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NAMM — Non-Anthropic Mathematics Mode

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.


Research program

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.


Epistemic stance

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_INFERENCEnon-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.


Hypothesis

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.


Experiments and phases

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-2026-007first 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]".


Documentation

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

North star

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.


What counts as success

A result is interesting only when all of the following hold (not when it merely sounds novel):

  1. Verified — ground truth is the certificate (AST hash, eval witness), not the human projection.
  2. Compression asymmetry — (K_A \ll K_H): machine artifact smaller and more precise than its human explanation.
  3. Independence — passes correlation, simplify, and non-equivalence gates vs known baselines.
  4. 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.


Clone and run

Requires Python 3.12+. From the project root (after cloning):

python -m pip install -e ".[dev,nd]"
python -m pytest tests/ -v

The [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.

Run program synthesis experiment (NAMM-2026-003) — Priority 1

python -m namm.cli run-experiment --id NAMM-2026-003

Evolutionary AST search with sympy equivalence checks only. Held-out families: trees, bipartite, cubic.

Run rewriting experiment (NAMM-2026-002) — Priority 2

python -m namm.cli run-experiment --id NAMM-2026-002

Produces certificate.json for confluent rewriting systems.

Run open-problem shadow (NAMM-2026-005) — Kotzig P_k

python -m namm.cli run-experiment --id NAMM-2026-005

Exhaustive finite shadow counterexample search for Kotzig's conjecture. See docs/OPEN_PROBLEMS_TIERLIST.md.

Run meta-evaluator experiment (NAMM-2026-004) — Priority 3

python -m namm.cli run-experiment --id NAMM-2026-004

Searches for meta-evaluator fixed points E ≈ F(E) on graphs order ≤ 6. See docs/AI_THINKING_TOPOLOGY.md.

Run TDA frame experiment (NAMM-2026-006) — ND frame

pip install -e ".[dev,nd]"
python -m namm.cli run-experiment --id NAMM-2026-006

Persistent homology on graph geodesic metric via Gudhi. See docs/FRAME_LADDER.md.

Run raw tensor experiment (NAMM-2026-007) — first operational signal

python -m namm.cli run-experiment --id NAMM-2026-007

Raw tensor invariants without named human-invariant vocabulary. See experiments/NAMM-2026-007/EXPERIMENT_REPORT.md.

Run calibration experiment (NAMM-2026-001) — closed

python -m namm.cli run-experiment --id NAMM-2026-001

Valid null result; no further search budget allocated per docs/RESEARCH_DIRECTION.md.

Health loop (Cursor)

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.ps1

Cross-platform equivalent:

python -m pytest tests/ -q
python -m namm.cli run-experiment --id NAMM-2026-001

Verify a candidate

namm verify --expr "2*num_edges + 1*clustering" --baseline "1*wiener_index"

Project layout

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.

CI/CD (GitHub Actions)

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/ -v

Details: .github/workflows/README.md


License and citation

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:

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.

About

NAMM: verification-first research on machine-native math discovery. Math structures as observer-independent objects; human formalism as bounded coordinates. Falsifiable SNH gates, K_A/K_H asymmetry, experiments 001-006. Updates: https://x.com/agiminister · https://anthemium.tech

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