 0.001  # 0.1%
+    components = {
+        'F3 (=2, binary charge)': (F3 * (1 + perturbation), F4, PHI, F10, F7),
+        'F4 (=3, spatial dims)': (F3, F4 * (1 + perturbation), PHI, F10, F7),
+        'phi (golden ratio)': (F3, F4, PHI * (1 + perturbation), F10, F7),
+        'F10 (=55, EM depth)': (F3, F4, PHI, F10 * (1 + perturbation), F7),
+        'F7 (=13, gauge closure)': (F3, F4, PHI, F10, F7 * (1 + perturbation)),
+    }
+
+    all_sensitive = True
+    sensitivity_results = {}
+    for name, args in components.items():
+        alpha_pert = alpha_from_components(*args)
+        ppm_pert = abs(alpha_pert - ALPHA_EM_CODATA) / ALPHA_EM_CODATA * 1e6
+        ratio = ppm_pert / ppm_base if ppm_base > 0 else float('inf')
+        sensitive = ratio > 5
+        all_sensitive = all_sensitive and sensitive
+        sensitivity_results[name] = {'ppm': float(ppm_pert), 'ratio': float(ratio)}
+        print(f"    Perturb {name}: {ppm_pert:.0f} ppm ({ratio:.0f}x base)")
+
+    # Fixed-point verification
+    fp_error = abs(PHI**2 - PHI - 1.0)
+    fp_ok = fp_error < 1e-14
+    print(f"    phi^2 - phi - 1 = {fp_error:.2e} (<1e-14: {fp_ok})")
+
+    passed = within_6ppm and all_sensitive and fp_ok
+    print(f"    -> {'PASS' if passed else 'FAIL'}")
+
+    return {
+        'test': 'T1_alpha_invariance',
+        'alpha_dft': float(alpha_dft),
+        'alpha_codata': float(ALPHA_EM_CODATA),
+        'ppm': float(ppm_base),
+        'sensitivity': sensitivity_results,
+        'all_sensitive': all_sensitive,
+        'fixed_point_error': float(fp_error),
+        'PASS': passed,
+    }
+
+
+# ============================================================
+# T2: Line ratios are epoch-invariant
+# ============================================================
+
+def hydrogen_ratio(n, m):
+    """Hydrogen transition energy ratio E_n→m / E_Rydberg = |1/m² - 1/n²|."""
+    return abs(1.0/m**2 - 1.0/n**2)
+
+
+def test_T2_epoch_invariant_ratios():
+    """T2: A_8 spectral line ratios match hydrogen and don't drift with z."""
+    print("\n  T2: Line ratios are PAC-determined and epoch-invariant")
+
+    # Build A_8 path graph
+    n = 8
+    adj = np.zeros((n, n))
+    for i in range(n - 1):
+        adj[i, i+1] = adj[i+1, i] = 1.0
+
+    D = np.diag(np.sum(adj, axis=1))
+    L = D - adj
+    eigvals = np.sort(np.linalg.eigvalsh(L))
+    pos = eigvals[eigvals > 1e-10]
+    E = np.sort(1.0 / pos)[::-1]
+
+    # Compare transition ratios: Lyman series (m=1)
+    transitions = [(2,1), (3,1), (4,1), (3,2), (4,2), (5,2)]
+    errors = []
+    details = []
+    for n_upper, m_lower in transitions:
+        if n_upper - 1 >= len(E) or m_lower - 1 >= len(E):
+            continue
+        graph_ratio = abs(E[m_lower-1] - E[n_upper-1]) / E[0]
+        h_ratio = hydrogen_ratio(n_upper, m_lower)
+        if h_ratio > 0:
+            rel_error = abs(graph_ratio - h_ratio) / h_ratio
+            errors.append(rel_error)
+            details.append({
+                'transition': f'{n_upper}->{m_lower}',
+                'graph': float(graph_ratio),
+                'hydrogen': float(h_ratio),
+                'error': float(rel_error),
+            })
+
+    max_error = max(errors) if errors else 1.0
+    matches_hydrogen = max_error < 0.05
+    print(f"    A_8 vs hydrogen max error: {max_error:.1%} (<5%: {matches_hydrogen})")
+
+    # Epoch invariance: same ratios at all z
+    z_values = [0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0]
+    ratios_at_z = {}
+    for z in z_values:
+        ratios_at_z[z] = [d['graph'] for d in details]
+
+    all_identical = all(
+        np.allclose(ratios_at_z[z], ratios_at_z[0.0]) for z in z_values
+    )
+    print(f"    Ratios identical across z={z_values}: {all_identical}")
+
+    passed = matches_hydrogen and all_identical
+    print(f"    -> {'PASS' if passed else 'FAIL'}")
+
+    return {
+        'test': 'T2_epoch_invariant_ratios',
+        'graph': 'A_8',
+        'n_transitions': len(details),
+        'max_error': float(max_error),
+        'matches_hydrogen': matches_hydrogen,
+        'all_identical_across_z': all_identical,
+        'transition_details': details,
+        'PASS': passed,
+    }
+
+
+# ============================================================
+# T3: Line widths are epoch-dependent
+# ============================================================
+
+def test_T3_epoch_dependent_widths():
+    """T3: Line widths vary with redshift via cascade clock disequilibrium."""
+    print("\n  T3: Line widths are SEC-determined and epoch-dependent")
+
+    # Fit cascade clock
+    a_clock, slope, rms = cascade_clock_fit(constrained=True)
+    print(f"    Cascade clock: a={a_clock:.3f}, slope=1/ln(phi)={slope:.4f}")
+
+    # Build A_6 graph for line width computation
+    n_graph = 6
+    adj = np.zeros((n_graph, n_graph))
+    for i in range(n_graph - 1):
+        adj[i, i+1] = adj[i+1, i] = 1.0
+
+    z_values = [0.1, 0.3, 0.5, 0.7, 1.0, 1.5, 2.0, 2.5, 3.0]
+    cascade_data = []
+
+    for z in z_values:
+        t_look = z_to_lookback(z)
+        N_z = cascade_clock(t_look, a_clock, B_DFT)
+        N_z = max(N_z, 1.0)
+
+        # Disequilibrium: 1.0 at integer N (transition), 0.0 at half-integer (settled)
+        dist_to_int = abs(N_z - round(N_z))
+        diseq = 1.0 - 2.0 * dist_to_int
+
+        # Map to perturbation fraction
+        diseq_frac = 0.01 + 0.19 * max(0, diseq)
+
+        lw = line_width_from_disequilibrium(adj, vertex=0,
+                                             disequilibrium_frac=diseq_frac,
+                                             n_trials=500, seed=42)
+
+        cascade_data.append({
+            'z': float(z),
+            't_lookback_gyr': float(t_look),
+            'N': float(N_z),
+            'disequilibrium': float(diseq),
+            'diseq_frac': float(diseq_frac),
+            'width_variance': float(lw['variance']),
+        })
+        print(f"    z={z:.1f}: N={N_z:.2f}, diseq={diseq:.3f}, width={lw['variance']:.6f}")
+
+    widths = [d['width_variance'] for d in cascade_data]
+    diseqs = [d['disequilibrium'] for d in cascade_data]
+
+    width_variation = (max(widths) - min(widths)) / np.mean(widths) if np.mean(widths) > 0 else 0
+    varies = width_variation > 0.01
+
+    rho, p_val = spearmanr(diseqs, widths)
+    correlated = abs(rho) > 0.9
+
+    print(f"    Width variation: {width_variation:.1%} (>1%: {varies})")
+    print(f"    Spearman rho(diseq, width): {rho:.3f} (>0.9: {correlated})")
+
+    passed = varies and correlated
+    print(f"    -> {'PASS' if passed else 'FAIL'}")
+
+    return {
+        'test': 'T3_epoch_dependent_widths',
+        'cascade_clock': {'a': float(a_clock), 'slope': float(slope)},
+        'cascade_data': cascade_data,
+        'width_variation': float(width_variation),
+        'spearman_rho': float(rho),
+        'spearman_p': float(p_val),
+        'PASS': passed,
+    }
+
+
+# ============================================================
+# T4: Clean PAC/SEC separation
+# ============================================================
+
+def test_T4_clean_separation(t2_result, t3_result):
+    """T4: Ratios don't drift (PAC), widths do (SEC)."""
+    print("\n  T4: Clean PAC/SEC separation")
+
+    # Ratio variability: should be zero
+    ratio_values = [d['graph'] for d in t2_result['transition_details']]
+    cv_ratios = np.std(ratio_values) / np.mean(ratio_values) if ratio_values else 0
+    ratio_invariant = cv_ratios < 0.05  # some variation from graph vs hydrogen
+
+    # Width variability across z
+    widths = [d['width_variance'] for d in t3_result['cascade_data']]
+    cv_widths = np.std(widths) / np.mean(widths) if np.mean(widths) > 0 else 0
+    width_varies = cv_widths > 0.01
+
+    # The key test: ratios are FIXED (no z-dependence by construction),
+    # widths VARY with z
+    ratio_spread_across_z = 0.0  # exactly zero — graph doesn't change
+    width_spread_across_z = (max(widths) - min(widths)) / np.mean(widths) if widths else 0
+
+    print(f"    Ratio spread across z: {ratio_spread_across_z:.6f} (PAC: invariant)")
+    print(f"    Width spread across z: {width_spread_across_z:.1%} (SEC: epoch-dependent)")
+    print(f"    Ratio CV: {cv_ratios:.6f}")
+    print(f"    Width CV: {cv_widths:.4f}")
+
+    separation = width_spread_across_z > 0.01 and ratio_spread_across_z < 1e-10
+
+    passed = separation
+    print(f"    -> {'PASS' if passed else 'FAIL'}")
+
+    return {
+        'test': 'T4_clean_separation',
+        'ratio_spread_across_z': float(ratio_spread_across_z),
+        'width_spread_across_z': float(width_spread_across_z),
+        'ratio_cv': float(cv_ratios),
+        'width_cv': float(cv_widths),
+        'separation': separation,
+        'PASS': passed,
+    }
+
+
+# ============================================================
+# Main
+# ============================================================
+
+if __name__ == '__main__':
+    print("=" * 70)
+    print("exp_03: Photon Archaeology")
+    print("Alpha Invariance and SEC-Encoded Line Widths")
+    print("Midnight Initiative, Thread 1")
+    print("=" * 70)
+
+    t1 = test_T1_alpha_invariance()
+    t2 = test_T2_epoch_invariant_ratios()
+    t3 = test_T3_epoch_dependent_widths()
+    t4 = test_T4_clean_separation(t2, t3)
+
+    score = sum(1 for t in [t1, t2, t3, t4] if t['PASS'])
+    print(f"\n{'=' * 70}")
+    print(f"  Overall: {score}/4")
+    print(f"{'=' * 70}")
+
+    data = {
+        'experiment': 'exp_03_photon_archaeology',
+        'initiative': 'midnight',
+        'thread': 'photon_archaeology',
+        'test_results': {'T1': t1, 'T2': t2, 'T3': t3, 'T4': t4},
+        'score': f"{score}/4",
+        'n_pass': score,
+        'n_total': 4,
+    }
+
+    save_midnight_results('exp_03_photon_archaeology', _convert_numpy(data))