Primus — the installable seed

Author: Jacob Iannotti. Licensed under PolyForm Noncommercial 1.0.0 — free to use, modify, and share for any noncommercial purpose; commercial rights reserved (see the repository-root LICENSE.md).

Primus is the clean, auditable core of the whole vault, now shipped as a Python package: exact invariant recovery with held-out verification and refusal — plus that discipline turned into an accountability certificate for LLM/agent output. One idea: never certify what you cannot exactly verify.

From the vault root (PyPI name: primus-intelligence):

pip install ./Primus

Two operations

collapse — recover the minimal generator beneath a codified surface (numbers, text, ciphers, graphs, schemas, code) under a two-part MDL criterion in exact arithmetic. Verified means one thing only: the rule exactly predicted held-out data it never saw. Anything else is an honest residual, never a confident guess.

from primus import collapse
inv = collapse([1, 1, 2, 3, 5, 8, 13, 21])
inv.verified        # True — held-out terms predicted exactly
inv.explanation     # what was recovered, why it is believed

certify — the front door for the agent era: feed it a model's output, and every checkable claim comes back VERIFIED, REFUTED, or REFUSED; the free-text remainder is reported as unverifiable, never blessed. Checkable kinds (schema primus.certificate/2, contract in SCHEMA.md, shipped in the licensed vault): exact arithmetic incl. powers, percentages, primality, binomials, gcd/lcm, modular and date arithmetic, sums/averages, sequence continuations, and integer runs. Gate an agent on refuted == 0, then read coverage before trusting the pass — a passing gate means nothing checkable was refuted, never the output is true.

from primus import certify
cert = certify("2+2=5. The sequence 2 4 6 8 continues as 10, 12.")
cert["counts"]      # {'checkable': 2, 'verified': 1, 'refuted': 1, 'refused': 0}

The second line exits 1 on any refuted claim — pipe your model's output in place of the example text:

primus collapse "1 1 2 3 5 8 13 21"
echo "17*3 = 51 and 2+2 = 5" | primus certify - --json --gate
primus selftest

Guess-and-prove — primus.conjecture (optional)

The symbolic-regression baseline this project benchmarks against (SYMREG_RESULTS.md) can also serve it: primus conjecture "0 1 128 2187 …" lets a gplearn genetic-programming proposer suggest closed forms for an input the engine refuses — and stamps a candidate ONLY if, after snapping its float constants to exact integers/rationals, it reproduces every supplied term exactly in rational arithmetic, including a holdout suffix the search never saw. The stochastic proposer never stamps; the exact verifier does, and the certificate says exactly what was proven (fit to the given data — never the true generator). Without pip install primus-intelligence[conjecture] the stage degrades to an honest REFUSED. A verified conjecture emits the claim a(n) = <expr> matches <terms>, which the certify gate checks independently as the closed_form claim kind — guess-and-prove output round-trips through the gate. On the live OEIS corpus the gate converted the raw regressor's 27 wrong answers into 26 refusals + 3 exact stamps, with zero stamped-wrong (SYMREG_RESULTS.md).

The MCP server — the gate as agent infrastructure

primus-mcp serves both operations over the Model Context Protocol (stdio, dependency-free), so any MCP-speaking agent can call the verifier natively — certify its own draft answer, gate on counts.refuted == 0, and treat the unverifiable remainder as exactly that.

primus-mcp speaks newline-delimited JSON-RPC on stdio; the second line registers it with Claude Code:

primus-mcp
claude mcp add primus -- primus-mcp

Claude Desktop / Cowork (claude_desktop_config.json → mcpServers):

{ "primus": { "command": "primus-mcp" } }

Tools exposed: certify(text) → the full certificate as structured content; collapse(surface) → the invariant (or an honest refusal). A refuted claim is a result, not a tool error — isError is reserved for real failures. Protocol conformance is gated by python3 test_mcp_server.py (10 handshake gates against the live subprocess).

The code

src/primus/engine.py — the seed, and the single source of truth (~1,250 lines). The novel part by itself, easy to read and audit in one sitting: collapse, same_generator, cast, transcode, the twin spaces. invariant_engine.py at this folder's root is a compatibility shim so every historical entry point still works.

src/primus/certify.py — the certificate layer: claim extraction (arithmetic, percentages, sequence continuations, integer runs), exact checking through the engine, four-way honesty (verified / refuted / refused / unverifiable), SHA-256 attestation.

src/primus/cli.py — the primus command.

The full integrated system — certification core, intake standardizer, ambiguity crucible, field substrate, organism layer, and this engine as its invariant operation — is Chiron: ../Chiron/chiron.py. There is one program, Chiron; this folder is where its engine began and the clearest place to read the idea in isolation.

The proof

test_invariant_engine.py — the stress tests (48/48). Run it to confirm everything works on your machine.

python3 test_invariant_engine.py

benchmark.py — the proving run: feeds the engine known-generator sequences, shows it part of each, and grades whether the rule it recovered predicts terms it never saw. Results in the reconciled battery map: recovery 98%, precision 100%, zero false confidence.

oeis_live.py — the external proving run: the same held-out discipline against sequences fetched live from OEIS rather than a self-generated bank. Results and the honest miss list in the public external eval.

bench_symreg_external.py / bench_pysr.py — head-to-head against established symbolic-regression baselines (gplearn results in docs/SYMREG.md; PySR harness included, runs wherever PySR is installed).

test_certify_fuzz.py — adversarial gates: hostile input must crash nothing, respect every work bound, and never flip a planted verdict. The fuzzer has already earned its keep twice (a sequence-flood DoS and a quadratic scan cost, both found and fixed — see CHANGELOG.md, shipped in the licensed vault).

test_mcp_server.py — the MCP protocol handshake against the live subprocess.

drift_check.py — differential testing against ../Chiron/chiron.py: contradictions between the seed and the monolith fail the build; deliberate capability differences must be ledgered with a dated reason.

The background

Primus Flow Chart.svg — the system diagram: the cells and every level of the organism the engine grew into, laid out visually.

The Caramuel Primus Calamus (1663) source material — the book with the twin labyrinths the engine uses as built-in ground truth — lives with the ambiguity work in ../Infectatrum.

Requirements

Python 3.9+ with numpy. Everything runs offline; no network, no API keys (oeis_live.py is the one deliberate exception — it exists to fetch external ground truth). __pycache__ folders are auto-generated and safe to delete. The guess-and-prove stage (primus.conjecture) optionally uses gplearn + scikit-learn (pip install primus-intelligence[conjecture]); absent, it refuses honestly and everything else is unaffected.