Midnight exp_07: Deep cascade probe — honest failure reveals z-confound (1/4)

Critical finding: z-detrending kills the MgII EW spread signal. After
removing a quadratic z-trend, cascade correlation goes from rho=0.29
(p=0.026) to rho=-0.02 (p=0.87). The exp_05 result was substantially
confounded with smooth z-evolution of EW distributions.

FeII subset (53K): same direction but p=0.12 (sample too small).
CIV Doppler b-parameter: cascade-correlated at p=0.004 (different ion,
different metric — harder to dismiss as z-trend).
Multi-ion confirmation: fails.

What still stands after this:
- Doublet coherence (exp_06, p=0.018) — inter-line coupling
- CIV Doppler b spread (p=0.004) — different physical quantity
- Population KS separations — overwhelming but may reflect selection

What doesn't stand:
- EW spread signal was mostly z-trend confound
- The clean p=0.007 from exp_05 was not cascade-specific

Honest failures are more valuable than false passes.

Author: lornecodes

foundational/experiments/midnight/README.md

@@ -2,7 +2,7 @@
 
 *Night removes the noise. Midnight sees the structure.*
 
-**Status**: Active | **Score**: 19/24
+**Status**: Active | **Score**: 20/28
 **Created**: 2026-06-03
 **Confidence**: 0.3 (exploratory)
 **Journals**:
@@ -186,6 +186,7 @@ Timeline and priorities TBD.
 | 02 | PAC Tree Correlation Profile | Phase-Rate | 3/4 | T1 PASS (conservation exact to 10^{-17}). T2 FAIL: correlation decay base = 1.13, not phi (30% off). The level-mean correlation doesn't decay as phi^(-delta) — the averaging across all nodes at each level washes out the phi structure. **Key finding:** the PAC tree is deterministic, so correlations come from the noise, not from the conservation structure directly. T3 PASS: Fibonacci-index separations DO show enhanced correlation above trend (mean residual +0.003 vs -0.001). T4 PASS: phi-split is closest to phi-decay of all tested splits (29.6% vs 33-36% for others), and all others are >10% from phi. Phi is privileged but the effect is subtle. |
 | 03 | Photon Archaeology | Photon Arch. | 4/4 | T1 PASS: alpha = 5.7 ppm from CODATA, 0.1% perturbation of any component breaks it by 8-181x. F7 is least sensitive (8x) because it only appears in the near-unity correction term. phi is a unique fixed point (phi^2-phi-1=0 to machine precision). T2 PASS: A_8 line ratios match hydrogen to 2.5%, identical at all z by construction (discrete graph topology). T3 PASS: **line widths vary 220% across z=[0.1,3]**, perfectly correlated with cascade disequilibrium (Spearman rho=1.000). Widths peak near cascade transitions (z=0.1: N≈2, z=0.3: N≈4) and collapse between (z=3: N=6.46, diseq=0.07). T4 PASS: clean PAC/SEC separation — ratio spread = 0, width spread = 220%. |
 | 04 | Cascade Width Oscillation | Photon Arch. | 4/4 | T1 PASS: five cascade transition redshifts mapped — N=2 at z=0.101, N=3 at z=0.171, N=4 at z=0.302, N=5 at z=0.579, N=6 at z=1.416. Troughs at half-integers correctly interleaved. T2 PASS: **5 oscillation cycles** in 150-point W(z) curve, all 5 peaks aligned with transition redshifts. Width range 0.001 to 0.336. T3 PASS: oscillatory model fits **24x better** than monotonic power law (chi2 ratio 24.1). Standard broadening cannot produce this. T4 PASS: width contrast 398x at every transition. Observable in CaII K (z<1), MgII (z=0.3-2.5), CIV (z=1-3.5). **Prediction: quasar absorption lines at z=0.101, 0.171, 0.302, 0.579, 1.416 should be hundreds of times broader than at adjacent half-integer-N redshifts.** |
+| 07 | Deep Cascade Probe | Photon Arch. | 1/4 | **HONEST FAILURE.** T1 FAIL: FeII subset (53K) same direction (rho=0.237) but p=0.12 — not significant with smaller sample. T2 PASS: CIV Doppler b spread correlates at **p=0.004** and KS p=10^{-157}, but EW spread does NOT correlate (rho=-0.113). T3 FAIL: **Z-DETRENDING KILLS THE SIGNAL.** MgII EW std vs diseq goes from rho=0.288 (p=0.026) to rho=-0.021 (p=0.87) after removing quadratic z-trend. The exp_05 result was substantially confounded with smooth z-evolution. T4 FAIL: no multi-ion confirmation. **Key finding: exp_05's EW spread signal (p=0.007) was partially a z-trend artifact. The doublet coherence (exp_06, p=0.018) and CIV b-param (p=0.004) remain — these are harder to explain as z-trend.** |
 | 06 | Doublet Coherence (SDSS) | Photon Arch. | 3/4 | **REAL DATA: doublet coupling oscillates with cascade.** T1 PASS: FWHM discrepancy anticorrelates with disequilibrium (rho=-0.334, **p=0.018**) — doublet lines LOCK together at cascade transitions, diverge between. T2 FAIL: cascade rho at 97.2nd percentile of shuffled (needs 0.05 on median). T3 PASS: inter-line FWHM correlation tighter at transitions (r=0.540) than troughs (r=0.453). T4 PASS: **KS separation p=10^{-11} (FWHM discrepancy), p=10^{-7} (doublet ratio), p=10^{-4} (FWHM ratio).** Transition absorbers: discrepancy 0.123 vs trough 0.134 — doublet 9% more coherent at transitions. |
 | 05 | Bifractal Mesh Signal (SDSS) | Photon Arch. | 3/4 | **REAL DATA: SDSS DR16, 89,851 absorbers, zero tuning.** T1 PASS: EW spread correlates with cascade disequilibrium — EW IQR rho=0.343 **p=0.0073**, EW std rho=0.290 p=0.025. Wider distributions at cascade transitions. T2 FAIL: FWHM kurtosis correlation suggestive (rho=-0.234, p=0.07) but doesn't reach significance. T3 PASS: cascade correlation above 99.5th percentile of shuffled controls. Plain z-correlation is stronger (rho=0.813) — cascade signal is a modulation ON TOP of z-trend. T4 PASS: **KS test: transition vs trough populations distinguishable at p=10^{-42} (EW) and p=10^{-30} (FWHM).** Transition absorbers: EW median 1.478 vs trough 1.357; FWHM median 178.7 vs 168.8. |
 

foundational/experiments/midnight/results/exp_07_deep_cascade_probe_20260606_231758.json

@@ -0,0 +1,72 @@
+{
+  "experiment": "exp_07_deep_cascade_probe",
+  "initiative": "midnight",
+  "thread": "photon_archaeology",
+  "data_sources": [
+    "SDSS DR16 FeII-confirmed MgII (69,675 systems)",
+    "SDSS DR12 CIV catalog (445,765 systems, Monadi+2023)",
+    "SDSS DR16 MgII full (159,524 systems)"
+  ],
+  "cascade_clock": {
+    "a": 1.36,
+    "slope": 2.0780869212350273
+  },
+  "test_results": {
+    "T1": {
+      "test": "T1_feii_subset",
+      "n_absorbers": 53025,
+      "n_bins": 45,
+      "ew_std_rho": 0.23675889328063238,
+      "ew_std_p": 0.11737436606165755,
+      "ew_iqr_rho": 0.15573122529644268,
+      "ew_iqr_p": 0.3070040266908792,
+      "PASS": false
+    },
+    "T2": {
+      "test": "T2_civ_high_z",
+      "n_absorbers": 443109,
+      "full_rho": -0.11346938775510206,
+      "full_p": 0.4326911145065587,
+      "high_z_rho": 0.08209121245828699,
+      "high_z_p": 0.666282464059791,
+      "b_param_rho": -0.3996638655462184,
+      "b_param_p": 0.004034309408885499,
+      "ks_ew": 0.13347341291477996,
+      "ks_ew_p": 1.6341262264265826e-157,
+      "ks_b": 0.6021948135027613,
+      "ks_b_p": 0.0,
+      "n_transition": 11647,
+      "n_trough": 76542,
+      "PASS": true
+    },
+    "T3": {
+      "test": "T3_detrended",
+      "n_bins": 60,
+      "rho_raw": 0.28824673520422345,
+      "p_raw": 0.02552140663547236,
+      "rho_detrended": -0.021116976938038347,
+      "p_detrended": 0.8727642431290874,
+      "detrend_strengthens": false,
+      "PASS": false
+    },
+    "T4": {
+      "test": "T4_multi_ion",
+      "p_values": {
+        "FeII MgII EW std": 0.11737436606165755,
+        "FeII MgII EW IQR": 0.3070040266908792,
+        "CIV full range": 0.4326911145065587,
+        "CIV high z": 0.666282464059791,
+        "CIV KS EW": 1.6341262264265826e-157,
+        "MgII detrended": 0.8727642431290874
+      },
+      "n_significant": 1,
+      "mgii_signal": false,
+      "civ_signal": true,
+      "both_ions": false,
+      "PASS": false
+    }
+  },
+  "score": "1/4",
+  "n_pass": 1,
+  "n_total": 4
+}