# 2026-11-01 — ECDLP studies (Axis A/B, H04, H08–H12)

- Engine: `experiments/synthetic_ecdlp/rho_engine` (Rust, built by a sub-agent; 8 cargo tests, 553 pytest fixtures). Driver `ecdlp_study.py` generates instances with PARI/GP (laptop), `run_batch_remote.py` runs K engine processes on a node and records provenance there.
- Pilot (20 instances/size) on M3U96a + M2U64 showed noisy class speed-ups (CV ≈ 0.52 per instance); final runs use 60 instances/size (3 840 generic jobs on M3U96a in ≈ 5 min with 26 processes; 2 400 j=0 jobs on M2U64 in 56 s). Pilot files kept in `results/synthetic_ecdlp/pilot20/`.
- Bug found: `memory` must be a decimal string in the batch format (first tmto run failed; fixed and rerun).
- Parallel study moved from 48-bit (runs of 0.03 s at 28 threads, start-up dominated, efficiency 0.72) to 56-bit instances (8.8 s single-thread): 22.1× on 28 threads.
- Findings: rho constant 1.254·√n (theory 1.2533); α ∈ [0.478, 0.500]; order-6 orbits 2.42× in iterations (√6 = 2.449) but ≈ 1.0× in wall time in this engine (canonicalisation cost); negation alone 0.73× wall; BSGS 1.5·√n because the x-keyed table resolves ±j; DP-rho time–memory curve two-sided (restart cost vs overshoot).
- Classification: H04/H08/H10/H11 known_reproduced; H09 rejected shortcut (no iteration design beats the random-mapping constant); H12 known_reproduced (Python).