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Timeline of recent additions and substantive revisions to the paper corpus. Only reviewed and math-verified papers are shown — unreviewed drafts are excluded until they pass the review gate.

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2026-08-08 · updated
The Structured Latent Basis: Feature Engineering as Basis Selection
Core Theory Working Paper DOI
We introduce the Structured Latent Basis (SLB) framework, a perspective that compares feature engineering, meta-learning, and representation learning through a common diagnostic question: does the chosen representation make a regularized linear predi
2026-08-07 · updated
An Audited Contract Boundary for COS Caplet Pricing
quantitative_finance Working Paper Lean DOI
We present a bounded verification case study for COS caplet pricing. The numerical component expands the payoff of a log-forward rate, pairs characteristic-function coefficient proxies with raw payoff integrals, and reproduces Black benchmark values in a lognormal special case.
2026-08-06 · updated
Machine-Checked Scalar Foundations for SGD Analysis
optimization and formal methods Short Draft Lean DOI
We present a machine-checked source containing 78 named real-arithmetic declarations that occur as local steps in standard analyses of stochastic gradient descent (SGD). This declaration count includes support identities, recovery variants, and direct restatements; it is not a co…
2026-07-28 · updated
The Latent: Finite Sufficient Representations of Smooth Systems
Core Theory Draft DOI
We define the **Latent** of a smooth system as the basis-free element of a graded Hilbert tensor algebra that completely characterizes the system's distributional, dynamic, and functional properties.
2026-07-22 · updated
Conditional BSD Implications with Twelve Explicit Debt Assumptions
number_theory Working Paper Lean DOI
The Birch and Swinnerton-Dyer conjecture predicts that for an elliptic curve $E/\mathbb{Q}$ the Mordell-Weil rank equals the order of vanishing of the Hasse-Weil $L$-function at $s = 1$.
2026-07-20 · updated
From Design Points to Machine-Checked Parameter Regions: Reusable Certificate Templates for Engineering Models
Formal Verification Draft Lean DOI
We present a reusable algebra for machine-checked certificates in declared engineering models, where supplied equations, inequalities, monotonicity directions, and perturbation bounds imply an encoded safety, lifetime, stability, or performance predicate.
2026-07-20 · updated
A Finite-Dimensional Bounded-Perturbation Certificate
mathematics Draft Lean DOI
Saddle-point approximations replace an action by its quadratic part, but transferring a quantitative error statement between applications requires an explicit remainder estimate.
2026-07-19 · updated
The Fenton Distribution: An Elementary Representation
Quantitative Finance Draft Lean DOI
An elementary representation route for sums of correlated lognormals; published with DOI and stated for review.
2026-07-19 · updated
Conditional Bounds on AI Self-Improvement in an Antitone Threshold Model
Formal Verification Draft Lean DOI
We establish conditional bounds in a stylized antitone threshold model of recursive AI self-improvement. A mode $k$ is model-learnable at budget $N$ when the stipulated predicate $N g(k)\ge 1$ holds, where $g$ is positive and antitone.
2026-07-18 · updated
Toward Dimension-Independent Finiteness of Central Configurations for Positive Masses: A Scope-Audited Reduction with Named Open Bridges
Formal Verification Working Paper DOI
A proposed route toward finiteness of central configurations for positive masses, with formalized components and explicit assumptions.
2026-07-13 · updated
Spectral Error Mitigation: Model-Based Noise Inversion for Quantum Computers via Cluster Lindblad
Physics Working Paper DOI
2026-07-12 · updated
Formal Koide Structure: Mass Bounds, Generation Counting, and Neutrino Predictions from the Z_N Ansatz
Formal Verification Short Draft Lean DOI
The Z₃ Ansatz $\sqrt{m_r} = a(1 + b\cos(\theta_0 + 2\pi r/3))$ with $b^2 = 2$ is a parametrization — not a dynamical model — that encodes the Koide mass relation $Q = 2/3$.
2026-07-10 · updated
Toward the Riemann Hypothesis: A Superquadratic-Growth Framework for Zeta Moments and its Limits
Mathematics Draft Lean DOI
We present an algebraic framework relating the growth of the zeta moments to Hankel-determinant structure, together with an honest account of where the framework does and does not reach the Riemann Hypothesis.
2026-07-10 · updated
Toward an Exact Latent Encoding of the Gravitational Three-Body Problem
Physics Draft DOI
A proposed finite Latent encoding for gravitational three-body trajectories, with convergence and formalization status separated from the main claim.
2026-07-07 · updated
Harvestability
Formal Verification Working Paper Lean DOI
This paper studies **harvestability** as a horizon object for portfolio allocation within a CRRA investor model facing Ornstein-Uhlenbeck eigenmodes.
2026-07-05 · updated
Resolving the Equity Premium Requires at Least Two Dimensions: A Machine-Checked Class No-Go and a Term-Structure Discriminator
Formal Verification Draft Lean DOI
The equity premium puzzle of Mehra and Prescott (1985) is the observation that the standard consumption-based asset pricing model, calibrated to plausible risk aversion and the observed smoothness of aggregate consumption, predicts an equity premium
2026-06-27 · updated
The Riemann Hypothesis via Fourier-Euler Product: A Short Conditional Reduction
Mathematics Working Paper Lean DOI
We give a short conditional reduction of the Riemann Hypothesis to three classical inputs — Kronecker-Weyl equidistribution, the Bessel I₀ product identity, and Mertens' divergence theorem — plus a cited pair-correlation step.
2026-06-27 · updated
Full Density of Zeta Zeros on the Critical Line via GUE Universality
Mathematics Working Paper DOI
We prove that 100% of the nontrivial zeros of $\zeta(s)$ lie on the critical line in the density sense: $N_0(T)/N(T) \to 1$ as $T \to \infty$. The proof combines two results.
2026-06-17 · updated
The Projected-Generator Method for Path-Dependent Derivative Pricing
Quantitative Finance Draft Lean DOI
Derivative pricing has a clear mathematical target: compute the discounted risk-neutral value of a payoff under a specified model. For European vanilla contracts this target is often analytic or nearly analytic.
2026-06-15 · updated
Architectural Optimizations of the In-Context Gradient-Descent Mechanism
machine_learning Short Draft Lean DOI
The companion core paper establishes, and machine-checks, a single identity: a transformer's forward pass can implement one gradient-descent step on an implicit least-squares objective (the ICL=GD mechanism).
2026-06-15 · updated
Capacity, Scaling, and Grokking from the In-Context Learning = Gradient Descent Mechanism
machine_learning Short Draft Lean DOI
The companion core paper establishes, and machine-checks, a single identity: a transformer's forward pass can implement one gradient-descent step on an implicit least-squares objective (the ICL=GD mechanism). This satellite asks what that verified identity forces to be true about…
2026-06-15 · updated
Training Dynamics and Inference Guarantees of the In-Context Gradient-Descent Mechanism
machine_learning Short Draft Lean DOI
The companion core paper establishes, and machine-checks, a single identity: a transformer's forward pass can implement one gradient-descent step on an implicit least-squares objective (the ICL=GD mechanism).
2026-06-15 · updated
When In-Context Learning Implements Gradient Descent: A Learned Mechanism, Mechanically Verified and Empirically Tested
machine_learning Draft Lean DOI
We turn the gradient-descent account of in-context learning (ICL) into machine-checked mathematics and falsifiable predictions about real transformers. The formal target is the linear-attention regression identity: a forward pass can implement one gradient-descent step on an impl…
2026-05-19 · new
Explicit Flat Palm Weights for the Second Class Particle in a Three-State Attractive Interacting Particle System
Formal Verification Working Paper Lean DOI
2026-04-27 · updated
The Universal Spectral Representation Theorem: Breaking the Curse of Dimensionality
Quantitative Finance Working Paper DOI
How many parameters does it take to represent a smooth probability density on a bounded domain to accuracy $\varepsilon$? We prove that for densities extending holomorphically to the Bernstein ellipse with parameter $\rho > 1$, the answer is $N = \Th
2026-04-27 · updated
The Yang-Mills Mass Gap via Gauge Absorption and Perelman W-Entropy
Formal Verification Draft Lean DOI
**Theorem A (Main result, conditional).** Conditional on the 20 named Tier A–D hypotheses of §7.1 — in particular the three Tier-D perturbative-QFT inputs (`tomboulis_formula`, `b_zero_from_feynman`, `beta_1_rge_def`) — we establish that Yang-Mills t
2026-04-25 · updated
The Latent of Latents: Hierarchical Finite Representations of Knowledge Families
Machine Learning Draft Lean DOI
The Latent Theorem guarantees that any smooth system has a finite representation whose size depends on regularity and accuracy, not on ambient dimensionality. We extend this result to **families** of smooth systems.
2026-04-25 · updated
Contaminated by Construction: Separating Simulation Noise from Model Risk in ES Backtests
Quantitative Finance Working Paper Lean DOI
Expected Shortfall backtesting under Basel III/IV suffers from an unmeasured structural weakness: Monte Carlo estimation of ES injects computational noise into the Acerbi-Székely (2014) test statistic, but the magnitude of this contamination has not
2026-04-25 · updated
Deterministic Portfolio VaR Without Monte Carlo: The Eigen-COS Method
Quantitative Finance Working Paper Lean DOI
We present the Eigen-COS method, a deterministic algorithm that computes exact Value-at-Risk, closed-form Expected Shortfall, and the full CDF/PDF for weighted sums of correlated lognormal assets — without Monte Carlo simulation.
2026-04-25 · updated
Terminal Portfolio Value Distribution to Machine Precision
Quantitative Finance Draft Lean DOI
We present a deterministic, semi-analytical framework for computing the complete distribution of a portfolio's terminal value at horizon $T$ for correlated lognormal assets. Unlike traditional approaches, this method requires no Monte Carlo simulation.
2026-04-25 · updated
What Is a Return? (Especially When Prices Can Be Negative)
Quantitative Finance Draft Lean DOI
Every formula in quantitative finance — CAPM, Markowitz, VaR, Sharpe ratio, GARCH — takes returns as input. Yet the standard definitions of return fail when prices cross zero: log-returns are undefined, and simple returns produce sign errors.
2026-04-25 · updated
Spectral Importance Sampling: Optimal Rare-Event Simulation via Eigenvalue-Conditioned Measure Change
Quantitative Finance Working Paper DOI
We develop a variance reduction framework for simulating rare events in correlated portfolios by exploiting the eigenvalue decomposition of the correlation matrix. The central observation is that the eigenvalue modes $Z_k$ — projections of the asset vector onto the eigenvectors o…
2026-04-25 · updated
Grade Decomposition and Gevrey Regularity for Navier-Stokes: A Machine-Checked Conditional Framework
Formal Verification Working Paper Lean DOI
We introduce a grade decomposition of the Gevrey energy balance for the incompressible Navier-Stokes equations. The physically correct model uses $\mathbb{C}$-valued Fourier coefficients with a factor of $i$ in the advection; the real-coefficient model trivializes all grade-3 ter…
2026-04-25 · updated
Practical Padé Representations of the Gravitational Three-Body Problem
Physics Short Draft Lean DOI
We demonstrate that Padé resummation of Taylor-series solutions provides a practical, machine-precision representation of the full gravitational three-body problem.
2026-04-25 · updated
A refuted-and-vindicated pre-registration test of a spectral error model on a superconducting processor
Physics Working Paper DOI
We pre-register and test a spectral-error-mitigation prediction for the two-qubit gate fidelity of Quantum Inspire's Tuna-9 9-qubit transmon processor and execute it in four cryptographically timestamped stages.
undated · updated
The Spectral Lognormal Distribution
Quantitative Finance Draft Lean DOI
The CDF of a weighted sum of correlated lognormal random variables has lacked a tractable characterization since Fenton (1960). We show that eigenvalue conditioning of the correlation matrix, followed by Fourier-cosine inversion, yields an analytic, grid-free $N$-term spectral re…
undated · updated
Fundamental Constants as Grade-Ratio Hypotheses
Physics Draft Lean DOI
A speculative grade-ratio model for fundamental constants, with formalized arithmetic components and explicit physical assumptions.