NAMM (Non-Anthropic Mathematics Mode) is a verification-first research program testing whether machine-native artifacts can certify mathematical structure before compact human projection exists.
Anthemium + NAMM: Anthemium (AGI cognitive frame from the May 2025 AGI Manifesto) directs machine-native discovery; NAMM executes the verification-first experiment cycle — certificates, frame escalation, open-problem shadows. See
docs/ANTHEMIUM_NAMM_SYNERGY.md.
Research governance: AI-led search under human-set falsifiability gates — the author defines acceptance criteria and attack checklists; the AI researcher allocates search budget across domains. See docs/RESEARCH_DIRECTION.md.
Author: Roman Kuznetsov · NAMM research program · Project site · AGI Manifesto
Updates & discussion: https://x.com/agiminister
Lineage: NAMM experiments develop the Anthemium research program — operationalizing the May 2025 AGI Manifesto as falsifiable runs under Protocol v2. Synergy is Anthemium + NAMM — machine-native discovery directed by the Anthemium cognitive frame, executed via NAMM verification cycles. See docs/ANTHEMIUM_LINEAGE.md and docs/ANTHEMIUM_NAMM_SYNERGY.md.
NAMM tests a falsifiable claim, not a metaphysical proof:
Machine-native search can surface structures whose canonical form is a verified program or certificate, with compression asymmetry (K_A \ll K_H), independence from named baselines, and generative power on held-out families — before a compact human formula exists.
We report computational evidence under explicit gates. Negative and null results are first-class (rejections.jsonl). We claim methodology and reproducible experiments — not breakthrough theorems.
Research targets (Anthemium-led queue): 11D configuration shadows, M-theory moduli enumeration, trans-level Θ (semantic transition algebra over raw structure), and open-problem shadows (Kotzig (P_k)-graphs, Graceful Tree conjecture as calibration). Some descriptive levels lie beyond anthropic projection reach — humans discover via bounded projections; NAMM searches frames where compact human notation may not exist yet.
| Layer | Content | Status |
|---|---|---|
| Operational | SNH gates, certificate.json, independence checks, generative holdout, novelty ladder |
Executable; see docs/PROTOCOL_V2.md |
| Philosophical | Structure as discovery, not invention; MUH widens search space; ND frames as metaphors mapped to formal math | PHILOSOPHICAL_INFERENCE — non-evidential; not a proof premise |
Mathematical structures may exist at descriptive levels beyond anthropic projection reach. Humans access structure through bounded projections; machine-native search operates in different representational frames. Whether non-anthropic artifacts certify structure humans cannot yet compress is empirically testable via (K_A/K_H) and certificate reproducibility — not settled by metaphysics alone.
Credit: formulation by project author (agiminister on X). Label PHILOSOPHICAL_INFERENCE.
Humans access structure through anthropic projections ((\pi_H)): formulas, diagrams, prose. Machine search operates in different representational frames ((\pi_A)): AST programs, rewrite systems, relation tensors. Verification-first discovery anchors both in certificate.json.
Consolidated concept reference: docs/NON_HOMO_SYNTAX_AND_ND_FRAMES.md (non-anthropic syntax and ND frames). Philosophy detail: docs/PHILOSOPHY.md.
Mathematical structures may exist that are natural for machine cognition before anthropic projection — easier to search, verify, and compose as certificates or AST programs than to name in classical notation. Max Tegmark's Mathematical Universe Hypothesis (MUH) is used only as philosophical motivation to widen the search space; it is not a proof premise.
| Phase | Focus | Priority | Status |
|---|---|---|---|
| 001 | Finite graph invariant search (string formulas, baselines) | Closed | NAMM-2026-001 — calibration null result |
| 002 | String rewriting systems, confluence search, certificate-first | P2 | NAMM-2026-002 |
| 003 | Program AST synthesis (Graph → Int), evolutionary search | P1 | NAMM-2026-003 |
| 004 | Meta-evaluator fixed points under AI thinking topology | P3 | NAMM-2026-004 |
| 005 | Open-problem finite shadow — Kotzig (P_k)-graph counterexample search | P2 | NAMM-2026-005 |
| 006 | ND frame — TDA persistence on graph geodesic metric | P4 | NAMM-2026-006 — TDA frame scaffold |
| 007 | Raw tensor invariants — machine-native vocabulary (F3g) | P1 | NAMM-2026-007 — first operational signal |
| 008 | Open-problem shadow — Graceful Tree conjecture | P2 | NAMM-2026-008 |
| 009+ | 11D shadows, M-theory moduli, trans-level Θ | Planned | Anthemium-led queue — see docs/ANTHEMIUM_NAMM_SYNERGY.md |
| Protocol v2 | Hard acceptance gates, rejection logging, attack checklist | — | docs/PROTOCOL_V2.md |
| CI | pytest + smoke search on every push to main |
— | .github/workflows/ci.yml |
Domain libraries (optional [nd] extra): gudhi (TDA), qutip (quantum frame stubs), pure-Python category hom-set counts. Install: pip install -e ".[dev,nd]".
| Topic | Document |
|---|---|
| Classical math sections + Python libs (Layer 1) | docs/MATHEMATICS_LIBRARY_BASE.md · data/mathematics_library_base.yaml |
| Разделы математики — три слоя (RU, навигация) | docs/MATHEMATICS_SECTIONS_RU.md |
| Vision, falsifiability, pipeline | docs/VISION.md |
| Research direction and roadmap | docs/RESEARCH_DIRECTION.md |
| AI thinking topology (Phase 004 foundation) | docs/AI_THINKING_TOPOLOGY.md |
| Non-anthropic syntax + ND frames (concept, consolidated) | docs/NON_HOMO_SYNTAX_AND_ND_FRAMES.md |
| Non-anthropic syntax (reference) | docs/NON_HOMO_SYNTAX.md |
| ND frame ladder (F1–F∞) | docs/FRAME_LADDER.md |
| Open problems tierlist (finite shadows) | docs/OPEN_PROBLEMS_TIERLIST.md |
| Open-source landscape (automated discovery vs NAMM) | docs/OPEN_SOURCE_LANDSCAPE.md |
| Certificate-first Phase 2 | docs/AI_NATIVE_NAMM.md |
| Brief manifesto | docs/MANIFESTO.md |
| Anthemium lineage (Manifesto → NAMM) | docs/ANTHEMIUM_LINEAGE.md |
| Anthemium + NAMM synergy (experiments loop) | docs/ANTHEMIUM_NAMM_SYNERGY.md |
| PROACTIVE AI — endogenous initiative architecture | proactive-ai/README.md · docs/proactive-ai/INTEGRATION.md |
| Math object candidates (novelty registry) | docs/MATH_OBJECT_CANDIDATES.md |
| Math object hypotheses (falsifiable CONJECTURE registry) | docs/MATH_OBJECT_HYPOTHESES.md |
| Mathematical fabric hypotheses (topological fuzzy dynamics, H-F registry) | docs/MATHEMATICAL_FABRIC_HYPOTHESES.md |
| Philosophical inference registry (agent load) | docs/PHILOSOPHICAL_INFERENCE.md |
| Domain universe catalog (math/physics fields index + TOC, agent load) | docs/NAMM_DOMAIN_UNIVERSE.md |
Discover structures whose canonical representation is a verified program, not a formula; whose human explanation is longer and lossier than the machine artifact; and which predict behavior on families no named invariant spans.
From docs/AI_NATIVE_NAMM.md.
A result is interesting only when all of the following hold (not when it merely sounds novel):
- Verified — ground truth is the certificate (AST hash, eval witness), not the human projection.
- Compression asymmetry — (K_A \ll K_H): machine artifact smaller and more precise than its human explanation.
- Independence — passes correlation, simplify, and non-equivalence gates vs known baselines.
- Generative power — non-trivial on held-out graph families not used during search.
Negative results are logged to rejections.jsonl. We claim methodology and falsifiable experiments — not breakthroughs.
Requires Python 3.12+. From the project root (after cloning):
python -m pip install -e ".[dev,nd]"
python -m pytest tests/ -vThe [nd] extra installs gudhi (TDA) and qutip (quantum frame stubs). Core experiments run without it; NAMM-2026-006 requires [nd].
On Windows you can use py -3.12 instead of python if multiple versions are installed.
python -m namm.cli run-experiment --id NAMM-2026-003Evolutionary AST search with sympy equivalence checks only. Held-out families: trees, bipartite, cubic.
python -m namm.cli run-experiment --id NAMM-2026-002Produces certificate.json for confluent rewriting systems.
python -m namm.cli run-experiment --id NAMM-2026-005Exhaustive finite shadow counterexample search for Kotzig's conjecture. See docs/OPEN_PROBLEMS_TIERLIST.md.
python -m namm.cli run-experiment --id NAMM-2026-004Searches for meta-evaluator fixed points E ≈ F(E) on graphs order ≤ 6. See docs/AI_THINKING_TOPOLOGY.md.
pip install -e ".[dev,nd]"
python -m namm.cli run-experiment --id NAMM-2026-006Persistent homology on graph geodesic metric via Gudhi. See docs/FRAME_LADDER.md.
python -m namm.cli run-experiment --id NAMM-2026-007Raw tensor invariants without named human-invariant vocabulary. See experiments/NAMM-2026-007/EXPERIMENT_REPORT.md.
python -m namm.cli run-experiment --id NAMM-2026-001Valid null result; no further search budget allocated per docs/RESEARCH_DIRECTION.md.
Re-run tests + smoke experiment on a schedule:
/loop 30m Run scripts/health.ps1 from the project root; fix any failures.
Or manually (Windows PowerShell):
powershell -ExecutionPolicy Bypass -File scripts/health.ps1Cross-platform equivalent:
python -m pytest tests/ -q
python -m namm.cli run-experiment --id NAMM-2026-001namm verify --expr "2*num_edges + 1*clustering" --baseline "1*wiener_index"src/namm/ Core library (schemas, graph domain, verifiers, baselines, CLI)
experiments/ Per-experiment config and artifacts
tests/ pytest suite
prompts/ NAMM protocol prompts (from research repo)
See NAMM_PROTOCOL.md, docs/PROTOCOL_V2.md, and prompts/ for the discovery protocol.
Every push and pull request to main runs CI:
pip install -e ".[dev]"pytest tests/ -v- Lightweight smoke search (10 candidates)
A weekly scheduled workflow re-runs pytest on main. There is no production deployment — CI is the quality gate before merge.
Run the same checks locally:
python -m pip install -e ".[dev]"
python -m pytest tests/ -vDetails: .github/workflows/README.md
This research program is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). You may share and adapt the material for any purpose, including commercially, provided you give appropriate credit.
Required attribution:
- Non-Anthropic Mathematics Mode (NAMM) — Roman Kuznetsov
https://github.com/errorlogy/namm-experiments · https://anthemium.tech · https://x.com/AGIminister
Machine-readable metadata: CITATION.cff.
Sibling research program: Endogenous Initiative Architecture (EIA) — proactive AI with endogenous initiative; integrated in this repository via proactive-ai/. When you use that integration, cite both NAMM and EIA as described in LICENSE.