factorlab and latticelab

Code, tests and archived results behind two technical reports by Sean Ward and Maestro (iGent AI, 2026), distributed separately as PDFs:

• Floors for deterministic integer factoring: covering models, partial information, the additive structure of the Lehman–Harvey start set, and three further floors — a covering model containing Harvey's exponent-one-fifth algorithm, its floors $N^{1/3}$, $N^{1/5}$ and $N^{1/6}$ and their robustness; sharp floors and matching algorithms given partial information about a factor; the additive structure of the window starts that any explicit difference cover must respect; a deterministic curve for moduli whose $p-1$ and $q-1$ share a large factor; exposure labels for a fixed list of elliptic curves; coefficient floors for number-field-sieve polynomial selection.
• Certified conditional profile optima for block reduction, and the Kyber round-3 primal chain re-evaluated — a linear programme over Gram–Schmidt profiles under the block Gaussian-heuristic inequalities, its exact dual certificates, the prefix-volume floor, the round-3 Kyber primal chain re-evaluated with certified crossings, and an audit of the class on real reduced bases.

Every measured or certified statement in either report has a row in REPRODUCING.md naming the function that produced it, the archive under results/ that holds it, and the command that regenerates it. Nothing here is a lower bound on factoring or on attacking a deployed scheme; every floor is a theorem inside a stated model, and the reports say so.

Layout

path	contents
factorlab/	the factoring harness: numth (gmpy2 primitives), gen (seeded semiprime generation by rejection sampling), result/registry/audit/bench (work counters, factor validation, registration, benchmarks), algorithms/ (trial division, Fermat, Lehman, Hart, SQUFOF, Pollard rho, Pollard–Strassen, babystep–giantstep on $p+q$, ECM, a quadratic sieve, Schnorr–Lenstra class groups, a deterministic fixed-list ECM), experiments/ (one module per experiment of the factoring report; each has a __main__ or a run_* driver)
latticelab/	the lattice arm: profile_floor (the profile floor, its $O(d)$ exact dual certificate, interval-arithmetic decisions), check_certificate (an independent checker), spec_chain (the round-3 chain and the detection chain with certification), head_slack, uniform_slack, qceiling (the $q$-ary ceiling, the head-clipped extremal profile, the dual route), simulator_chain (the detection condition on Chen–Nguyen and Bai–Stehlé–Wen simulated profiles), certify_audit and audit_detection (exact certification of the audit bases and their weighted deficits), dual_census, residual, insertion, schedule_game, poisson_world, lattices, sieve, profile
tests/	the test suite (python -m pytest -q; 366 tests, about a minute)
results/	the archives: JSON and JSONL outputs of every experiment and certification named in the reports, with the logs of the long runs; these are the datasets of the release
REPRODUCING.md	statement → producing function → archive → command, for both reports
requirements.txt	the pinned Python stack the archives were produced with
CITATION.cff	how to cite

Installation

Ubuntu 24.04, Python 3.12. System packages for the lattice arm (fpylll):

sudo apt-get install -y libfplll-dev fplll-tools libgmp-dev libmpfr-dev libqd-dev

Python stack, pinned to the versions the archives were produced with:

python3 -m pip install --user -r requirements.txt

fpylll's pruned reduction needs its strategies file; if SVP.shortest_vector or pruned BKZ reports "Cannot open strategies file", link the system file into the path fpylll expects:

sudo mkdir -p /project/local/share/fplll/strategies
sudo ln -s /usr/share/libfplll8/strategies/default.json /project/local/share/fplll/strategies/default.json

On macOS the binary wheel's strategies path points into its own build tree (/Users/runner/work/fpylll/...), so the symlink does not apply and exact-SVP calls raise FileNotFoundError (the suite crashes in tests/test_schnorr_lattice.py). Install fplll with Homebrew (brew install fplll) and reinstall fpylll from its source distribution against that library, e.g. pip install --no-binary fpylll --force-reinstall fpylll==0.6.4 with Homebrew's include and lib directories on CFLAGS/LDFLAGS if the build does not find them; the suite then passes on arm64 with Python 3.12.

Run the tests from the repository root:

python3 -m pytest -q

Reproducing

REPRODUCING.md gives, for each statement, an executed command. Short computations run in seconds to minutes; the long ones (exhaustive certification of the detection chains, the strict-tour censuses, the head-slack and uniform-slack certificates) take hours and write their archives incrementally. All work is counted in machine-independent units (modular multiplications, gcds, candidates, babies and giants, BKZ tours, oracle calls), never wall time, and every experiment is seeded; seeds are in the reproduction guide and in the archives.

Conventions

• Certified means an exact rational dual certificate together with interval (ball) arithmetic from exact rational inputs and a directed comparison; a double-precision scan is a pre-screen and is labelled as such. A dual-feasible bound certifies a failure, never a pass; a pass needs a primal witness.
• Archives record exact values where the computation is exact (integers, rationals, ball endpoints as exact rationals) and say where floating point was used.
• Every negative literature claim in the reports names the nearest related work; every priority claim was searched on the statement.

Authors and citation

Sean Ward and Maestro, iGent AI. Maestro is a research system; the work was produced in an interactive session and every result was checked by computation and by adversarial review before it entered a report. See CITATION.cff.

Licence

MIT; see LICENSE. The licence covers the code and the archived results alike.