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v2_corrected_evaluation/IDENTITY_V2_REPORT_20260122_144008.md

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+# Identity Reconstruction V2: Fixed Evaluation
+
+**Date:** 2026-01-22T14:40:08.858456
+
+## Critical Fix
+
+The previous version had inverted PASS/FAIL logic:
+- ❌ Old: "PASS if curve is steep" (shape-based)
+- ✓ New: "PASS if preserved_rate >= 50% at K >= L/2" (performance-based)
+
+## Results
+
+### Collapsed (No Regularization)
+
+| Checkpoint | c6a8102da1ad8c77 |
+|------------|---|
+| tau range | [2.4, 9.8] |
+| tau mean | 6.6 |
+
+| K | Preserved Rate | Mean Retention |
+|---|----------------|----------------|
+| 0 | 100% ✓ | 100.0% |
+| 64 | 20% ✗ | 32.2% |
+| 128 | 0% ✗ | 15.1% |
+| 256 | 20% ✗ | 34.6% |
+| 512 | 20% ✗ | 28.7% |
+| 1,024 | 0% ✗ | 8.9% |
+| 2,048 | 0% ✗ | 23.7% |
+| 4,096 | 20% ✗ | 29.6% |
+| 8,192 | 20% ✗ | 27.9% |
+
+**Verdict:** FAIL
+**Basin Width:** 0 (0.0% of L=4096)
+**Explanation:** Identity collapses by K=0. No meaningful long-range coherence.
+
+### Regularized
+
+| Checkpoint | c3ca1ce88b2083bf |
+|------------|---|
+| tau range | [0.5, 6931.1] |
+| tau mean | 433.9 |
+
+| K | Preserved Rate | Mean Retention |
+|---|----------------|----------------|
+| 0 | 100% ✓ | 100.0% |
+| 64 | 100% ✓ | 88.2% |
+| 128 | 100% ✓ | 77.6% |
+| 256 | 100% ✓ | 67.4% |
+| 512 | 40% ✗ | 49.0% |
+| 1,024 | 0% ✗ | 29.8% |
+| 2,048 | 0% ✗ | 19.5% |
+| 4,096 | 0% ✗ | 15.5% |
+| 8,192 | 0% ✗ | 17.6% |
+
+**Verdict:** FAIL
+**Basin Width:** 256 (6.2% of L=4096)
+**Explanation:** Identity collapses by K=256. No meaningful long-range coherence.
+
+## Comparison
+
+| Metric | Collapsed | Regularized |
+|--------|-----------|-------------|
+| Verdict | FAIL | FAIL |
+| Basin Width | 0 | 256 |
+| Basin Width Ratio | 0.0% | 6.2% |
+
+**Improvement:** YES
+**Improvement Factor:** infx
+
+## Per-Oscillator Half-Lives
+
+### Collapsed
+```
+[8.191648388447712, 5.5110275180164185, 8.868783359291054, 7.578944232474908, 2.7534187831011967, 9.80497881309404, 8.08911761592282, 8.288514442215634, 3.0249090614043674, 5.603087503164535, 4.966384193860649, 9.414119910788811, 7.150920960645315, 8.582092906166643, 5.54731359061865, 3.8179097742782147, 6.436678296126676, 2.510538048833402, 8.62104937594066, 7.053315192976514, 8.064701920682985, 4.836207745038946, 9.765584195159231, 9.144968970577576, 8.227067976590098, 3.557109662815741, 5.733768029816274, 2.35043012629783, 3.234315936540382, 7.464391625939635, 7.958097247262541, 9.740077859473676]
+```
+
+### Regularized
+```
+[0.5986606020374855, 0.5028913517239931, 1.0160728924654787, 0.5986606020347446, 0.47764157767363097, 1.0160728924446252, 0.5986606020368003, 0.5986606020354299, 0.48694254072470705, 0.5028913517239931, 0.5028913517227875, 1.016072892460572, 0.47764157767363097, 0.7330948926419327, 0.5028913517179652, 0.5025812461450115, 0.7330948926535658, 6931.125226233421, 0.5028913517227875, 0.7330948926435946, 0.5986606020368003, 0.5028913517203764, 1.0160728924507585, 1.0160728924507585, 0.5986606020368003, 0.5025812461377809, 0.4869425407241158, 6931.125226233421, 0.4869425407264809, 4.8104604306517835, 0.5986606020368003, 1.0160728924507585]
+```
+
+## Honest Assessment
+
+The regularizer improves basin width, but the improvement is **marginal**.
+Basin width is still far below the sequence length.
+
+---
+
+*Report generated by identity_reconstruction_experiment_v2.py*