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Quantitative Finance

124 papers · 57 Lean-verified

Spectral Interest Rate Pricing: COS-Based Derivatives from Yield Curve Coefficients
We present the first formally verified interest rate derivatives pricing engine. The Nagy spectral yield curve represents yields as a finite cosine series $y(\tau) = A_0 + \sum_{k=1}^K A_k \cos(k\pi\tau/\tau_{\max})$ with each mode following independent Ornstein-Uhlenbeck dynamics.
Verified 13 claims 6,508 words
Constraint-Forced Absorption: A General Mechanism for Singularity Prevention in Gauge-Invariant PDE Systems
We identify a general mechanism — **constraint-forced absorption (CFA)** — in PDE systems where a differential identity constrains the dynamics. In the $(D, C, P)$ framework (dissipation, coupling, constraint): **Theorem** (Constraint-Forced Absorption).
2 claims 5,290 words
An Eigenvalue-Conditioned Copula with Positive Tail Dependence: A Machine-Verified Alternative to the Gaussian Copula
The Gaussian copula's failure to capture tail dependence was a central factor in the 2008 credit crisis: CDO tranche losses far exceeded model predictions because the model assigned near-zero probability to simultaneous defaults.
6 claims 6,074 words
Credit Portfolio Loss
Credit Portfolio Loss Distribution — Beyond the Gaussian Copula. This paper presents 33 machine-verified theorems building on 0 established facts and 52 hypotheses.
Verified 32 claims 815 words
The Fenton Distribution Solved
The moment-based Latent representation of correlated lognormal sums (Nagy, 2026, *The Exact Latent Distribution of Correlated Lognormal Sums*) relies on scaled moments $c_k = m_k/k!$ that grow as $e^{\sigma_{\max}^2 k^2/2}$.
Verified 10 claims 14,277 words
Pricing Allocation
Pricing Allocation — clean ProofEnv proof. This paper presents 142 machine-verified theorems.
Verified 132 claims 1,670 words
Spectral Portfolio
Spectral Portfolio — ProofEnv proofs (covariance / PC risk split). This paper presents 93 machine-verified theorems.
Verified 91 claims 1,092 words
Stochastic Portfolio Theory
This paper presents 0 machine-verified theorems. All results are formally verified in the Lean 4 (125 verification units, 39 proved statements) and exportable to Lean 4. <!-- TODO: Write a proper abstract summarizing the key contributions -->
Verified 138 words
Spectral Counterparty Credit Risk: Deterministic EPE, PFE, and Regulatory Capital Without Monte Carlo
We derive the full counterparty credit risk (CCR) metric stack --- Expected Positive Exposure (EPE), Potential Future Exposure (PFE), Effective Expected Positive Exposure (EEPE), and Exposure at Default (EAD) --- from the Fokker--Planck spectral generator without Monte Carlo simulation.
3,990 words
Spectral Market Risk: Deterministic VaR, ES, and Stress Testing Without Monte Carlo
We present a benchmark of the Spectral Fenton method --- a deterministic alternative to Monte Carlo simulation for computing Value-at-Risk, Expected Shortfall, and full stress surfaces --- on realistic multi-asset portfolios representative of bank trading desks.
3,859 words
Spectral XVA vs Nested Monte Carlo: A Three-Engine Benchmark
We present a controlled benchmark comparing three computational engines for Credit Valuation Adjustment (CVA) on an identical 10-swap interest rate portfolio under Vasicek dynamics: (i) a **spectral method** based on the Fokker--Planck generator, imp
4,260 words
The Bridge Method: Systematic Cross-Domain Discovery via Shared Mathematical Structure
We formalize the concept of a **mathematical bridge** — a theorem establishing that conclusions proved in domain $A$ imply structure in domain $B$ — and develop a methodology for systematic bridge discovery.
Verified 20 claims 11,767 words
Eigenvalue Conditioning: A Universal Computational Primitive for Correlated Systems
We present eigenvalue conditioning as a universal computational primitive: given an $n$-dimensional problem governed by a positive semidefinite structure matrix $\Sigma$, eigendecompose $\Sigma$, project onto its $K$ dominant eigenmodes, solve $K$ independent one-dimensional problems, and combine.
Verified 11 claims 7,165 words
The Grade Method: Structural Decomposition of ODE Vector Fields via the Grade Hierarchy
We present the **grade decomposition method** as a general-purpose structural analysis tool for smooth dynamical systems. Any analytic vector field $F$ decomposes into interaction grades $F = \sum_{k=0}^{\infty} A^{(k)}$ with exponential suppression $\|A^{(k)}\| \leq C_0/\rho^k$, where $\rho$ is the analyticity radius.
1 claims 9,626 words
Two Lenses, One Invariant: Empirical Confirmation That ρ Is Basis-Independent
The Latent Number $\rho$ — the analyticity parameter that governs computational complexity in smooth systems — can be measured through at least two independent methods: **spectral decay** (fitting the exponential decline of expansion coefficients in
4,277 words
Autocallable Pricing as a Latent Computation: Spectral Methods with Formal Error Bounds
We show that the price of a worst-of autocallable with step-down barriers, discrete monitoring, and stochastic volatility is computable as a composition of seven Latent operations (Nagy 2026).
Verified 5 claims 4,516 words
Residual Monte Carlo: A Unifying Framework for Variance Reduction
We introduce Residual Monte Carlo (RMC), a variance reduction framework that decomposes high-dimensional integrals into an exactly computable dominant part and a simulated residual.
3 claims 5,893 words
Contaminated by Construction: Separating Simulation Noise from Model Risk in ES Backtests
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
Verified 12,334 words
Full-Tail Backtesting: Beyond Pointwise Validation for Expected Shortfall
Every existing Expected Shortfall backtest evaluates a risk model at a single confidence level. This paper introduces four backtesting methods that test the entire tail distribution simultaneously — methods that are structurally impossible without exact closed-form computation of the CDF and density.
Verified 10,211 words
Reducing the Contamination: Variance Reduction Strategies for Monte Carlo ES Backtests
Monte Carlo estimation of Expected Shortfall contaminates the Acerbi-Székely (2014) backtest statistic with computational noise.
4,528 words
The Cascade Depth Theorem
We formalize the *tool-building cascade*: a recursive decision process in which an agent, instead of solving problem instances directly, invests in tools that solve problem classes, thereby revealing higher-level problems amenable to the same strategy.
6 claims 5,010 words
Spectral Importance Sampling: Optimal Rare-Event Simulation via Eigenvalue-Conditioned Measure Change
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 of the correlation matrix — are mutually independent.
3 claims 5,351 words
Terminal Portfolio Value Distribution to Machine Precision
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.
Verified 3 claims 5,172 words
The Fenton Distribution: A Complete Analytical Characterization
We provide the first complete analytical characterization of the distribution of weighted sums of correlated lognormal random variables — the **Fenton distribution** $\mathcal{F}(w, \mu, \sigma, C)$. The distribution is determined by the finite generative latent $(w, \mu, \Sigma) \in \mathbb{R}^{n(n+5)/2}$.
14 claims 2,492 words
Nonlinear Portfolio Risk in Closed Form
We extend the Hermite-COS framework from linear portfolios (weighted sums of correlated lognormals) to portfolios containing options, structured products, and arbitrary derivative payoffs.
2 claims 2,124 words
The Exact Latent Distribution of Correlated Lognormal Sums
The distribution of $S = \sum_{i=1}^n w_i e^{Y_i}$, $Y \sim \mathcal{N}(\mu, \Sigma)$, has no closed-form CDF.
10 claims 7,869 words
The Minimal Sufficient Spectral State for Decision and Risk
Decision systems often carry excessive state, obscuring both theory and implementation. We define and characterize the minimal sufficient spectral state needed to preserve optimal decision value and calibrated risk estimation.
3 claims 1,793 words
A Nonlinear Spectral Fundamental Theorem of Asset Pricing
Classical FTAP characterizes no-arbitrage in linear pricing systems. We develop a nonlinear spectral extension in which state prices are represented as mode-dependent functionals over a spectral decomposition of market states.
Verified 4 claims 1,654 words
Spectral Causal Identifiability Under Partial and Noisy Observation
Causal identification typically requires rich interventions or full-state observability. We show that partial, noisy observations can still identify causal structure when signals admit a stable spectral decomposition with separation conditions.
2 claims 1,641 words
Spectral Ergodic Control with Provable Regret Guarantees
Ergodic control and online regret analysis are usually developed with different tools and assumptions. We present a spectral ergodic control framework where long-run average control objectives and finite-time regret can be analyzed jointly.
3 claims 1,775 words
Topological Obstructions in Market Dynamics
We introduce a topological perspective on market dynamics and prove obstruction results: under specific global state-space constraints, no arbitrage-free dynamics satisfying given regularity and observability axioms can exist.
4 claims 2,018 words
Spectral Time: Optimal Stopping, First Passage, and Subordination via the Fokker-Planck Generator
We develop a unified spectral framework for three fundamental problems in stochastic analysis: optimal stopping, first passage times, and time-changed (subordinated) processes.
4 claims 6,294 words
Theory and Measure of Decomposability
This paper develops a general theory of decomposability for structured systems, problems, and phenomena.
4,835 words
Emergent Complexity in Reality and Engineered AI Systems
We study emergent complexity as a regime property of open dynamical systems rather than as an intrinsic label of objects.
6,536 words
Intelligence as Organized Difficulty Compression
We propose a system-level theory of intelligence centered on a single claim: **intelligence is organized difficulty compression**. The motivating problem is that the term *intelligence* is routinely asked to cover too much at once, ranging from consciousness and general reasoning to benchmark success and adaptive control.
8 claims 6,126 words
Scientific Venture Design
We propose a formal framework for **scientific venture design**: a falsifiable theory of how to build large businesses under uncertainty.
4 claims 3,969 words
The Universal Spectral Representation Theorem: Breaking the Curse of Dimensionality
How many parameters does it take to represent a smooth high-dimensional probability law to accuracy $\varepsilon$? We prove that the answer is $N = \Theta(\log(1/\varepsilon)/\log\rho)$, where $\rho > 1$ is the analyticity radius, and that this repre
Verified 15 claims 7,243 words
Bayesian Live Risk
We propose Bayesian Live Risk (BLR), a framework in which the spectral representation of portfolio loss is treated as a posterior state updated in real time.
Verified 5 claims 11,538 words
Calibrating Harvestability
Starting from the canonical fin_harvestability object \(h(T,\tau)=1-e^{-T/\tau}\), this paper studies the calibration problem: when does expected return begin to dominate volatility strongly enough that the premium can be treated as genuinely availab
2,491 words
Common Pricing, Different Portfolios
We propose a mode-space formulation in which equilibrium pricing and portfolio choice are organized around a common benchmark rather than treated as separate layers. Let returns be resolved into orthogonal modes \(c_k\) with per-mode premiums \(\pi_k\), variances \(v_k = \mathrm{Var}(c_k)\), and market weights \(w_k^{\mathrm{mkt}}\).
Verified 7,021 words
The Spectral Volatility Surface
We construct a low-rank arbitrage-aware volatility surface with $O(rm)$ parameters and closed-form COS reuse for pricing and Greeks. Total implied variance is expressed as a finite cosine series in log-moneyness, $w(k, T) = c(T) + \sum_j u_j(T)\cos(\omega_j k)$, with $r = 6$–$12$ modes per maturity.
Verified 10 claims 8,745 words
The Latent Generator
We introduce the **latent generator**: a dynamical operator $M$ that is not directly observed, but is inferred from observable data. In general, the latent generator is the law behind a family of snapshots: the operator that generates the observables rather than merely fitting them pointwise.
4,041 words
Knowability
We propose that the central object of scientific description is not the sample path but the law, and that observable structure is shaped jointly by latent aggregation, dynamical evolution, and the lens through which a phenomenon is measured. In this view, many operations that appear distinct in observation space arise from a smaller latent grammar.
2,243 words
Spectral Granger Causality: Mode-by-Mode Causal Bandwidth
Granger causality (Granger, 1969) tests whether the past of $X$ helps predict $Y$ beyond $Y$'s own past.
Verified 7 claims 3,170 words
Trading the Eigenvalues: Statistical Arbitrage via the Implied Generator
We develop a systematic trading framework based on the **implied generator** — the Fokker--Planck generator matrix $M$ recovered from option prices without parametric assumptions.
2,542 words
The Anomaly Functional: Real-Time Arbitrage Detection via Spectral Risk Coefficients
We define a scalar functional $\mathcal{A}[F]$ on probability distributions that quantifies the total magnitude of arbitrage violations --- negative densities (butterfly arbitrage) and decreasing total variance across maturities (calendar arbitrage)
7 claims 4,250 words
Arbitrage-Free Term Structure via Spectral Coefficient Constraints
We propose a yield curve model that combines three properties rarely found together: (i) arbitrage-free dynamics by construction, (ii) strong empirical fit with interpretable factors, and (iii) partial formal verification in Lean 4.
Verified 6 claims 4,168 words
High-Precision Greeks for Multi-Asset Spread Options via Eigenvalue-Conditioned Fourier Inversion
Spread options on three or more correlated assets are fundamental hedging instruments in energy, commodity, and agricultural markets.
Verified 3 claims 5,063 words
Basket Option Pricing Under Stochastic Volatility via Eigenvalue-Conditional Heston Mixing
The eigenvalue-conditional mixing framework (Nagy, 2026a, 2026c) prices basket options under geometric Brownian motion by decomposing the correlation matrix, conditioning on dominant factors, and mixing per-scenario Black-Scholes prices.
4,581 words
How Much Bitcoin? Spectral Portfolio Allocation Beyond Mean-Variance
We show that mean-variance optimization systematically overestimates the optimal Bitcoin allocation in institutional portfolios. The Markowitz framework assumes returns are Gaussian, but Bitcoin has excess kurtosis $\kappa_4 \approx 8$--$13$ and negative skewness --- making its tails 3--5$\times$ heavier than the Gaussian approximation.
Verified 3 claims 3,195 words
Three Numbers for Risk: A Data-Driven Spectral Basis for Portfolio Loss Distributions
The Spectral Fenton Distribution represents a portfolio loss distribution with 128 Fourier coefficients.
4,109 words
The Pythagorean Gap: A Mode-Decomposition Indicator for Financial Crises
We introduce the *Pythagorean Gap*, a single scalar metric that measures the dispersion of risk-adjusted returns across spectral modes of a return distribution. When asset returns are decomposed into orthogonal modes via PCA, the tangency portfolio's Sharpe ratio satisfies a Pythagorean identity: $SR^2_{\text{tangency}} = \sum_k SR^2_k$.
Verified 2 claims 3,855 words
Spectral Schrödinger Bridges: Optimal Transport Between Portfolio Distributions in Fourier Space
The Schrödinger Bridge Problem (SBP) finds the most likely stochastic evolution between two probability distributions, minimizing the Kullback--Leibler divergence from a reference process.
Verified 11 claims 4,878 words
Spectral Alpha: Trading Signals from Fourier Risk Coefficients
The Spectral Fenton Distribution compresses a portfolio's loss distribution into 130 parameters: 128 Fourier coefficients plus a location and scale anchor.
4,305 words
Spectral Bitcoin VaR: High-Accuracy Risk Measures for Cryptocurrency via Fourier Expansion
We apply the Spectral Fenton Distribution framework (Nagy, 2026a) to Bitcoin return modeling and show that the COS (Fourier-cosine) expansion captures the BTC/USD daily return density with controllable numerical precision.
Verified 3,600 words
Spectral XVA: Replacing Monte Carlo in Counterparty Credit Risk
We propose a spectral method for computing Credit Valuation Adjustment (CVA) and related XVA metrics that eliminates Monte Carlo simulation entirely.
3,187 words
Spectral Kernel Risk: The Fourier--Gaussian Process Duality for Portfolio Loss Distributions
We establish a formal duality between the Spectral Fenton (Fourier) representation of portfolio loss densities and Gaussian Process (GP) regression via Mercer's theorem.
Verified 2 claims 3,337 words
Spectral Regime Detection: Change-Point Identification via Eigenmode Drift
We introduce spectral regime detection: a method to identify structural breaks in time series and panel data by monitoring the drift of spectral coefficients over sliding windows.
2 claims 2,179 words
The Spectral Tensor Representation of Stochastic Processes
We prove that every Itô diffusion $dX_t = \mu(X_t)\,dt + \sigma(X_t)\,dW_t$ admits a complete, finite-dimensional representation through its Fokker--Planck generator discretized in cosine basis.
6 claims 3,789 words
When Simulation Is Unnecessary: An Information-Theoretic Characterization of Analytically Tractable Distributions
Monte Carlo simulation exists because we cannot compute integrals analytically. But for how large a class of distributions *can* we compute them? We characterize this class precisely via a single number: the analyticity radius $\rho$.
Verified 10 claims 5,565 words
The Spectral Unity: Risk, Pricing, and Hedging from a Single Representation
For portfolios of correlated lognormal assets, we show that risk measurement, derivative pricing, and hedging --- traditionally treated as separate disciplines --- reduce to operations on a single object: the $N$-term Fourier-cosine (COS) expansion of the portfolio density.
Verified 5 claims 3,855 words
What Your XGBoost Learned: Spectral Knowledge Extraction from Black-Box Models
We introduce **spectral knowledge extraction**: a method to decompose the learned function of a black-box model (XGBoost, random forest, neural network) into explicit Fourier cosine modes, each with a direct interpretation.
Verified 3 claims 3,400 words
Spectral FX: Eigenvalue Classification of Currency Dynamics
We show that vector autoregression (VAR), cointegration, geometric Brownian motion (GBM), and the Ornstein--Uhlenbeck (OU) process are four eigenvalue regimes of a single linear stochastic differential equation \(dX = AX\,dt + \Sigma\,dW\).
Verified 1 claims 4,041 words
Adaptive COS Option Pricing via Per-Mode Convergence Rates
The COS method (Fang and Oosterlee, 2008) for option pricing via Fourier-cosine expansion uses a uniform number of backward steps $T$ across all $N$ Fourier modes. We prove that each mode $k$ converges at its own rate $\delta|\varphi(k)|$, where $\delta$ is the per-step discount and $\varphi(k)$ the characteristic function value.
Verified 5 claims 4,094 words
Extended Bellman Equations for Spectral Finance: Per-Mode Convergence, Shadow Prices, and Model-Free Bounds
The Bellman equation $V = \max_a [R + \gamma \sum P V]$ is the foundation of dynamic programming, yet its standard form obscures three structural properties critical for financial applications.
Verified 17 claims 5,403 words
When Q-Learning Meets Black-Scholes: A Machine-Verified Bridge Between Reinforcement Learning and Option Pricing
Reinforcement learning and quantitative finance independently discovered the same mathematical framework.
Verified 1 claims 7,990 words
Spectral Dynamic Programming: Per-Mode Convergence Rates and Computational Acceleration for American Options
We show that eigendecomposing the transition kernel of a Markov decision process yields a spectral Bellman equation: each eigenmode $k$ satisfies an independent scalar recurrence $v_k' = r_k + \gamma \mu_k v_k$, converging at rate $\gamma |\mu_k| \le
Verified 6 claims 5,769 words
Eigenvalue Conditioning as Universal Optimizer: Cross-Domain Transfer Between Finance, Robustness, and Machine Learning
We prove that eigenvalue conditioning — decompose a structure matrix into eigenmodes, condition on the $K$ dominant modes, solve $K$ independent one-dimensional problems, and combine — is a universal optimization principle that transfers across five
Verified 14 claims 7,094 words
Pricing Basket Options via Eigenvalue-Conditional Black-Scholes Mixing
Pricing European basket options requires the distribution of a weighted sum of correlated lognormals — the Fenton Distribution (Nagy, 2026a) — which has no closed form.
4 claims 7,132 words
The Geometry of Risk: Spectral Distance and Topological Structure in Portfolio Space
We introduce a metric on the space of portfolio risk profiles derived from the spectral representation of loss distributions. Each portfolio's loss distribution is encoded as a vector of $N = 128$ Fourier--cosine coefficients via the Eigen-COS method (Nagy, 2026a).
Verified 6 claims 5,482 words
The Information-Theoretic Cost of Risk Measurement
Shannon (1948) proved that the fundamental limit of communication is the channel capacity, not the message length. We prove an analogous result for risk measurement: the fundamental limit of computing coherent risk measures is the **analyticity radius** $\rho$ of the loss density, not the dimension $n$ of the underlying risk factors.
Verified 11 claims 7,050 words
Correlation Is Not a Number — It's a Spectrum: Frequency-Domain Dependence for Portfolio Risk
The Pearson correlation $\rho_{ij}$ between two assets is a single number. It is blind to frequency: it cannot distinguish whether two assets co-move in long-term trends or in daily noise.
Verified 2 claims 4,439 words
Deterministic Portfolio VaR Without Monte Carlo: The Eigen-COS Method
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.
Verified 3 claims 11,097 words
Noise-Free Risk: Deterministic VaR, ES, and Spectral Risk Measures for Lognormal Portfolios
We present a deterministic framework for computing Value-at-Risk, Expected Shortfall, and arbitrary spectral risk measures for portfolios of correlated lognormal assets, without Monte Carlo simulation.
Verified 7,919 words
The Geometry of Risk: Connecting Spectral Fenton to TQFT and Witten Invariants
595 words
Semi-Analytic Portfolio VaR via Eigenvalue-Conditioned COS Inversion
We present a deterministic, grid-free method for computing Value-at-Risk of portfolios whose assets follow correlated geometric Brownian motion. The portfolio value is a weighted sum of correlated lognormals — the Fenton Distribution — whose CDF has no closed form but whose characteristic function is exactly computable.
2,691 words
Paper Draft — Portfolio VaR via Eigenvalue-Conditioned Lognormal Mixtures
We present a method for computing Value-at-Risk of portfolios whose assets follow correlated geometric Brownian motion. The portfolio value is a weighted sum of correlated lognormals — the Fenton Distribution — whose CDF has no closed form.
4,114 words
The Spectral Fenton Distribution: Exact Portfolio VaR via Eigenvalue-Conditioned Fourier Inversion
We introduce the Spectral Fenton Distribution — a 130-parameter spectral representation of the distribution of weighted sums of correlated lognormals (the Fenton Distribution).
3 claims 4,225 words
Pricing Basket Options via Eigenvalue-Conditioned Fourier Expansion
Pricing basket options (options on a weighted sum of assets) is computationally demanding due to the lack of a closed-form distribution for the underlying sum. We apply the Spectral Fenton Representation [Nagy 2026a] to derive a semi-analytic pricing formula for European basket calls and puts.
300 words
The Spectral Fenton Distribution: Exact Portfolio Risk via Eigenvalue-Conditioned Fourier Inversion
The probability distribution of the sum of correlated lognormal random variables—known as the Fenton Distribution—has lacked a closed-form cumulative distribution function (CDF) since its description in 1960.
2 claims 1,405 words
Eigen-COS VaR: Real-Time Exact Risk for High-Dimensional Portfolios
Value-at-Risk (VaR) and Expected Shortfall (ES) for non-normal portfolios typically require a trade-off: slow Monte Carlo simulations or inaccurate parametric approximations (Cornish-Fisher). We present the Eigen-COS VaR method, which computes exact risk measures for sums of correlated lognormals in milliseconds.
307 words
Two Representations of the Fenton Distribution: Generative and Spectral Forms
The weighted sum of correlated lognormal random variables — the Fenton Distribution — has been considered to lack a closed-form CDF for over sixty years. We show this is a representation problem, not a mathematical one.
2,726 words
Asset Pricing Anomalies as Latent SDF Decomposition: A Formal Derivation of Multi-Factor Models
The Capital Asset Pricing Model (CAPM) predicts that a single market factor prices all assets. Empirically, this fails: value stocks (high book-to-market) earn ~5% annual premium, small-cap stocks earn ~3%, and momentum strategies earn ~8%.
1 claims 1,827 words
Convolution–Correlation Duality: A Universal Principle for Spectral Damping
We present a universal spectral damping principle that classifies the tractability of problems across number theory, probability, signal processing, combinatorics, PDE, and finance. The core mechanism is elementary: convolution of independent components damps oscillatory Fourier coefficients, while autocorrelation preserves them.
Verified 1 claims 2,747 words
Core Spectral Pattern Theory
We propose a universal, quantitative definition of "pattern": a pattern is a low-rank spectral component of a data tensor whose eigenvalue exceeds the Marchenko--Pastur noise floor.
15 claims 15,294 words
Core Spectral Phase Transition
We prove that a single dimensionless parameter — the spectral decay rate ρ of a Markov generator — governs a universal phase transition in the compressibility of stochastic systems. For ρ > 1, any Lipschitz functional can be computed to accuracy ε using N = Θ(log(1/ε)/log ρ) spectral modes, independent of the system's dimension.
Verified 6 claims 4,165 words
The Universal Representation Theorem: From Portfolio Risk to the Three-Body Problem
How many numbers does it take to describe a smooth system? We prove the answer is $N = \Theta(\log(1/\varepsilon)/\log\rho)$ — regardless of the system's dimension.
Verified 8 claims 2,912 words
Billion-Dollar Ideas from Analytical Physics Design
1,887 words
Fin American Basket
We prove the first quantitative convergence guarantees for a deterministic American basket pricer with dimension-free cost.
Verified 20 claims 7,137 words
Fin Arcsinh Bs
We derive a closed-form European option pricing formula valid for all spot prices \( S_0 \in \mathbb{R} \), including negative values. The formula replaces the logarithmic transform of Black-Scholes with the inverse hyperbolic sine, yielding a three-term call price \( C = S_+ \Phi(d_+) - S_- \Phi(d_-) - K e^{-rT} \Phi(d) \).
Verified 8 claims 8,413 words
Bayesian Live Risk
We introduce Bayesian Live Risk (BLR), a framework for live risk management in which risk measurement is formulated as a posterior state rather than a single tail statistic.
Verified 2,782 words
The Fenton Distribution Solved
We consider $S = \sum_{i=1}^n w_i e^{Y_i}$ with $Y \sim N(\mu,\Sigma)$, the central object in the “Fenton distribution” problem.
13 claims 9,665 words
Fin Fenton Spectral
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 representation of that CDF: the **Spectral Lognormal Distribution**.
Verified 19 claims 10,471 words
Fin Generative Portfolio
Classical portfolio optimization minimizes a single risk metric — variance, VaR, or CVaR — subject to return constraints. This produces portfolios that are optimal in one dimension but unconstrained in all others: two portfolios with identical VaR can have radically different skewness, kurtosis, or tail structure.
5 claims 5,628 words
Calibrating Harvestability
Starting from the canonical fin_harvestability object \(h(T,\tau)=1-e^{-T/\tau}\), this reviewer-facing submission studies the calibration problem: when does expected return dominate volatility strongly enough that the premium can be treated as genui
1 claims 2,369 words
Fin Markowitz
We present two results. **Part I** is the first machine-checked formalization of Markowitz (1952) mean-variance optimization in Lean 4, covering the Merton (1972) closed-form solution, two-fund separation, the efficient frontier, and the Capital Market Line.
Verified 16 claims 6,507 words
Why Rational Investors Hold Different Portfolios
We study a persistent tension in financial economics. Markowitz gives an optimizer, equilibrium theory points to a common market benchmark, and lifecycle finance implies investor-specific holdings that vary with horizon, mortality, bequest motive, learning, and constraints.
4,609 words
Pricing Is Allocation Submission Contract
912 words
Fin Progressive Spectral
We formalize the *Progressive Spectral Decomposition* (PSD): computing eigenvalues of a symmetric matrix one at a time via deflation, with a combination of properties no existing method provides simultaneously.
Verified 9 claims 2,765 words
Fin Return Paradox
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.
Verified 5 claims 8,108 words
Spectral Valuation of Compound Exchange Options under Stochastic Volatility
363 words
Spectral Importance Sampling for Rare Events in Correlated Systems
1,065 words
The Spectral Volatility Surface
We introduce a low-rank implied-variance surface in which total variance is represented as \[ w(k, T) = c(T) + \sum_{j=1}^{r} u_j(T)\cos(\omega_j k), \] with structural constraints enforced directly on the coefficient vectors. The resulting object is not a new stochastic-volatility law.
Verified 3,346 words
Knowability Theory: Latent Generator Models and Spectral Pricing in Finance
We present a formally verified mathematical theory of *knowability* in financial modeling — the framework connecting unobservable latent generators to observable price dynamics.
Verified 19 claims 1,818 words
Effective-α framework: LR k-point structure at SR exponents
1,097 words
The Fishing Rod Proverb Is Half-Right
2,351 words
A Numerical Demonstration of Knowledge Artifact Extraction and Algebra Across 26 Model Types
The Knowledge Artifact framework (Nagy 2026a) claims that any model with `.predict()` can be projected into a portable spectral representation that reproduces 87–99% of its predictions. This paper provides the numerical evidence.
1,988 words
Draft Message to Nicolas Cerrajero
Verified 283 words
PDE Tensor Algebra SSOT — Lossless Refactor Plan
1,572 words
Venue-split decision — main paper + short letter
1,433 words
Near-Koide Structure Across the Standard Model Fermion Spectrum
We extend the Koide structure analysis of our companion paper [I] beyond the charged lepton sector.
3,143 words
Phy Qnm Latent — PAPER IDEAS
418 words
The Thought Line: Black Hole Ringdown Has a Universal Compression Constant
1,082 words
Outreach Drafts — Prospective Validation Collaborations
Verified 2,402 words
Executive Summary — Yang-Mills Existence and Mass Gap
1,505 words
Phy Yang Mills Mass Gap — explanation noncollapsing
799 words
Publications — EFFECTIVE RHO
The Fourier-cosine (COS) method achieves exponential convergence for option pricing and risk computation when the underlying density is analytic — but domain truncation can destroy this convergence entirely.
Verified 12 claims 4,099 words
Publications — NOUS SPECTRAL RESOLUTION CAPSTONE
We prove that a single spectral quantity \(K^* = \Theta(\log(1/\varepsilon)/\log\rho)\) — determined entirely by the analyticity radius \(\rho > 1\) and target accuracy \(\varepsilon\) — simultaneously governs seven distinct statistical and financial
Verified 4,805 words
Reference Extract: Acerbi (2002) — Spectral Measures of Risk
606 words
Rough Volatility: The Exponent Architecture of Options Markets
We present a complete formal derivation of the ATM implied volatility skew power law ψ(T) ∼ C · T^{H−1/2} from the rBergomi model definition through an explicit chain of verified lemmas.
Verified 32 claims 3,564 words
The Strong CP Problem: A Formal Treatment of QCD CP Violation and Axion Solutions
We present a formal treatment of the Strong CP problem in QCD and its solutions. The physical θ-parameter, which would induce CP violation through a neutron electric dipole moment, is bounded by experiment to |θ| < 10⁻¹⁰.
9 claims 3,145 words
Tools — LATEX FIXUP PROMPT
546 words
Tools — MD AUTHORING GUIDE
1 claims 677 words
Tropical-Spectral Hybrid Algebra
We introduce a tropical-spectral hybrid algebra that enriches tropical numbers with a spectral entropy component, unifying optimization (tropical) and equilibrium (spectral) descriptions of the same phenomena.
Verified 3 claims 1,939 words