Physics — thalens.org

A refuted-and-vindicated pre-registration test of a spectral error model on a superconducting processor

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.

7,875 words

The Double Gate Theorem: Cascade Instabilities Require Two Independent Conditions

We prove that gravitational cascade instabilities (such as the N-body problem's runaway collisions) and debris cascade instabilities (such as the Kessler syndrome in orbital mechanics) share a common mathematical structure: both require the simultane

17 claims 1,396 words

Turbulence Scaling Laws from the Grade Equation: Kolmogorov Spectrum and Intermittency from Analyticity

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 derivation proceeds in three steps.

Verified 3 claims 12,483 words

The Quantum Compressibility Threshold

We prove a structural dichotomy for open quantum systems.

43 claims 22,715 words

Spectral Error Mitigation: Exact Noise Inversion for Quantum Computers via Cluster Lindblad

3 claims 4,368 words

Resonance Algebra Rh

Representation Theory — Diamond for Characters, Plancherel, Branching This paper presents 673 machine-verified theorems building on 85 established facts and 817 hypotheses.

Verified 446 claims 10,429 words

The Exact Latent Solution of the Gravitational Three-Body Problem

We argue that **every trajectory of the planar gravitational three-body problem** (excluding measure-zero triple collision) admits a finite Latent representation to arbitrary accuracy — an exact, implicit, constructive *encoding* in Fourier space — u

3 claims 11,407 words

Braid Realization at Zero Angular Momentum for the Planar N-Body Problem

We prove that for the planar Newtonian $N$-body problem with arbitrary positive masses and zero angular momentum ($J = 0$), every reduced free homotopy class of periodic orbits with all pairwise winding numbers nonzero is realized by a collision-free periodic orbit.

Verified 5 claims 5,937 words

Turbulence Grade

Turbulence Grade — Kernel Proof Suite v2.0 This paper presents 102 machine-verified theorems.

Verified 95 claims 1,149 words

Morphogenesis as Spectral Selection

We apply the Latent framework to reaction-diffusion systems that exhibit Turing pattern formation, revealing that pattern selection, stability, and convergence are governed by a single spectral quantity: the Latent Number $\rho$ of the linearized reaction-diffusion operator.

Verified 5 claims 3,185 words

The Latent Solution of the Gravitational N-Body Problem

We present a complete treatment of the gravitational N-body problem through the lens of the Latent framework — finite, sufficient representations of smooth dynamical systems.

Verified 18 claims 8,965 words

The Latent of Black Hole Ringdown: Spectral Sufficiency and the Overtone Problem

The gravitational wave ringdown of a perturbed Kerr black hole is a sum of quasinormal modes (QNMs) — damped oscillations with complex frequencies determined by the black hole's mass and spin.

4 claims 7,205 words

Spectral Grade Decomposition of Pulsar Timing Residuals: Separating Gravitational Waves from Intrinsic Noise

Pulsar timing arrays (PTAs) detect the stochastic gravitational wave background (GWB) through correlated timing residuals across a network of millisecond pulsars. The key detection statistic — the Hellings-Downs angular correlation — must be separated from intrinsic pulsar noise, spatially correlated red noise, and solar system ephemeris errors.

Verified 1,729 words

The Grade Equation: A Universal Structural Law for Smooth Dynamical Systems

We prove that every analytic dynamical system $\dot{\mathbf{x}} = F(\mathbf{x})$ satisfies a universal structural law — the **Grade Equation** — which decomposes the dynamics into a hierarchy of interaction grades $F = \sum_{k=0}^{\infty} A^{(k)}$ wi

Verified 5 claims 4,839 words

Grade-2 Universality: A Formally Verified Unification of Fluid Turbulence, Gravitational Singularities, Orbital Debris Cascades, and Epidemic Thresholds

We identify and formally verify a universal algebraic structure — the **Grade-2 equation** — that governs threshold phenomena in four physically distinct domains: (I) the Navier–Stokes equations for incompressible fluid flow, (II) the Painlevé classi

Verified 3 claims 6,085 words

The Fine Structure Constant from First Principles: A Two-Axiom Derivation via the Latent Grade Hierarchy

We derive the fine-structure constant $\alpha$ ($1/\alpha = 137.036$, CODATA) from two axioms — the Hurwitz classification of normed division algebras and a self-duality condition on the vacuum — with **zero free parameters**.

Verified 11 claims 9,504 words

The Feynman Integral as a Latent: Constructive Quantum Field Theory from Grade Decay

The constructive quantum field theory (CQFT) program, initiated by Glimm and Jaffe in the 1970s, seeks to build interacting quantum field theories satisfying the Osterwalder-Schrader axioms from mathematically rigorous first principles.

Verified 4 claims 6,280 words

UV-IR Grade Duality: The Fine-Structure Constant and Cosmological Constant from a Single Scale

We show that the fine-structure constant $\alpha$ (an ultraviolet observable, measured at $M_Z \approx 91$ GeV) and the cosmological constant $\Lambda$ (an infrared observable, measured at $H_0 \approx 10^{-33}$ eV) are both determined by a single pa

Verified 3,295 words

The Latent Theory of Fusion Plasma Confinement

**Methodological contribution.** Alongside the physics result below, this paper establishes a reproducible standard for *kernel-verified derived physics* that we argue is portable across domains in which classical analytic derivations have hardened into opaque community consensus. The standard has four requirements.

15 claims 26,429 words

The Cosmological Constant as a Grade-0 Residual: Smooth Vacuum Energy Flow in the Latent Hierarchy

We identify the cosmological constant $\Lambda$ as the grade-0 component of the gravitational Latent hierarchy and show that the **double grade seesaw** — two consecutive grade-2 → grade-0 projections — closes the cosmological constant problem.

Verified 1 claims 5,485 words

What DESI Tells Us About the Grade Structure of Dark Energy

The DESI DR2 baryon acoustic oscillation measurements, published in *Nature Astronomy* (2025), report 2.8–4.2$\sigma$ evidence for dynamical dark energy with an evolving equation of state $w(z) \neq -1$.

Verified 3 claims 4,295 words

Supercavitation Dynamics from the Grade Equation: The Analyticity Boundary as Cavity Interface

We propose a new theoretical framework for supercavitation dynamics based on the Grade Equation — a universal structural decomposition for analytic dynamical systems.

Verified 4 claims 3,803 words

The Exact Latent Solution of the Gravitational N-Body Problem

We extend the exact Latent solution of the gravitational three-body problem [Nagy 2026g] to the general $N$-body case.

Verified 11 claims 4,613 words

Practical Padé Representations of the Gravitational Three-Body Problem

We demonstrate that Padé resummation of Taylor-series solutions provides a practical, machine-precision representation of the full gravitational three-body problem.

Verified 1 claims 2,886 words

Spectral Matrix Evolution of the Mandelbrot Iteration: Jacobian Products, Coherence, and Meta-Modes

The Mandelbrot set $\mathcal{M} = \{c \in \mathbb{C} : z_n = z_{n-1}^2 + c \text{ stays bounded}\}$ is traditionally visualized by escape-time coloring.

4 claims 2,247 words

Spectral of Spectrals: Second-Order Mode Decomposition for Complex Systems

Spectral decomposition extracts modes from data: eigenvectors of a covariance or kernel operator that capture maximal variance per component. We introduce a **second-order spectral layer**: the eigenanalysis of the spectral features themselves.

7 claims 2,105 words

Spectral Vorticity Bridge for Turbulent Flows

We introduce a Spectral Vorticity Bridge for incompressible turbulent flow, designed to connect vortex-centered and mode-centered descriptions through a shared operator framework. The bridge has three layers.

1,892 words

Information and Causal Access

We propose a manifestation-and-causality view of information. The motivating problem is that the term `information` is used for several different objects at once: raw differences, symbols, messages, semantic content, causal signals, and epistemic gain.

1,540 words

The One Behind Everything

We propose a generator-first extension of the repo's broader spectral program. The starting question is not how a latent state is quantized into a discrete observable, but how a structured latent state may itself arise from repeated application of a local operator.

9,254 words

The Spectral Theory of Observation

We propose a spectral framework for understanding how discrete outcomes arise from smooth latent structure. The core move is to represent a finite-valued or countable observable not as an object outside continuous analysis, but as an atomic measure \[ \mu = \sum_{j=1}^{m} p_j \,\delta_{x_j}, \] already living on a continuous state space.

26,608 words

The Three-Body Problem Solved Distributionally: Spectral Fokker-Planck for the Circular Restricted Three-Body Problem

Poincaré (1890) proved that the three-body problem admits no globally convergent power-series trajectory solution. We do not contradict that result.

1 claims 4,741 words

The α-Continuum: Spectral Gap Controls the Quantum-Classical Transition

We define an effective quantumness parameter $\alpha_{\text{eff}}(t) = 1 + (\text{Tr}(\rho^2) - 1/d)/(1 - 1/d) \in [1, 2]$ that interpolates continuously between quantum ($\alpha = 2$, pure state, full interference) and classical ($\alpha = 1$, maximally mixed, no interference).

4 claims 3,204 words

There Is No Collapse: Measurement as Spectral Projection

We reformulate quantum measurement using the language of spectral pattern theory. The pre-measurement state is not a "wave" (misleading: it does not propagate in 3D space) and not a "probability distribution" (incomplete: it has phase).

3 claims 2,190 words

The Spectral Theory of Observation: Modes, Collapse, and the Information Content of Reality

We identify a single mathematical structure underlying seven apparently distinct physical frameworks: stochastic processes (Fokker--Planck), quantum mechanics (Schrödinger), statistical mechanics (transfer matrix), dynamical systems (Koopman), and information theory (rate-distortion).

2 claims 3,311 words

Falsification Protocol and a Quantitative Dimits-Bypass Prediction for Stochastic-Field-Line Transport

We test a kernel-verified reduced transport law against published tokamak confinement data.

Verified 1 claims 7,594 words

Core The Latent — RESTRUCTURE LOG

977 words

Gravity Theory Divergence: Newton vs MOND

We present a complete formal proof suite establishing the mathematical foundations of Modified Newtonian Dynamics (MOND) and its divergence from Newtonian gravity.

3,822 words

Lyapunov Stability of the Figure-Eight Three-Body Orbit via Z₃ Symmetry Decomposition

We prove Lyapunov stability of the figure-eight choreographic solution to the planar three-body problem using a symmetry decomposition approach. The Z₃ cyclic symmetry of the orbit decomposes the 3 degrees of freedom into a 2-dimensional internal sector and a 1-dimensional normal sector.

Verified 1 claims 2,117 words

Rigorous $-1$ exponent for the laminar-turbulence transition amplitude in a spectrally stratified 1D PDE

In a spectrally stratified 1D mixed advection–reaction PDE used as a diagnostic model for laminar-to-turbulent transitions, we derive a rigorous exponent $-1$ for the initial-condition amplitude threshold $\Pi_c$ in the lowest active wavenumber $k_{\min}$.

5,013 words

Universal Difficulty Exponents in Dissipative PDE Systems: A Renormalization-Group View of the (D, C, P) Framework

**Main thesis.** The ratio of nonlinear coupling to dissipation in a PDE — the scale-dependent *difficulty* $\mathcal{D}(k)$ — obeys a renormalization-group-style flow whose structure is universal across dissipative PDE systems.

11,309 words

General Relativity as a $(0, C, P)$ System: Penrose Singularity as Difficulty Divergence

We reinterpret the Einstein field equations within the $(D, C, P)$ tensor framework of [27]. In the ADM decomposition, vacuum GR is a $(0, R_{\mu\nu}[g], \text{Bianchi} + \text{gauge})$ system: zero dissipation, Ricci coupling, 8-component constraint projector.

Verified 3,397 words

Navier–Stokes Regularity via Leray Bilinear Spreading and Two-Level Decoherence

We prove global regularity of the 3D incompressible Navier–Stokes equations on $\mathbb{T}^3$ for smooth initial data with finite energy. The argument has three stages.

2,007 words

Two Millennium Problems Through the PDE Tensor Algebra: Navier–Stokes Regularity and the Yang–Mills Mass Gap

We present a unified framework — the PDE Tensor Algebra — that addresses two Clay Mathematics Institute Millennium Prize Problems through a single structural principle.

1 claims 1,749 words

Universal Difficulty Exponents in Advective-Dissipative PDE Systems

We show that the scale-dependent difficulty of any advective–dissipative PDE system obeys a universal power law $\mathcal{D}(k) \sim k^{-1}$ in the inertial range, independent of the solution's spectral structure.

1,329 words

The Yang–Mills Mass Gap as a Difficulty Transition in the PDE Tensor Algebra

We analyze the $SU(N)$ Yang–Mills equations through the PDE Tensor Algebra framework, representing them as a triple $(D, C, P)$ of dissipation, coupling, and constraint tensors. Classical pure Yang–Mills is a $(0, C, P)$ system with zero dissipation and structurally infinite difficulty $\mathcal{D} = \|C\|_F / \lambda_{\min}(D) = \infty$.

2,783 words

Unified Celestial Mechanics Latent Monograph — Structure Plan

Verified 3,260 words

Spectral Compression of Charged Black Holes: ρ(Q) for Kerr-Newman

The quasinormal mode analyticity parameter ρ = γ₁/γ₀ ≈ 3 is universal for Kerr (uncharged) black holes [Paper I]. We extend this analysis to Kerr-Newman spacetimes, computing ρ(a, Q) across the full parameter space.

595 words

An Exact Algebraic Bifurcation in the Triangle-Plus-Center Central Configuration

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

7 claims 3,083 words

Montgomery's Four Questions and the Grade Hierarchy of the N-Body Problem

Montgomery (2026) identifies four central open questions for the Newtonian $N$-body problem: (Q1) finiteness of central configurations, (Q2) Lyapunov stability of periodic orbits, (Q3) braid realization at zero angular momentum, and (Q4) density of the scattering map.

Verified 19 claims 11,844 words

The Analyticity Parameter of Neutron Star Post-Merger Oscillations

For black hole ringdown, the analyticity parameter ρ = γ₁/γ₀ ≈ 3 is universal — independent of mass, spin, and multipole [Paper I]. This universality originates from the topological structure of the photon sphere via the WKB approximation.

578 words

Pseudospectral Robustness of the Analyticity Parameter ρ

Jaramillo et al. (2021) demonstrated that individual quasinormal mode frequencies of black holes are spectrally unstable — small perturbations to the effective potential can cause O(1) shifts in higher overtone frequencies. This raises fundamental concerns about the physical relevance of overtone measurements.

828 words

Phy Qnm Latent — email stein draft

233 words

Universal Spectral Compression of Black Hole Ringdown

1 claims 1,503 words

Companion Papers Plan — Quantum USRT Publication Strategy

Verified 1,870 words

A Spectral Dichotomy for Quantum Computing Feasibility: Effective Budget, Advantage Frontier, and Observable-Level Mitigation

We formulate a structural dichotomy for open quantum systems governed by Lindblad dynamics in terms of a single dimensionless parameter, $\rho_Q = e^{|\lambda_1|/v_{LR} - 1}$, constructed from the Lindblad spectral gap $|\lambda_1|$ and the Lieb-Robinson velocity $v_{LR}$.

Verified 2 claims 4,784 words

Tuna-9 Calibration Battery — Self-measured Hardware Parameters

3,286 words

Unique Testable Prediction: The Contested-Band Discrimination Protocol

1,744 words

Phy Smale6 — email draft 20260423 albouy

Verified 1,463 words

Phy Turbulence Scaling Grade — attack

1,986 words

First-Principles Kolmogorov Constant from the Local Analyticity Radius, and the Structural Disqualification of Gamma Intermittency Models

We report three results for the statistics of turbulent dissipation at $\mathrm{Re}_\lambda = 433$, derived from the Grade Equation framework and verified on 226,981 local analyticity-radius measurements from the Johns Hopkins Turbulence Database.

Verified 3,593 words

Mirtill Adversarial Review: Vorticity as a Universal Controller

2,380 words

Existence and Mass Gap for Yang-Mills Theory on R^4

We prove that for any compact simple gauge group $G$, quantum Yang-Mills theory on $\mathbb{R}^4$ exists as a Wightman quantum field theory and has a mass gap $\Delta > 0$, solving the Clay Mathematics Institute Millennium Problem of Jaffe-Witten in

Verified 1 claims 25,669 words

The Pump Cycle Bridge: Structural Isomorphism Between Gravitational Singularities and Debris Cascades

We prove a structural isomorphism between gravitational noncollision singularity (NCS) thresholds and orbital debris cascade thresholds. Both phenomena require a "pump cycle" mechanism—the sustained transfer of energy or momentum between subsystems—which in turn requires at least two independent binary subsystems.

19 claims 1,817 words

Quantum Gravity Bounds: Theory-Independent Constraints on Quantum Gravity

We present a collection of formally verified, theory-independent bounds that constrain any viable theory of quantum gravity. These bounds emerge from the mutual inconsistency of general relativity and quantum mechanics when extrapolated to extreme scales.

Verified 9 claims 2,537 words

Solar Cell Efficiency Bounds: A Formal Framework for Thermodynamic Limits and Improvement Strategies

We present a formally verified mathematical framework for solar cell efficiency bounds. Starting from the second law of thermodynamics, we derive the Carnot limit η ≤ 1 − T_cell/T_sun and prove that practical efficiency is bounded below unity.

Verified 1,756 words