atpx 0.0.1

Agentic mathematics workbench: every result is a certificate

🇧🇷 🇲🇽 🇯🇵 🇨🇳

Agentic mathematics workbench: every result is a certificate

atpx (Automatic Theorem Prover Accelerated, formerly published as prova) is the ledger underneath an agentic math loop. Every operation returns a Certificate stamping the claim, the result, the engine name and version, the hostname, device, seed, git revision, timestamp, and exit status. There are no naked results anywhere, no daemon, and no database, just three surfaces over one filesystem state.

1. Python API. atpx.workspace() returns a Workspace whose methods are the verbs.
2. CLI. atpx <verb> exposes the same methods through fire.
3. Filesystem. Blueprint directories hold per-host append-only evidence ledgers at evidence/<hostname>.json, and vault zettels carry node status.

Install

pip install atpx

For a persistent CLI install:

uv tool install atpx   # or: pipx install atpx

Use

A workspace root is any directory whose atpx.toml declares a [workspace] table pointing at the blueprints directory and the zettel vault.

atpx check <slug> <claim>      # run a blueprint claim, stamp + persist a certificate
atpx check <slug> <claim> --background   # detach it, the child persists the certificate
atpx checks <slug>             # background submissions, pending or landed
atpx verify [<slug>]           # freshness sweep, re-run cheap claims, flag stale evidence
atpx brief <slug>              # the full agent context bundle for one node, as markdown
atpx judge_brief <slug>        # what changed since the last refuter judgment
atpx status                    # nodes grouped by zettel status
atpx graph                     # open nodes whose dependencies are all settled
atpx recall '"<query>"'        # federated search, one certificate of hits per source
atpx connect <slug>            # OEIS lookups for integer runs in the node's evidence
atpx strategies                # close-rates by strategy tag over the append-only logs
atpx lean_candidates           # sketched nodes ranked for formalization
atpx log <zettel> <role> <tag> "message" --status sketched   # role-gated journal
atpx index --write             # regenerate the results index note
atpx compute <engine> <operation> <payload>                  # one typed engine op
atpx prove "<goal>"            # try ATP engines in order, certify who closed it
atpx cross_check <operation> <payload>   # same probe on independent engines

Status transitions are enforced in code, not prose. Only a refuter sets sketched or refuted and only the formalizer sets verified.

import atpx

ws = atpx.workspace()
certificate = ws.check("voronoi-e8-codec", "bijectivity-m1")
ws.cross_check("evaluate", "exp(pi*sqrt(163))")   # sympy vs mpmath, certified agreement
ws.recall("196560, 16773120")   # the Leech theta series turns up OEIS A008408

A blueprint claim is either a bare command string or a table with command and requires. A claim whose requirement this host cannot meet, requires = "cuda" on a machine without an NVIDIA driver, is skipped gracefully: the certificate says so and nothing enters the evidence ledger, since a skip is not a run.

[claims]
bijectivity-m1 = "python {dir}/checks.py bijectivity 1"

[claims.gaussian-ladder]
command = "python {dir}/checks.py claim3"
requires = "cuda"

Recall

recall fans one query out to every engine with the search capability and returns a single certificate listing the hits per source. A source that is unavailable or fails at run time becomes an entry under errors and the certificate exits nonzero, so a partial recall is never mistaken for a complete one. The network engines carry short timeouts and no API keys; loogle expects a Lean identifier or pattern such as Real.sqrt _ * _ and reports plain-English queries as errors.

Loop mechanics

These verbs exist because loop bookkeeping, not mathematics, is what slows an agentic prove-and-refute cycle down.

brief <slug> assembles the whole opening context in one command, the node text, its dependency statuses from the wikilink walk, the per-host evidence summary with stale flags against the current git revision, the last refuter judgment verbatim, and the blueprint file list, all as markdown on stdout.

judge_brief <slug> keeps re-judgment rounds cheap. Every refuter log line on a node with a blueprint snapshots the full node text into the blueprint's judgments/ directory (a verbatim snapshot rather than a hash or git, since it needs no repository around the vault and always yields a real diff). The verb then prints the unified diff since that snapshot plus the claims whose certificates landed after it.

check <slug> <claim> --background detaches the run in its own session with stdout under the blueprint's checks/ directory. The child stamps and persists the certificate exactly as a foreground check does, and checks <slug> reports each submission as pending or landed by reading the evidence ledgers. Remote stays composition, lote runs this same CLI on another host.

verify [<slug>] is the freshness sweep. It re-runs every claim this host can run (requires-gated claims it cannot meet are reported skipped), appends the fresh certificates, and flags claims whose latest prior certificate carries a git revision different from the tree now. Nothing is ever deleted.

strategies aggregates the [who/strategy date] journal lines across all nodes into close-rates per strategy tag, and lean_candidates ranks sketched nodes by backlink count over statement length. Both are v1 tables built on documented heuristics, no learning and no scoring model.

connect <slug> extracts integer runs from the node's persisted certificate payloads and queries each through the OEIS search engine via recall, ambient conjecture generation under the same certificate discipline.

Adversarial probes

atpx.adversarial is the refuter's typed toolkit, four reusable attack probes that turn folklore into one-liners.

from atpx.adversarial import boundary_ties, precision_tilt, rederive, seed_sensitivity

sweep = seed_sensitivity(lambda seed: run_check(seed), seeds=range(8))
assert sweep.stable, sweep.outcomes          # a nonzero spread is a refutation lead

ties = boundary_ties([[2, 0], [1, 1]])       # exact dyadic midpoints v/2, decoder tie bait
batches = precision_tilt(ties, [2**-20, 2**-30, 2**-40])   # verdicts must survive tilts

verdict = rederive(basis_a, basis_b)         # exact unimodular change-of-basis check
assert verdict.same_lattice, verdict.determinant

boundary_ties returns points exactly halfway between the origin and nearby lattice vectors, exactly representable in binary floating point, so a decoder must break the tie deterministically. rederive runs over exact rationals through flint and reports integrality and the determinant of the basis-change matrix.

Free threading

The parallel surfaces (recall sources, cross_check engines, the verify sweep) run on ThreadPoolExecutor, they are I/O and subprocess bound. Standard CPython 3.14 is the supported runtime; free-threaded 3.14t is currently blocked by one dependency and is not required for anything.

The table below was measured on cpython-3.14.3+freethreaded (macOS arm64, uv-managed, 2026-06).

dependency	free-threaded wheel	imports under PYTHON_GIL=0
pydantic-core	yes	yes, GIL stays off
z3-solver	yes	yes, GIL stays off
python-flint	yes (0.8.0)	yes, GIL stays off
cvc5	no (through 1.3.4, cp38-cp314 only)	n/a
sympy, mpmath, httpx, fire, plumbum, patos	yes	yes

uv pip install atpx on 3.14t therefore fails to resolve because of cvc5. With cvc5 stubbed out for the experiment, 130 of the 132 tests pass under PYTHON_GIL=0 (the two that exercise the real cvc5 solver cannot run), so the package itself is free-threading clean and the status flips to supported the moment cvc5 ships a cp314t wheel.

Engines

Engines self-register through a typed registry and stamp their name and version into every certificate. Each declares one capability.

engine	capability	availability
sympy	evaluate	always (hard dependency)
mpmath	evaluate	always (hard dependency)
flint	factor	always (hard dependency, python-flint)
pari	factor	linux only, and only when cypari2 is installed
z3	solve-smt	always (hard dependency, z3-solver)
cvc5	solve-smt	always (hard dependency)
eprover	prove-tptp	only when the eprover binary is on PATH
vampire	prove-tptp	only when the vampire binary is on PATH
vault	search	only when the chefe binary is on PATH
oeis	search	always, network EAFP at run time
loogle	search	always, network EAFP at run time
arxiv	search	always, network EAFP at run time
zbmath	search	always, network EAFP at run time

cypari2 is not a dependency because its wheel only installs cleanly on linux x86-64, so the pari engine reports unavailable everywhere else. The two first-order provers are subprocess engines and never Python dependencies.

The vault engine searches the Zettelkasten through qmd search inside the chefe env, the no-LLM BM25 surface, so recall never waits on a model download. The four web sources are keyless: OEIS by sequence values or words, loogle for mathlib declarations, arXiv full-field phrase search, and the zbMATH Open REST API, which answers without a key.

Documentation

Full documentation lives at https://phvv.me/atpx.

For LLM-assisted use, start with llms.txt.

Development

The dev environment is managed by uv.

• Install: uv sync --extra dev
• Lint: uv run ruff check . && uv run ruff format --check .
• Typecheck: uv run mypy src && uv run pyrefly check
• Test: uv run pytest -q
• Docs: uv run --extra docs mkdocs build -d site
• Build: uv build