Pre‑Emergence Mechanics Framework (PEMF) — ARC‑AGI

Short summary
The Pre‑Emergence Mechanics Framework (PEMF) frames ARC tasks as a boundary‑constrained field problem solved by minimizing irreducible residue (o) under writability gates. PEMF implements four core primitives — Scalar Potential (+), Gradient Ordering (V), Residue (o), and Boundary Charge (p_q) — and composes atomic transforms (tile, shifted tile, fill_enclosed, rotate, reflect, etc.) in a beam search to drain residue and produce stable outputs.

Why this matters
PEMF shows how ARC tasks can be solved mechanically (o‑minimization + gates) rather than by symbolic heuristics. The approach maps CTS/ITT primitives to executable operators (potential fields, gradients, Dirichlet masks, complex projections) and yields a reproducible solver recipe.

Key concepts (one line each)

Scalar Potential (+): represent grid as numeric potential field (initialize_potential).
Gradient Ordering (V): discrete gradients direct admissible edits.
Residue (o): L1 misalignment after quantize+tile; objective to minimize.
Boundary Charge (p_q): Dirichlet boundary mask that enforces writability gates.
Layer‑1 diagnostics: complex projection (FFT imag component) to find latent edit zones when real signal is weak.

Files and examples

Skill artifacts: SKILLS/pre_emergence_mechanics_framework/ — howto, runnable example references/examples/verify_pemf.py, and README for the skill.
Postprocess logs: experiments/postprocess_logs.py — coerce gate booleans and attach candidate snapshots for offline inspection.
Headless entry: scripts/entrypoint.py — run experiments from CLI; --use_wandb flag is optional and defaults to off.

Quick verification (headless)

Run the PEMF example to verify primitives and a tiny compositional loop:

python SKILLS/pre_emergence_mechanics_framework/references/examples/verify_pemf.py

Run a single experiment (example):

python scripts/entrypoint.py --task example1 --out_dir experiments

Postprocess logs to attach candidate snapshot and coerce gates:

python experiments/postprocess_logs.py

Acceptance checks

verify_pemf.py prints a residue trace and reports at least one admissible edit zone from the complex projection.
experiments/*_phi_best.npy and experiments/*_logs.fixed.json exist after a run and contain candidate snapshot and boolean gates for inspection.

References and provenance This README summarizes the executable PEMF recipe derived from the ARC‑AGI exposition (PEMF / CTS / ITT). See SKILLS/pre_emergence_mechanics_framework/references/ for runnable examples and a step‑by‑step how‑to.