Updates
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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2026-04-23
· updated
mathematical_biology
Short Draft
Lean
Phylogenetic inference turns molecular sequences into historical relationships. Classical likelihood-based methods excel in practice, yet the information geometry of alignment data relative to tree topology is rarely summarized in coordinates comparable across studies.
2026-04-23
· updated
Formal Verification
Working Paper
Lean
DOI
We prove that for any $N \geq 3$ bodies with positive masses in $\mathbb{R}^d$ ($d \geq 2$), the number of central configurations modulo similarity is finite, resolving Smale's 6th Problem in **every spatial dimension $d \geq 2$ simultaneously**.
2026-04-22
· new
Machine Learning
Working Paper
We introduce the Structured Latent Basis (SLB) framework, a perspective on supervised learning that unifies feature engineering and modeling as a single problem: selecting a mathematical basis in which the target function is linear.
2026-04-22
· updated
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 $Q = 2/3$.
2026-04-22
· updated
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
2026-04-21
· new
Machine Learning
Working Paper
We introduce the Smooth-Step Spectral Method (S³M), a structured basis
regression approach that unifies smooth spectral features with learned
threshold features for tabular data.
2026-04-21
· updated
number_theory
Short Draft
Lean
DOI
Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh [BGST23] proved the first unconditional asymptotic for Montgomery's pair-correlation function $F(\alpha, T)$, with error $O(1/\sqrt{\log T})$ uniformly for $\alpha \in [0,1]$.
2026-04-21
· updated
Formal Verification
Draft
Lean
We introduce the **PDE Tensor Algebra**, a framework that represents any PDE system as a triple $(D, C, P)$ of tensors encoding dissipation, nonlinear coupling, and geometric constraints. The decomposition converts qualitative PDE questions — existence, uniqueness, regularity, st…
2026-04-21
· updated
Formal Verification
Short Draft
Lean
We present a machine-verified derivation chain connecting the E₈ Lie algebra to the electromagnetic fine structure constant $\alpha \approx 1/137$.
2026-04-21
· updated
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.
2026-04-20
· updated
Core Theory
Draft
Lean
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.
2026-04-19
· updated
number_theory
Draft
Lean
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 $s = 1$, and that the leading Taylor coefficient is expressed by an expl
2026-04-19
· updated
number_theory
Draft
Lean
Under grade-2 dominance of the correction field $X_T = \log|\zeta/P_T|^2$ (the per-prime Fourier cumulant bound $|\kappa_m(f_p)| \leq c_m p^{-\lceil m/2 \rceil}$ with $c_m \leq A^m m!$ giving a positive CGF-tail convergence radius $r_\star \geq 1/A$;
2026-04-18
· new
celestial_mechanics
Short Draft
Lean
We prove that the triangle-plus-center central configuration of the planar four-body problem with masses $(1, 1, 1, \mu)$ undergoes an exact stability transition at the critical mass ratio
$$\mu^* = \frac{81 + 64\sqrt{3}}{249},$$
the unique positiv
2026-04-18
· new
Formal Verification
Proof Record
Lean
We present formal proofs of six foundational theorems in integer arithmetic: commutativity of addition and multiplication over ℤ, absorption of zero under multiplication, non-negativity of squared differences, and the dichotomy that every natural number is either zero or positive…
2026-04-18
· updated
Physics
Working Paper
Lean
We derive the Kolmogorov energy spectrum $E(k) \sim \varepsilon^{2/3} k^{-5/3}$ and anomalous intermittency corrections to the structure function exponents $\zeta_p$ from the Grade Equation — a universal structural decomposition theorem for analytic dynamical systems. The derivat…
2026-04-17
· updated
Quantitative Finance
Working Paper
Lean
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 dynamic…
2026-04-17
· updated
Formal Verification
Draft
Lean
2026-04-17
· updated
number_theory
Short Draft
Lean
We identify the total zero energy $D_\infty = \sum_\rho 1/|\rho|^2 = 2 + \gamma - \log(4\pi) \approx 0.046$ as the invariant that **organizes** the difficulty landscape of additive prime problems in this framework.
2026-04-17
· updated
number_theory
Draft
Lean
We develop a conditional proof program for the Goldbach conjecture through the generating function $G(z) = P(z)^2$, where $P(z) = \sum_{p \text{ prime}} z^p$.
2026-04-13
· updated
machine learning / model analysis
Draft
Lean
2026-04-11
· updated
Quantitative Finance
Working Paper
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.
2026-04-11
· updated
mathematics
Draft
Lean
Many of the deepest theorems in mathematics were not proved within a single domain but by transferring the problem through a sequence of domains, applying tools native to each, and returning.
2026-04-11
· updated
Physics
Working Paper
2026-04-10
· updated
mathematical_biology
Short Draft
Lean
Allostery couples distant sites in a macromolecule: ligand binding at one pocket reshapes dynamics and thermodynamics elsewhere.
2026-04-10
· updated
mathematical_biology
Short Draft
Lean
Many neural systems are hypothesized to operate near a critical point between ordered and disordered dynamics, balancing sensitivity and stability.
2026-04-10
· updated
mathematical_biology
Short Draft
Lean
Evolutionary fitness landscapes encode how genotypes map to reproductive success. Rugged landscapes—with many local peaks and epistatic interactions—shape adaptation, evolvability, and the predictability of evolutionary paths.
2026-04-10
· new
Formal Verification
Proof Record
Lean
Gene Regulatory Network Dynamics — Stability, Inference & Latent Connection.
This paper presents 50 machine-verified theorems building on 3 established facts and 54 hypotheses.
2026-04-10
· new
Formal Verification
Proof Record
Lean
This paper presents 0 machine-verified theorems. All results are formally verified in the Lean 4 (629 verification units, 102 proved statements) and exportable to Lean 4.
<!-- TODO: Write a proper abstract summarizing the key contributions -->
2026-04-10
· new
Mathematics
Proof Record
Lean
Neural Manifold — Spectral Dimension Bound, Optimal Decoding & BCI Theory.
This paper presents 47 machine-verified theorems building on 5 established facts and 32 hypotheses.
2026-04-10
· updated
mathematical_biology
Short Draft
Lean
Waddington’s epigenetic landscape metaphor remains the dominant intuitive picture for cell fate: stable types are valleys, differentiation is downhill flow, and reprogramming lifts cells across ridges.
2026-04-10
· new
Formal Verification
Proof Record
Lean
Wright-Fisher Population Genetics — Spectral Convergence + Latent.
This paper presents 24 machine-verified theorems building on 0 established facts and 35 hypotheses.
2026-04-10
· updated
Core Theory
Draft
Lean
We define the **Latent Algebra** $\mathfrak{L}(\mathcal{H}) = \bigoplus_{r \geq 0} \mathcal{H}^{\otimes r}$ as the graded tensor algebra over a separable Hilbert space $\mathcal{H}$, equipped with four primitive operations — addition, tensor product,
2026-04-10
· updated
climate economics / integrated assessment
Short Draft
Lean
The central debate in climate economics — between Nordhaus-style moderate carbon pricing and Stern-style aggressive policy — is fundamentally a disagreement about the tail behavior of the damage distribution.
2026-04-10
· updated
financial networks / systemic risk
Short Draft
Lean
We formalize financial contagion as a Grade-2 hazard model on networks and show how the cascade threshold is tied, under explicit spectral proportionalities, to a concentration index: the Latent Number $\rho$ of the interbank network.
2026-04-10
· updated
dynamic pricing / bayesian learning / revenue optimization
Short Draft
Lean
A seller facing unknown demand must balance exploration (learning the demand curve) against exploitation (maximizing immediate revenue). We organize the explore-exploit tradeoff through the Latent Number $\rho$ of the demand function.
2026-04-10
· updated
macroeconomics / heterogeneous agent models
Short Draft
Lean
Heterogeneous agent models (Aiyagari, 1994; Bewley, 1986) have become the workhorse of quantitative macroeconomics, but their computational demands are severe: the state variable is the entire wealth distribution — an infinite-dimensional object.
2026-04-10
· updated
mechanism design / game theory
Short Draft
Lean
We apply the Latent spectral framework to mechanism design, framing bilateral-trade tensions through a spectral parameter $\rho$ (Latent Number) of the type distribution.
2026-04-10
· updated
market microstructure / financial economics
Short Draft
Lean
We recast Kyle's (1985) insider-trading and price-discovery story in the Latent spectral framework: price impact $\lambda$, spreads, and depth are read through the Latent Number $\rho$ of the price signal.
2026-04-10
· updated
public economics / optimal taxation
Short Draft
Lean
We apply the Latent spectral framework to the Mirrlees (1971) optimal taxation problem, showing that the information rent, tax schedule complexity, and welfare cost of progressive taxation are all governed by the Latent Number $\rho$ of the ability distribution.