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routing/ROUTING_REPORT.md
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# Routing Experiment: τ-Weighted Identity Encoding
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**Date:** 2026-01-22T15:10:07.345243
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## Question
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Does preferentially routing identity to long-τ oscillators improve basin width?
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## Conditions
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| Condition | Distribution | Routing | Description |
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|-----------|-------------|---------|-------------|
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| A | Collapsed | Uniform | Baseline |
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| B | Anchored-tail | Uniform | Distribution fix only |
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| C | Anchored-tail | τ-Weighted | Distribution + soft routing |
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| D | Anchored-tail | τ-Gated | Distribution + hard routing |
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## Results
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### Basin Width (50% threshold)
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| Condition | Basin Width | Ratio |
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|-----------|-------------|-------|
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| A) Collapsed + Uniform | 0 | 0.0% |
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| B) Anchored + Uniform | 1024 | 25.0% |
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| C) Anchored + τ-Weighted | 4096 | 100.0% |
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| D) Anchored + τ-Gated | 4096 | 100.0% |
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### Preservation Curves
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#### A) Collapsed + Uniform
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| K | Preserved Rate | Mean Retention |
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|---|---|---|
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| 0 | 100% | 100.0% |
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| 64 | 10% | 23.2% |
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| 128 | 10% | 23.7% |
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| 256 | 8% | 21.3% |
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| 512 | 5% | 17.1% |
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| 1024 | 10% | 22.2% |
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| 2048 | 8% | 21.1% |
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| 4096 | 5% | 23.4% |
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#### B) Anchored + Uniform
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| K | Preserved Rate | Mean Retention |
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|---|---|---|
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| 0 | 100% | 100.0% |
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| 64 | 100% | 95.5% |
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| 128 | 100% | 91.6% |
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| 256 | 100% | 85.1% |
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| 512 | 95% | 72.1% |
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| 1024 | 65% | 56.9% |
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| 2048 | 45% | 47.1% |
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| 4096 | 22% | 32.6% |
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#### C) Anchored + τ-Weighted
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| K | Preserved Rate | Mean Retention |
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|---|---|---|
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| 0 | 100% | 100.0% |
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| 64 | 100% | 99.6% |
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| 128 | 100% | 99.3% |
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| 256 | 100% | 98.7% |
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| 512 | 100% | 97.0% |
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| 1024 | 100% | 93.2% |
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| 2048 | 100% | 87.2% |
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| 4096 | 100% | 72.9% |
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#### D) Anchored + τ-Gated
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| K | Preserved Rate | Mean Retention |
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|---|---|---|
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| 0 | 100% | 100.0% |
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| 64 | 100% | 99.7% |
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| 128 | 100% | 99.4% |
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| 256 | 100% | 98.8% |
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| 512 | 100% | 97.3% |
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| 1024 | 100% | 93.8% |
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| 2048 | 100% | 88.1% |
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| 4096 | 100% | 74.4% |
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## Conclusion
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**Verdict: ROUTING_SOLVES**
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τ-weighted or τ-gated encoding achieves basin width >= 2048.
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Routing was the bottleneck. Identity must be written to slow modes.
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Next step: Implement routing during training.
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---
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*Report generated by identity_routing_experiment.py*
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