Principia Artificialis
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
Full notes index (auto-generated)
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:
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.
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.
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.