| # P1 Parameterization Deep-Dive |
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| **Date:** March 7, 2026 |
| **Role:** Evidence and rationale record |
| **Status:** Supporting doc, not a live planning or contract SSOT |
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| This document keeps the durable evidence behind the repaired low-dimensional `P1` environment: |
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| - why the historical 3-knob family failed |
| - what the original winning session actually did |
| - what the recorded 4-knob sweep proved |
| - why the current environment is intentionally a playable stepping stone rather than a leaderboard-matching optimizer |
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| ## 1. Structural Blocker |
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| ### Symptom |
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| The old 3-parameter action space: |
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| - `aspect_ratio` |
| - `elongation` |
| - `rotational_transform` |
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| could not satisfy the `P1` constraints under the real `constellaration` verifier path. |
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| ### Evidence |
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| A 125-point grid sweep over the historical 3-knob range produced `0/125` feasible designs. |
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| Observed behavior: |
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| - `average_triangularity` stayed near `+0.005` |
| - `p1_feasibility` stayed near `1.00995` |
| - varying `n_field_periods` did not resolve the blocker |
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| ### Root Cause |
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| `generate_rotating_ellipse(aspect_ratio, elongation, rotational_transform, n_field_periods)` does not meaningfully expose the Fourier mode that controls triangularity. |
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| The historical `rotational_transform` range was also too low to reach the `abs(edge_iota_over_nfp) >= 0.3` requirement reliably. |
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| ## 2. Original Winning Session |
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| The original successful `P1` path in `ai-sci-feasible-designs` did not rely on the raw 3-knob family alone. |
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| The winning session: |
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| 1. built a low-dimensional sweep with a fourth knob |
| 2. found feasible seeds quickly |
| 3. refined around those seeds with stronger optimizers |
| 4. used leaderboard-quality anchors later in the pipeline |
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| ### Missing Fourth Knob |
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| The historical script added `tri_scale` by injecting the `m=2, n=0` Fourier mode after generating the base rotating-ellipse shape. |
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| That missing triangularity control is the key reason the raw 3-knob family was structurally blocked. |
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| ### Recovered Useful Ranges |
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| The original script used substantially different useful ranges than the blocked runtime: |
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| ```text |
| aspect_ratio: [3.0, 3.6] |
| elongation: [1.4, 2.2] |
| rotational_transform: [1.5, 2.2] |
| tri_scale: [0.55, 0.8] |
| ``` |
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| ## 3. Harness Campaign Comparison |
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| Recorded `P1` campaign runs in `ai-sci-feasible-designs` also found zero feasible candidates. |
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| That failure does not disprove the repaired low-dimensional path. It mostly shows that the campaign guidance and search style diverged from the winning approach: |
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| - the campaigns pushed the agent away from broad low-dimensional exploration |
| - the winning session did broad sweeps and large early moves |
| - the campaign path used richer Fourier candidates, but not the same successful cold-start behavior |
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| ## 4. Recorded 4-Knob Sweep |
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| A recorded 4-knob sweep using explicit triangularity injection showed that the repaired family can reach `P1` feasibility. |
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| Recorded sweep family: |
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| ```text |
| aspect_ratio: [3.2, 3.8] |
| elongation: [1.2, 1.8] |
| rotational_transform: [1.2, 1.8] |
| tri_scale: [0.4, 0.7] |
| n_field_periods: 3 |
| mpol / ntor: 3 / 3 |
| ``` |
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| What that sweep established: |
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| - explicit triangularity control fixes the structural blocker |
| - repaired-family feasibility is reachable in principle |
| - repaired-family defaults still need measured calibration before they should be narrated as stable |
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| ## 5. Verifier Alignment Evidence |
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| The current runtime verifier alignment is sound: |
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| - the official `GeometricalProblem` API is used for feasibility and objective semantics |
| - score conversion matches the official `P1` objective direction |
| - the runtime split is boundary-based: build boundary first, then evaluate boundary |
| - low-fidelity `run` and high-fidelity `submit` are treated as separate truth surfaces |
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| This matters because the repair belongs in the boundary family, not in redefined verifier semantics. |
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| ## 6. Reward Implications |
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| The repaired family changes what is possible, but it does not justify a complicated reward. |
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| The main reward conclusions remain: |
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| - keep reward tied to official verifier scalars |
| - keep feasibility-first behavior |
| - do not add per-constraint or knob-specific shaping |
| - tune from playtest evidence, not from theory alone |
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| ## 7. Why The Environment Is Still Valid |
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| The repaired 4-knob family is not a leaderboard-matching optimizer. That is acceptable for this repo. |
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| The purpose of the environment is: |
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| - teach and evaluate constrained design behavior |
| - keep the observation/action/reward loop legible |
| - preserve an explainable path from action to verifier feedback |
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| The winning high-fidelity score chase used a much richer downstream optimization story. This repo does not need to reproduce that full pipeline to be a valid hackathon environment artifact. |
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| ## 8. Design Implications Kept From This Analysis |
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| - keep multiple frozen reset seeds rather than one memorized starting state |
| - keep reward based on official scalars rather than hand-coded constraint bonuses |
| - keep known winners as calibration fixtures, not direct reward targets |
| - keep domain knowledge in seeds and fixtures, not in opaque reward tricks |
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| ## 9. Primary References |
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| Fusion Design Lab: |
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| - [`server/physics.py`](../server/physics.py) |
| - [`server/environment.py`](../server/environment.py) |
| - [`fusion_lab/models.py`](../fusion_lab/models.py) |
| - [`docs/P1_ENV_CONTRACT_V1.md`](P1_ENV_CONTRACT_V1.md) |
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| Reference repo: |
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| - `ai-sci-feasible-designs/docs/harness/raw-session.md` |
| - historical `scripts/search_p1_lowdim.py` |
| - `ai-sci-feasible-designs/docs/P1_SCORE_CHASE_NOTES.md` |
| - `P1_CAMPAIGN_POSTMORTEM.md` |
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