AI-assisted mathematics. Arguments, evidence, and open questions.
Led by Joshua Gay. Review and limitations are stated with the work.Latest research ·
When completed rows all agree, an existing coverage mechanism certifies that agreement despite arbitrary temporary differences. A global specialization removes name-length restrictions and supports immediate reuse. Two final answer profiles remain the next discovery problem.
Read the composition and reuse investigationResearch papers are listed first. Books and overview reports provide broader entrances to work across several research areas.
A second proof that even binary palindromes have a finite scaffolding automaton, built from immutable typed receipts and a whole-client normalization theorem. Its explicit source-model bounds remain under review.
The transfer theorem from strict real-time multitape computation to parsing expression grammars. Persistent two-stack tape zippers turn each machine step into one bounded scaffold update, with the construction checked in Lean 4.
A resource audit and parameter retuning of the direct deterministic reduction from 3SAT to Euclidean closest vector. It reaches 1/30-hardness and isolates a 1/28 frontier for the retained proof architecture.
A study of scaffold histories as mathematical objects: what they build, what a bounded observer can distinguish, and which local rewrites connect behaviorally equivalent histories. Develops causal presentations, guarded folding, sewing, and feedback.
Lifts the algebra of unary scaffold histories from moves to relations among moves. Corrected order-ideal lattices, CAT(0) cube complexes, and a bounded list of critical cells provide a coherent higher-dimensional presentation.
report
A concise overview of the Lab’s research questions, methods, and mathematical areas.
book
A self-contained introduction to the mathematical background and core FPRD constructions, with exercises and solutions.
Explore questions and results in automata, computation, logic, algorithms, algebra, number theory, and discrete dynamics.
Research area
Automata, grammars, parsing, language recognition, residuals, pushdown structure, and scaffolding automata.
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Finite persistent structures, abelian networks, schedule-sensitive computation, geometric machines, and exact interfaces between models.
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Reductions, lower bounds, automata resources, streaming memory, linear recurrences, matrix powers, and arithmetic circuits.
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Operational semantics, causal equivalence, rewriting histories, confluence, cubical coherence, proof dynamics, and verification.
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Tensor categories, representation theory, elliptic integrable systems, mathematical physics, formal series, semirings, metric groups, linear invariants, and discrete topology.
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Integer complexity, arithmetic iteration, guarded-affine traces, modular seams, recurrence, orbit structure, recovery budgets, and contraction.
Browse exact theorem, lemma, proposition, and corollary statements. Each one links to its location in the full paper.