# CLAUDE.md — UQO Working Paper 34

BEYOND THE SQUARE-ROOT BARRIER — Automated Discovery of Algebraic and Algorithmic Shortcuts in Bitcoin Cryptography

Project: WP34-UQO · Institution: Université du Québec en Outaouais · Author: Simon-Pierre Boucher Research domain: mathematical cryptography, computational number theory, algorithm discovery, automated scientific research. Target: a publication-quality theoretical and experimental research paper (English). Research mode: autonomous, hypothesis-driven, reproducible computational research.

The complete mandate (sections 1–19 as pasted by the author on 2026-11-01) is archived verbatim in docs/MANDATE.md. This file is the operational summary used by Claude Code while working in this repository.

# Mission (short form)

Investigate whether unexplored mathematical structures, algebraic transformations, algorithmic reductions or computational strategies can improve on established methods for: the ECDLP, the structure of secp256k1, ECDSA, BIP340 Schnorr, SHA-256, and the relations between curve arithmetic and hash functions. Do not assume shortcuts exist. A carefully documented failed hypothesis is a valid result. Every result is classified as one of: new verified result · known result independently reproduced · conditional result · empirical observation · rejected conjecture · unresolved direction. Never describe a constant-factor optimisation as a cryptographic break.

# Integrity boundaries (non-negotiable)

• Experiments run only on synthetic instances, reduced-security constructions, or keys generated for the experiments.
• No real Bitcoin/Ethereum wallets, live addresses, third-party public keys, deployed systems, blockchain scanning.
• Full-strength standards are analysed theoretically and benchmarked through legitimate implementations only.
• Every experiment preserves what is needed for independent replication (seed, parameters, host, versions, command).
• Never claim an experiment ran unless the command actually ran and its outputs are saved under results/.

# Repository conventions

• Python environment: .venv (uv, Python 3.12) — run everything with .venv/bin/python.
• Reusable exact-arithmetic code: src/wp34/ (pure Python integers, no floats in field arithmetic).
• Native engines: Rust crates under experiments/<family>/<crate>/ (built with cargo build --release).
• Experiments: experiments/<family>/ scripts; each writes results/<family>/<name>.json with the provenance block produced by wp34.provenance.record() (host, cpu, ram, os, versions, seed, command, timestamp).
• Hypotheses: hypotheses/HNN-<slug>.md with YAML front matter (axis, status, classification) — one file per hypothesis.
• Literature: literature/ (structured database literature/db.yaml + paper/references.bib, every entry verified).
• Formal: formal/ Lean 4 project (lake build must pass; machine-checked statements listed in formal/README.md).
• Research log: research_log/ dated entries + research_log/discovery_log.jsonl (one JSON line per evaluated hypothesis).
• Figures: generated by scripts into figures/ and copied to paper/figures/; tables into paper/tables/.
• Paper: paper/main.tex (UQO series template, pdflatex + bibtex/aer.bst, make in paper/).
• Tests: tests/ (pytest) — cross-implementation agreement is a gate for every arithmetic component.