The paper proposes five axioms that formalize the assumptions underlying systematic trading, each expressed through declared quantitative constants. It demonstrates that these axioms necessitate a five‑stage canonical structure for a quantitative investment system and proves that omitting any stage worsens performance under the axioms. Empirical tests on real market data show that the axioms hold, though certain declared constants (e.g., κ = 1 and an exponential decay assumption) are rejected.
arXiv:2606. 16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended.
arXiv:2606. 12502v1 Announce Type: cross Abstract: We propose that value -- the quantity goal-directed agents create, destroy, and exchange -- is a lawful structural quantity in the same category as information.
arXiv:2606. 12471v2 Announce Type: replace-cross Abstract: Klindt, LeCun, and Balestriero (arXiv:2605.
arXiv:2606. 28572v1 Announce Type: cross Abstract: The axiom of choice has divided the foundations of mathematics for over a century, but the distinction between classical and constructive proofs has remained a philosophical and methodological one.
arXiv:2303. 04203v4 Announce Type: replace Abstract: The theory of computation was built to answer Turing's question: what is effectively calculable by an unbounded, immortal, disembodied agent following rules?
arXiv:2606. 14688v1 Announce Type: cross Abstract: AI systems coupled to proof assistants now generate formal mathematics at scale, and the gap between what a checker can verify and what a mathematician would value has become the binding constraint.
arXiv:2607. 08986v1 Announce Type: new Abstract: We formalize a research result in the Lean 4 proof assistant by having a mathematician direct an AI system, and frame the activity as a formalization game.
arXiv:2607. 08986v2 Announce Type: replace Abstract: We formalize a research result in the Lean 4 proof assistant by having a mathematician direct an AI system, and frame the activity as a formalization game.
arXiv:2607. 11653v1 Announce Type: new Abstract: Black-box conditional quantile forecasts are widely used for sequential decisions under asymmetric costs, such as inventory planning in supply chain management.
The paper introduces Eigenius, a typed knowledge store built over constructive institutions, extending a dependent type theory with cumulative universes, an impredicative universe of propositions, inductive families, and an intensional identity type. Proof irrelevance is handled as an axiom with explicit witnesses, allowing distinct proofs to be provably equal while retaining their identity. The authors establish consistency via a set‑theoretic model, develop a justification logic for evidence tracking, formalize environments as institutions, and prove correctness of conversion, normalization, and bidirectional type checking, with a Lean 4 formalization provided.
The paper proposes measuring a language model’s understanding via no‑arbitrage, defining it as the inability of a bounded trader to profit from Dutch books against the model’s probabilities on logically related claims. It shows that full logical coherence is computationally infeasible, that standard next‑token training yields incoherent predictions across formats, and that uncertainty grows predictably along reasoning chains, creating arbitrage opportunities. The authors introduce Arbitr, a training framework that penalizes logical inconsistencies while maintaining accuracy, reducing exploitability by orders of magnitude and revealing a scaling illusion where large models appear coherent yet exhibit extreme unjustified confidence.
arXiv:2610.14007v1 Announce Type: cross Abstract: A familiar line of reasoning runs as follows: language models are flexible approximators trained under a strictly proper loss, so scale brings them c...