docs/P1_PARAMETERIZATION_DEEPDIVE.md

P1 Parameterization Deep-Dive

Date: March 7, 2026 Role: Evidence and rationale record Status: Supporting doc, not a live planning or contract SSOT

This document keeps the durable evidence behind the repaired low-dimensional P1 environment:

• 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

1. Structural Blocker

Symptom

The old 3-parameter action space:

• aspect_ratio
• elongation
• rotational_transform

could not satisfy the P1 constraints under the real constellaration verifier path.

Evidence

A 125-point grid sweep over the historical 3-knob range produced 0/125 feasible designs.

Observed behavior:

• average_triangularity stayed near +0.005
• p1_feasibility stayed near 1.00995
• varying n_field_periods did not resolve the blocker

Root Cause

generate_rotating_ellipse(aspect_ratio, elongation, rotational_transform, n_field_periods) does not meaningfully expose the Fourier mode that controls triangularity.

The historical rotational_transform range was also too low to reach the abs(edge_iota_over_nfp) >= 0.3 requirement reliably.

2. Original Winning Session

The original successful P1 path in ai-sci-feasible-designs did not rely on the raw 3-knob family alone.

The winning session:

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

Missing Fourth Knob

The historical script added tri_scale by injecting the m=2, n=0 Fourier mode after generating the base rotating-ellipse shape.

That missing triangularity control is the key reason the raw 3-knob family was structurally blocked.

Recovered Useful Ranges

The original script used substantially different useful ranges than the blocked runtime:

aspect_ratio:         [3.0, 3.6]
elongation:           [1.4, 2.2]
rotational_transform: [1.5, 2.2]
tri_scale:            [0.55, 0.8]

3. Harness Campaign Comparison

Recorded P1 campaign runs in ai-sci-feasible-designs also found zero feasible candidates.

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:

• 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

4. Recorded 4-Knob Sweep

A recorded 4-knob sweep using explicit triangularity injection showed that the repaired family can reach P1 feasibility.

Recorded sweep family:

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

What that sweep established:

• 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

5. Verifier Alignment Evidence

The current runtime verifier alignment is sound:

• 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

This matters because the repair belongs in the boundary family, not in redefined verifier semantics.

6. Reward Implications

The repaired family changes what is possible, but it does not justify a complicated reward.

The main reward conclusions remain:

• 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

7. Why The Environment Is Still Valid

The repaired 4-knob family is not a leaderboard-matching optimizer. That is acceptable for this repo.

The purpose of the environment is:

• teach and evaluate constrained design behavior
• keep the observation/action/reward loop legible
• preserve an explainable path from action to verifier feedback

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.

8. Design Implications Kept From This Analysis

• 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

9. Primary References

Fusion Design Lab:

• server/physics.py
• server/environment.py
• fusion_lab/models.py
• docs/P1_ENV_CONTRACT_V1.md

Reference repo:

• 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