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
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.
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 |
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).
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.
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 |
- 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.
- 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 infigures/. Refuted claims stay in, marked. - Run
python scripts/make_index.pyso 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.
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}
}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.