The three pillars of James (knowledge, safety, soul) as formal models proved in Lean 4, plus James's mathematical manifesto.
Byte-for-byte port of the toon CLI (toon_rust: JSON <-> TOON, the token-efficient format for LLM context) to Bend 2. Golden-tested against the pinned original on 4 executor lanes (interpreter, native C at 1 and N threads, JavaScript), 368 machine-checked laws, a software binary64, zero unsafe.
A machine-checked ledger of covering-code upper bounds K_q(n,R), with formally certified exact entries in Lean 4.
Tests that carry their own evidence: an Idris2 framework grading every test into three provenance tiers — Actually-Proven, Provisionally-Proven, Unproven — over a 17x14 category-by-aspect lattice whose coverage is derived from tests that ran and passed, never declared.
Machine-checked Lean 4 proofs for "Recursive Language Models Through the Admissibility-Dynamics Framework." Covers RLM sub-call architecture, three sufficient conditions for bounded-inconsistency deployment (safe abstention, bounded-decomposable predicates, runtime depth verification), training class closure, and the deployment-boundary synthesis.
Machine-checked Lean 4 / mathlib proofs and deterministic, reproducibility-first numerical audits of released PLDR-LLM checkpoints, backing the paper "Power law graph attention: exact generalization of scaled dot-product attention, empirical collapse at inference" (PLDR-LLM / PLGA).
Work in progress: evidence-indexed residual types; checked minimal Agda core, Echo/Epistemic comparisons and a separate finite explorer.
Machine-checked Lean 4 proofs for "Language Model Hallucinations: An Impossibility Theorem and Its Architectural Consequences." Covers Theorem 1 (impossibility of guaranteed consistency), certification-depth lower bounds, mitigation boundaries for CoT / grammar / rerank, and intrinsic/extrinsic DCF taxonomy.
Machine-checked Lean 4 proofs for "Projection Insufficiency and Trajectory Realization." Establishes that no function on a non-injective projection can recover a trajectory-dependent property, with specializations to language-model hallucination, planning, RL, POMDPs, and constraint propagation.
Zero-axiom Smithian Fold Theory with exact machine-checked derivations across physics, mathematics, classical computation, and quantum computation
Lean 4/mathlib proofs from minimal change: Gaussian source, natural-number arithmetic with expression histories, unique factorization, gauge and matter structures, generated Yang-Mills action and attained spectral gap. Machine-checked mathematics with explicit theorem-to-paper maps.
Lean 4 formalization of the constraint gap for realizable adversarial perturbations (mathlib v4.32.2, no sorry)
ARCHIVED duplicate/hologram. Canonical: https://github.com/szl-holdings/lutar-lean
A Constructive Formalization of Discrete Entanglement-Geometry Duality in Cubical Agda
Lean 4 + Mathlib formalization of the Λ aggregator — Λ uniqueness as Conjecture 1 (not a closed theorem). 749 declarations · 14 axioms · 163 tracked sorries. Backs the SZL governance gate. Doctrine v11 LOCKED · DOI 10.5281/zenodo.20434308
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