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.
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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.
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).
Claims are registered before running; instruments carry anti-vacuity controls; new scoring functionals must pass the Circularity Test.
No philosophy required. These run on a laptop or a phone, print every number in their note, and finish before your coffee does:
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).