1# CLAUDE.md — UQO Working Paper 3423**BEYOND THE SQUARE-ROOT BARRIER — Automated Discovery of Algebraic and Algorithmic Shortcuts in Bitcoin Cryptography**45Project: WP34-UQO · Institution: Université du Québec en Outaouais · Author: Simon-Pierre Boucher6Research domain: mathematical cryptography, computational number theory, algorithm discovery, automated scientific research.7Target: a publication-quality theoretical and experimental research paper (English). Research mode: autonomous,8hypothesis-driven, reproducible computational research.910The complete mandate (sections 1–19 as pasted by the author on 2026-11-01) is archived verbatim in `docs/MANDATE.md`.11This file is the operational summary used by Claude Code while working in this repository.1213## Mission (short form)1415Investigate whether unexplored mathematical structures, algebraic transformations, algorithmic reductions or computational16strategies can improve on established methods for: the ECDLP, the structure of secp256k1, ECDSA, BIP340 Schnorr, SHA-256,17and the relations between curve arithmetic and hash functions. **Do not assume shortcuts exist.** A carefully documented18failed hypothesis is a valid result. Every result is classified as one of: new verified result · known result independently19reproduced · conditional result · empirical observation · rejected conjecture · unresolved direction. Never describe a20constant-factor optimisation as a cryptographic break.2122## Integrity boundaries (non-negotiable)2324- Experiments run only on synthetic instances, reduced-security constructions, or keys generated for the experiments.25- No real Bitcoin/Ethereum wallets, live addresses, third-party public keys, deployed systems, blockchain scanning.26- Full-strength standards are analysed theoretically and benchmarked through legitimate implementations only.27- Every experiment preserves what is needed for independent replication (seed, parameters, host, versions, command).28- Never claim an experiment ran unless the command actually ran and its outputs are saved under `results/`.2930## Repository conventions3132- Python environment: `.venv` (uv, Python 3.12) — run everything with `.venv/bin/python`.33- Reusable exact-arithmetic code: `src/wp34/` (pure Python integers, no floats in field arithmetic).34- Native engines: Rust crates under `experiments/<family>/<crate>/` (built with `cargo build --release`).35- Experiments: `experiments/<family>/` scripts; each writes `results/<family>/<name>.json` with the provenance block36 produced by `wp34.provenance.record()` (host, cpu, ram, os, versions, seed, command, timestamp).37- Hypotheses: `hypotheses/HNN-<slug>.md` with YAML front matter (axis, status, classification) — one file per hypothesis.38- Literature: `literature/` (structured database `literature/db.yaml` + `paper/references.bib`, every entry verified).39- Formal: `formal/` Lean 4 project (`lake build` must pass; machine-checked statements listed in `formal/README.md`).40- Research log: `research_log/` dated entries + `research_log/discovery_log.jsonl` (one JSON line per evaluated hypothesis).41- Figures: generated by scripts into `figures/` and copied to `paper/figures/`; tables into `paper/tables/`.42- Paper: `paper/main.tex` (UQO series template, pdflatex + bibtex/aer.bst, `make` in `paper/`).43- Tests: `tests/` (pytest) — cross-implementation agreement is a gate for every arithmetic component.44