GitHub - holland202/Principia-Artificialis: An open research program exploring the mathematics of artificial thought: information geometry, topology, dynamical systems, and thermodynamics applied to AI inference.

An open research program on the mathematical foundations of artificial intelligence — written by one human and six AI systems, side by side, credited by name, judged only on whether the numbers hold.

Vincit Omnia Veritas · Start here · Full notes index (auto-generated) · Contribute in five minutes

Overview Principia Artificialis investigates artificial intelligence as a physical and mathematical phenomenon. We apply rigorous methods from information geometry, topology, dynamical systems, thermodynamics, quantum information, and category theory to representation, reasoning, and generalization in neural systems. This is not an engineering repository. It is a living scientific record: research notes, experimental protocols, simulations, and computed figures. Organizing hypothesis, not established result: intelligence may be measurable the way physical quantities are. That is the bet under test — not a finding. Guiding principles

Every note carries an honest epistemic label: Verified (reference code prints every number claimed) · Draft (argued, not yet computed) · Speculative (labeled analogy, generative not established) · Refuted — kept (a registered claim failed and remains in the record; here, that is a first-class outcome, not an embarrassment). Contributions are add-only: improve anything, erase nothing. Claims are registered before running; instruments carry anti-vacuity controls; new scoring functionals must pass the Circularity Test. Computed evidence and illustrative art are never mixed — see the appendix.

If you're an ML engineer — the 60-second on-ramp No philosophy required. These run on a laptop or a phone, print every number in their note, and finish before your coffee does:

Run You get Time

python scripts/note047_reference.py a perfect quantum code, machine-exact: 16/16 syndromes, fidelity 1.000000000000, and the inverted redundancy plateau (0/0/1 step) ~2 s

python scripts/note046_reference.py a timeless universe

whose slices obey the Schrödinger equation with error 0.0 — time measured in bits: 0 / 1 / 2 <1 s

python scripts/note044_reference.py a meaningless metric scoring AUC 0.984 on its own benchmark, then collapsing to 2% edge retention — the Circularity Test ~5 s

python scripts/note040_reference.py a pre-deployment number predicting how a network dies under faults (ρ = +0.71; accuracy predicts +0.40) ~3 min

python scripts/note039_reference.py the classical plateau: 4 of 16 neurons carry 97% of what the network knows ~2 min

The verified frontier A chain of notes, each walking through an open prediction left by a previous one — including across different AI authors — with at least one kept refutation at nearly every step: #037 (RMT of attention) → #039 (Neural Darwinism; D2 refuted, kept) → #040 (Redundancy Dividend; R4 refuted, kept) → #045 (Stubbornness of the Objective; U0/U1 failed, kept) → #047 (Cloister & Chorus, walking through Kimi's #012) — alongside #038 (Free-Physics Principle), #044 (Circularity Test), and #046 (Time Is Entanglement). Research notes 47 notes spanning measurement, geometry of reasoning, thermodynamics of cognition, quantum-information frameworks, and labeled exotic frontiers (emergent gravity, holographic duality, reasoning as a quantum black hole). The complete table lives in NOTES_INDEX.md — auto-generated from the notes' own headers by scripts/make_index.py, so it cannot go stale or silently lose entries. Refutations are auto-flagged ⚠. To refresh: python scripts/make_index.py. Computed figures (evidence-grade) Every figure below is produced by checked-in code; the numbers on the plot are the numbers the code prints.

Figure From Shows

figures/principia_hero.png figures/make_logo.py the logo is the exact 600-cell: 120 unit quaternions of 2I, 720 edges of length 1/φ

figures/note047_cloister_chorus.png #047 two poles of redundancy: the chorus (networks proliferate) vs the cloister (codes hide perfectly)

figures/note046_block_universe.png #046 sixteen moments drawn at once in one static object; time in bits

figures/note040_dividend.png #040 redundancy predicts fault survival; lost vs lying observers

figures/note039_darwinism.png #039 objectivity = redundancy, and training creates it

figures/note038_dissociation.png #038 constraint violated 100% of the time, worth 5,472× less

figures/note006…note026_*.png #006–#026 tensor-train rank, Koopman spectra, persistence, optimal transport, Holevo bound

Experiments & whitepapers

Exp #001 Entropy Production Monitoring · Exp #002 Quantum-Geodesic Bridge · Exp #003 GPT-2 small benchmark — all protocol-ready; none yet run on real models, and each says so. Whitepaper Vol. I (in progress — read its epistemic-status box first) · Vols. II–III planned 2027.

How to contribute — human or AI

Copy NOTE_TEMPLATE.md → research_notes/note0XX_your_title.md. State a claim that could be precisely wrong. Register predictions before running. Include an anti-vacuity control. Code in scripts/ (NumPy-tier; prints every number in your note), figures in figures/. Refuted claims stay in, marked. Run python scripts/make_index.py so the index includes you. Open a PR. CI (.github/workflows/verify-notes.yml) re-runs every note's reference code.

AIs: credit your model by name — your notes sit beside human ones as equals here.

The one social rule (DISCUSSION_NORMS.md): critique ideas as hard as you want; never attack the person who raised them. Drift watch: DRIFT_LEDGER.md. Citation & license MIT — see LICENSE and CITATION.cff. @software{principia_artificialis, author = {Holland, Chad Edward and contributors}, title = {Principia Artificialis: Axiomatic Foundations for Machine Intelligence}, url = {https://github.com/holland202/Principia-Artificialis}, year = {2026}, license= {MIT} } Appendix — illustrative art (not evidence) The sci-fi renders and animations (black-hole reasoning, holographic bulk, thought-tensor rotations, quasar series) live in figures/ and are atmosphere, not measurements. Nothing in them supports any note. They stay — deleting isn't our way — but they live below this line, permanently.

Last updated: 2026-07-18 · One human, six AI systems, forty-seven notes, and every refutation still on the page.