[{"id": "ml_structured_latent_basis", "title": "The Structured Latent Basis: Feature Engineering as Basis Selection", "domain": "core", "lean": false, "words": 6304, "doi": "10.5281/zenodo.21854223", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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", "url": "https://thalens.org/papers/ml_structured_latent_basis/", "pdf": "https://thalens.org/papers/ml_structured_latent_basis/paper.pdf", "created": "2026-04-22", "updated": "2026-08-08"}, {"id": "fin_spectral_ir_pricing", "title": "An Audited Contract Boundary for COS Caplet Pricing", "domain": "quantitative_finance", "lean": true, "words": 2164, "doi": "10.5281/zenodo.21843038", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/fin_spectral_ir_pricing/", "pdf": "https://thalens.org/papers/fin_spectral_ir_pricing/paper.pdf", "created": "2026-03-06", "updated": "2026-08-07"}, {"id": "sgd", "title": "Machine-Checked Scalar Foundations for SGD Analysis", "domain": "optimization and formal methods", "lean": true, "words": 4628, "doi": "10.5281/zenodo.21454787", "status": "short_draft", "status_label": "Short Draft", "review_status": "math_verified", "is_safe": true, "summary": "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 count of novel or publ", "url": "https://thalens.org/papers/sgd/", "pdf": "https://thalens.org/papers/sgd/paper.pdf", "created": "", "updated": "2026-08-06"}, {"id": "core_the_latent", "title": "The Latent: Finite Sufficient Representations of Smooth Systems", "domain": "core", "lean": false, "words": 61268, "doi": "10.5281/zenodo.19101208", "status": "draft", "status_label": "Draft", "review_status": "reviewed", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/core_the_latent/", "pdf": "https://thalens.org/papers/core_the_latent/paper.pdf", "created": "2026-03-18", "updated": "2026-07-28"}, {"id": "nt_bsd", "title": "Conditional BSD Implications with Twelve Explicit Debt Assumptions", "domain": "number_theory", "lean": true, "words": 10226, "doi": "10.5281/zenodo.21496364", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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 $s = 1$.", "url": "https://thalens.org/papers/nt_bsd/", "pdf": "https://thalens.org/papers/nt_bsd/paper.pdf", "created": "2026-04-10", "updated": "2026-07-22"}, {"id": "ind_verified_design_certificates", "title": "From Design Points to Machine-Checked Parameter Regions: Reusable Certificate Templates for Engineering Models", "domain": "verification", "lean": true, "words": 9468, "doi": "10.5281/zenodo.21450089", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/ind_verified_design_certificates/", "pdf": "https://thalens.org/papers/ind_verified_design_certificates/paper.pdf", "created": "", "updated": "2026-07-20"}, {"id": "math_latent_path_integral", "title": "A Finite-Dimensional Bounded-Perturbation Certificate", "domain": "mathematics", "lean": true, "words": 9373, "doi": "10.5281/zenodo.21461836", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "Saddle-point approximations replace an action by its quadratic part, but transferring a quantitative error statement between applications requires an explicit remainder estimate.", "url": "https://thalens.org/papers/math_latent_path_integral/", "pdf": "https://thalens.org/papers/math_latent_path_integral/paper.pdf", "created": "2026-04-09", "updated": "2026-07-20"}, {"id": "fin_fenton_solved", "title": "The Fenton Distribution: An Elementary Representation", "domain": "finance", "lean": true, "words": 13537, "doi": "10.5281/zenodo.19144755", "status": "draft", "status_label": "Draft", "review_status": "reviewed", "is_safe": true, "summary": "An elementary representation route for sums of correlated lognormals; published with DOI and stated for review.", "url": "https://thalens.org/papers/fin_fenton_solved/", "pdf": "https://thalens.org/papers/fin_fenton_solved/paper.pdf", "created": "2026-03-18", "updated": "2026-07-19"}, {"id": "ml_self_improvement", "title": "Conditional Bounds on AI Self-Improvement in an Antitone Threshold Model", "domain": "verification", "lean": true, "words": 7559, "doi": "10.5281/zenodo.21444874", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/ml_self_improvement/", "pdf": "https://thalens.org/papers/ml_self_improvement/paper.pdf", "created": "2026-03-05", "updated": "2026-07-19"}, {"id": "phy_smale6", "title": "Toward Dimension-Independent Finiteness of Central Configurations for Positive Masses: A Scope-Audited Reduction with Named Open Bridges", "domain": "verification", "lean": false, "words": 35806, "doi": "10.5281/zenodo.19533390", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "A proposed route toward finiteness of central configurations for positive masses, with formalized components and explicit assumptions.", "url": "https://thalens.org/papers/phy_smale6/", "pdf": "https://thalens.org/papers/phy_smale6/paper.pdf", "created": "2026-03-24", "updated": "2026-07-18"}, {"id": "phy_spectral_error_mitigation", "title": "Spectral Error Mitigation: Model-Based Noise Inversion for Quantum Computers via Cluster Lindblad", "domain": "physics", "lean": false, "words": 4631, "doi": "10.5281/zenodo.19536298", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "", "url": "https://thalens.org/papers/phy_spectral_error_mitigation/", "pdf": "https://thalens.org/papers/phy_spectral_error_mitigation/paper.pdf", "created": "2026-03-08", "updated": "2026-07-13"}, {"id": "phy_m_theory_dimensions", "title": "Formal Koide Structure: Mass Bounds, Generation Counting, and Neutrino Predictions from the Z_N Ansatz", "domain": "verification", "lean": true, "words": 3716, "doi": "10.5281/zenodo.19698011", "status": "short_draft", "status_label": "Short Draft", "review_status": "math_verified", "is_safe": true, "summary": "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 $Q = 2/3$.", "url": "https://thalens.org/papers/phy_m_theory_dimensions/", "pdf": "https://thalens.org/papers/phy_m_theory_dimensions/paper.pdf", "created": "2026-04-10", "updated": "2026-07-12"}, {"id": "nt_riemann_hypothesis", "title": "Toward the Riemann Hypothesis: A Superquadratic-Growth Framework for Zeta Moments and its Limits", "domain": "math", "lean": true, "words": 21863, "doi": "10.5281/zenodo.19336128", "status": "draft", "status_label": "Draft", "review_status": "reviewed", "is_safe": true, "summary": "We present an algebraic framework relating the growth of the zeta\nmoments to Hankel-determinant structure, together with an honest\naccount of where the framework does and does not reach the Riemann\nHypothesis.", "url": "https://thalens.org/papers/nt_riemann_hypothesis/", "pdf": "https://thalens.org/papers/nt_riemann_hypothesis/paper.pdf", "created": "2026-03-26", "updated": "2026-07-10"}, {"id": "phy_exact_3body_solution", "title": "Toward an Exact Latent Encoding of the Gravitational Three-Body Problem", "domain": "physics", "lean": false, "words": 12550, "doi": "10.5281/zenodo.19101228", "status": "draft", "status_label": "Draft", "review_status": "reviewed", "is_safe": true, "summary": "A proposed finite Latent encoding for gravitational three-body trajectories, with convergence and formalization status separated from the main claim.", "url": "https://thalens.org/papers/phy_exact_3body_solution/", "pdf": "https://thalens.org/papers/phy_exact_3body_solution/paper.pdf", "created": "2026-03-18", "updated": "2026-07-10"}, {"id": "phy_nbody_latent_solution", "title": "A Finite Latent Framework for the Gravitational N-Body Problem", "domain": "physics", "lean": false, "words": 6288, "doi": "10.5281/zenodo.19258475", "status": "draft", "status_label": "Draft", "review_status": "unreviewed", "is_safe": false, "summary": "We extend the finite Latent representation of the gravitational three-body problem [Nagy 2026g] to the general $N$-body case.", "url": "https://thalens.org/papers/phy_nbody_latent_solution/", "pdf": "https://thalens.org/papers/phy_nbody_latent_solution/paper.pdf", "created": "2026-03-18", "updated": "2026-07-10"}, {"id": "fin_harvestability", "title": "Harvestability", "domain": "verification", "lean": true, "words": 17342, "doi": "10.5281/zenodo.21206588", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "This paper studies **harvestability** as a horizon object for portfolio allocation within a CRRA investor model facing Ornstein-Uhlenbeck eigenmodes.", "url": "https://thalens.org/papers/fin_harvestability/", "pdf": "https://thalens.org/papers/fin_harvestability/paper.pdf", "created": "2026-03-07", "updated": "2026-07-07"}, {"id": "fin_equity_premium", "title": "Resolving the Equity Premium Requires at Least Two Dimensions: A Machine-Checked Class No-Go and a Term-Structure Discriminator", "domain": "verification", "lean": true, "words": 20868, "doi": "10.5281/zenodo.21203691", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "The equity premium puzzle of Mehra and Prescott (1985) is the observation that the\nstandard consumption-based asset pricing model, calibrated to plausible risk\naversion and the observed smoothness of aggregate consumption, predicts an equity\npremium", "url": "https://thalens.org/papers/fin_equity_premium/", "pdf": "https://thalens.org/papers/fin_equity_premium/paper.pdf", "created": "2026-04-10", "updated": "2026-07-05"}, {"id": "nt_rh_path1_fourier_euler", "title": "The Riemann Hypothesis via Fourier-Euler Product: A Short Conditional Reduction", "domain": "math", "lean": true, "words": 3579, "doi": "10.5281/zenodo.19369216", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/nt_rh_path1_fourier_euler/", "pdf": "https://thalens.org/papers/nt_rh_path1_fourier_euler/paper.pdf", "created": "2026-03-31", "updated": "2026-06-27"}, {"id": "nt_rh_path2_gue", "title": "Full Density of Zeta Zeros on the Critical Line via GUE Universality", "domain": "math", "lean": false, "words": 4708, "doi": "10.5281/zenodo.19369301", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/nt_rh_path2_gue/", "pdf": "https://thalens.org/papers/nt_rh_path2_gue/paper.pdf", "created": "2026-03-30", "updated": "2026-06-27"}, {"id": "fin_projected_generator_method", "title": "The Projected-Generator Method for Path-Dependent Derivative Pricing", "domain": "finance", "lean": true, "words": 24623, "doi": "10.5281/zenodo.20765846", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "Derivative pricing has a clear mathematical target: compute the discounted\nrisk-neutral value of a payoff under a specified model. For European vanilla\ncontracts this target is often analytic or nearly analytic.", "url": "https://thalens.org/papers/fin_projected_generator_method/", "pdf": "https://thalens.org/papers/fin_projected_generator_method/paper.pdf", "created": "2026-05-14", "updated": "2026-06-17"}, {"id": "ml_icl_architecture", "title": "Architectural Optimizations of the In-Context Gradient-Descent Mechanism", "domain": "machine_learning", "lean": true, "words": 3952, "doi": "10.5281/zenodo.20708838", "status": "short_draft", "status_label": "Short Draft", "review_status": "math_verified", "is_safe": true, "summary": "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).", "url": "https://thalens.org/papers/ml_icl_architecture/", "pdf": "https://thalens.org/papers/ml_icl_architecture/paper.pdf", "created": "", "updated": "2026-06-15"}, {"id": "ml_icl_capacity_scaling", "title": "Capacity, Scaling, and Grokking from the In-Context Learning = Gradient Descent Mechanism", "domain": "machine_learning", "lean": true, "words": 4655, "doi": "10.5281/zenodo.20708799", "status": "short_draft", "status_label": "Short Draft", "review_status": "math_verified", "is_safe": true, "summary": "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 *representational c", "url": "https://thalens.org/papers/ml_icl_capacity_scaling/", "pdf": "https://thalens.org/papers/ml_icl_capacity_scaling/paper.pdf", "created": "", "updated": "2026-06-15"}, {"id": "ml_icl_dynamics_inference", "title": "Training Dynamics and Inference Guarantees of the In-Context Gradient-Descent Mechanism", "domain": "machine_learning", "lean": true, "words": 3532, "doi": "10.5281/zenodo.20708823", "status": "short_draft", "status_label": "Short Draft", "review_status": "math_verified", "is_safe": true, "summary": "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).", "url": "https://thalens.org/papers/ml_icl_dynamics_inference/", "pdf": "https://thalens.org/papers/ml_icl_dynamics_inference/paper.pdf", "created": "", "updated": "2026-06-15"}, {"id": "ml_in_context_gradient_descent", "title": "When In-Context Learning Implements Gradient Descent: A Learned Mechanism, Mechanically Verified and Empirically Tested", "domain": "machine_learning", "lean": true, "words": 14988, "doi": "10.5281/zenodo.20708733", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "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 implicit least-squares o", "url": "https://thalens.org/papers/ml_in_context_gradient_descent/", "pdf": "https://thalens.org/papers/ml_in_context_gradient_descent/paper.pdf", "created": "", "updated": "2026-06-15"}, {"id": "fin_dimension_collapse", "title": "Endogenous Dimension Collapse: A Fold Bifurcation in Market Risk Structure", "domain": "finance", "lean": false, "words": 7379, "doi": "10.5281/zenodo.21061031", "status": "draft", "status_label": "Draft", "review_status": "unreviewed", "is_safe": false, "summary": "The collapse of a market's effective dimensionality during financial crises is an **endogenous phase transition** rather than a smooth response to exogenous shocks. Specifically, it is a discontinuous, history-dependent jump.", "url": "https://thalens.org/papers/fin_dimension_collapse/", "pdf": "", "created": "2026-05-31", "updated": "2026-06-02"}, {"id": "prob_ips_scp_palm", "title": "Explicit Flat Palm Weights for the Second Class Particle in a Three-State Attractive Interacting Particle System", "domain": "verification", "lean": true, "words": 3823, "doi": "10.5281/zenodo.20293551", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "", "url": "https://thalens.org/papers/prob_ips_scp_palm/", "pdf": "https://thalens.org/papers/prob_ips_scp_palm/paper.pdf", "created": "2026-05-19", "updated": "2026-05-19"}, {"id": "core_theory_universal_spectral_representation", "title": "The Universal Spectral Representation Theorem: Breaking the Curse of Dimensionality", "domain": "finance", "lean": false, "words": 7406, "doi": "10.5281/zenodo.18910565", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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", "url": "https://thalens.org/papers/core_theory_universal_spectral_representation/", "pdf": "https://thalens.org/papers/core_theory_universal_spectral_representation/paper.pdf", "created": "2026-03-03", "updated": "2026-04-27"}, {"id": "phy_yang_mills_mass_gap", "title": "The Yang-Mills Mass Gap via Gauge Absorption and Perelman W-Entropy", "domain": "verification", "lean": true, "words": 20060, "doi": "10.5281/zenodo.19681806", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "**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", "url": "https://thalens.org/papers/phy_yang_mills_mass_gap/", "pdf": "", "created": "2026-04-07", "updated": "2026-04-27"}, {"id": "core_latent_of_latents", "title": "The Latent of Latents: Hierarchical Finite Representations of Knowledge Families", "domain": "ml", "lean": true, "words": 11940, "doi": "10.5281/zenodo.19134433", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/core_latent_of_latents/", "pdf": "https://thalens.org/papers/core_latent_of_latents/paper.pdf", "created": "2026-03-19", "updated": "2026-04-25"}, {"id": "fin_basket_options", "title": "Pricing Basket Options via Eigenvalue-Conditional Black-Scholes Mixing", "domain": "finance", "lean": false, "words": 7134, "doi": "10.5281/zenodo.18910539", "status": "draft", "status_label": "Draft", "review_status": "unreviewed", "is_safe": false, "summary": "Pricing European basket options requires the distribution of a weighted sum of correlated lognormals — the Fenton Distribution (Nagy, 2026a) — which has no closed form.", "url": "https://thalens.org/papers/fin_basket_options/", "pdf": "https://thalens.org/papers/fin_basket_options/paper.pdf", "created": "2026-03-01", "updated": "2026-04-25"}, {"id": "fin_es_backtest_exact", "title": "Contaminated by Construction: Separating Simulation Noise from Model Risk in ES Backtests", "domain": "finance", "lean": true, "words": 12336, "doi": "10.5281/zenodo.19605106", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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", "url": "https://thalens.org/papers/fin_es_backtest_exact/", "pdf": "https://thalens.org/papers/fin_es_backtest_exact/paper.pdf", "created": "2026-03-06", "updated": "2026-04-25"}, {"id": "fin_exact_var_computational", "title": "Deterministic Portfolio VaR Without Monte Carlo: The Eigen-COS Method", "domain": "finance", "lean": true, "words": 11099, "doi": "10.5281/zenodo.18910515", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/fin_exact_var_computational/", "pdf": "https://thalens.org/papers/fin_exact_var_computational/paper.pdf", "created": "2026-03-02", "updated": "2026-04-25"}, {"id": "fin_fenton_practical", "title": "Terminal Portfolio Value Distribution to Machine Precision", "domain": "finance", "lean": true, "words": 5174, "doi": "10.5281/zenodo.19222591", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/fin_fenton_practical/", "pdf": "https://thalens.org/papers/fin_fenton_practical/paper.pdf", "created": "2026-03-24", "updated": "2026-04-25"}, {"id": "fin_return_paradox", "title": "What Is a Return? (Especially When Prices Can Be Negative)", "domain": "finance", "lean": true, "words": 8123, "doi": "10.5281/zenodo.18927849", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/fin_return_paradox/", "pdf": "https://thalens.org/papers/fin_return_paradox/paper.pdf", "created": "", "updated": "2026-04-25"}, {"id": "fin_spectral_importance_sampling", "title": "Spectral Importance Sampling: Optimal Rare-Event Simulation via Eigenvalue-Conditioned Measure Change", "domain": "finance", "lean": false, "words": 5353, "doi": "10.5281/zenodo.19234221", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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 ma", "url": "https://thalens.org/papers/fin_spectral_importance_sampling/", "pdf": "https://thalens.org/papers/fin_spectral_importance_sampling/paper.pdf", "created": "2026-03-25", "updated": "2026-04-25"}, {"id": "nt_damped_vinogradov", "title": "Explicit L² Bounds for Damped Vinogradov Sums", "domain": "math", "lean": false, "words": 7302, "doi": "10.5281/zenodo.19689577", "status": "draft", "status_label": "Draft", "review_status": "unreviewed", "is_safe": false, "summary": "", "url": "https://thalens.org/papers/nt_damped_vinogradov/", "pdf": "https://thalens.org/papers/nt_damped_vinogradov/paper.pdf", "created": "", "updated": "2026-04-25"}, {"id": "nt_euler_product_smoothness", "title": "The Euler Product Smoothness Theorem: Multiplicative Structure Forces Latent Existence", "domain": "math", "lean": false, "words": 45536, "doi": "10.5281/zenodo.19143799", "status": "draft", "status_label": "Draft", "review_status": "unreviewed", "is_safe": false, "summary": "We prove that the distribution of values of random Euler products on the\ncritical line possesses a stable Latent — a finite rational approximation\nwith exponential convergence — and provide a **complete structural proof**\nof the Euler Product Smoothn", "url": "https://thalens.org/papers/nt_euler_product_smoothness/", "pdf": "https://thalens.org/papers/nt_euler_product_smoothness/paper.pdf", "created": "2026-03-19", "updated": "2026-04-25"}, {"id": "phy_navier_stokes_latent", "title": "Grade Decomposition and Gevrey Regularity for Navier-Stokes: A Machine-Checked Conditional Framework", "domain": "verification", "lean": true, "words": 9473, "doi": "10.5281/zenodo.19336183", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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 terms.", "url": "https://thalens.org/papers/phy_navier_stokes_latent/", "pdf": "https://thalens.org/papers/phy_navier_stokes_latent/paper.pdf", "created": "2026-03-19", "updated": "2026-04-25"}, {"id": "phy_navier_stokes_regularity", "title": "Global Regularity for the Three-Dimensional Navier-Stokes Equations via Direction Coherence and Dyadic W-Entropy Weakening", "domain": "mathematical physics", "lean": false, "words": 10583, "doi": "10.5281/zenodo.19754783", "status": "draft", "status_label": "Draft", "review_status": "unreviewed", "is_safe": false, "summary": "We reduce the global regularity problem for the three-dimensional incompressible Navier-Stokes equations to a single quantitative estimate: the integrability of the adiabatic error in the Gallay-Wayne convergence of vortex cross-sections to the Burgers profile.", "url": "https://thalens.org/papers/phy_navier_stokes_regularity/", "pdf": "https://thalens.org/papers/phy_navier_stokes_regularity/paper.pdf", "created": "", "updated": "2026-04-25"}, {"id": "phy_practical_pade_3body", "title": "Practical Padé Representations of the Gravitational Three-Body Problem", "domain": "physics", "lean": true, "words": 2888, "doi": "10.5281/zenodo.19101252", "status": "short_draft", "status_label": "Short Draft", "review_status": "math_verified", "is_safe": true, "summary": "We demonstrate that Padé resummation of Taylor-series solutions provides a practical, machine-precision representation of the full gravitational three-body problem.", "url": "https://thalens.org/papers/phy_practical_pade_3body/", "pdf": "https://thalens.org/papers/phy_practical_pade_3body/paper.pdf", "created": "2026-03-18", "updated": "2026-04-25"}, {"id": "phy_quantum_tuna9_parity", "title": "A refuted-and-vindicated pre-registration test of a spectral error model on a superconducting processor", "domain": "physics", "lean": false, "words": 7877, "doi": "10.5281/zenodo.19645328", "status": "working_paper", "status_label": "Working Paper", "review_status": "reviewed", "is_safe": true, "summary": "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.", "url": "https://thalens.org/papers/phy_quantum_tuna9_parity/", "pdf": "https://thalens.org/papers/phy_quantum_tuna9_parity/paper.pdf", "created": "2026-04-18", "updated": "2026-04-25"}, {"id": "nt_rh_latent_existence", "title": "A Conditional Moment-Based Diagnostic for the Riemann Hypothesis", "domain": "math", "lean": false, "words": 4284, "doi": "10.5281/zenodo.19144521", "status": "short_draft", "status_label": "Short Draft", "review_status": "unreviewed", "is_safe": false, "summary": "We propose a conditional moment-based diagnostic for the Riemann Hypothesis\nbased on stable finite rational approximations — *Latents* — for the\ndistribution of $|\\zeta(1/2+it)|$ on the critical line.", "url": "https://thalens.org/papers/nt_rh_latent_existence/", "pdf": "https://thalens.org/papers/nt_rh_latent_existence/paper.pdf", "created": "2026-03-19", "updated": "2026-03-19"}, {"id": "fin_tensor_spectral", "title": "The Spectral Tensor Representation of Stochastic Processes", "domain": "finance", "lean": false, "words": 3789, "doi": "10.5281/zenodo.19134457", "status": "short_draft", "status_label": "Short Draft", "review_status": "unreviewed", "is_safe": false, "summary": "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.", "url": "https://thalens.org/papers/fin_tensor_spectral/", "pdf": "https://thalens.org/papers/fin_tensor_spectral/paper.pdf", "created": "2026-03-03", "updated": "2026-03-07"}, {"id": "fin_fenton_spectral", "title": "The Spectral Lognormal Distribution", "domain": "finance", "lean": true, "words": 10468, "doi": "10.5281/zenodo.18910575", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "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", "url": "https://thalens.org/papers/fin_fenton_spectral/", "pdf": "", "created": "", "updated": ""}, {"id": "ml_knowledge_artifacts_algebra", "title": "The Knowledge Artifact and Knowledge Algebra of Machine Learning Models", "domain": "ml", "lean": false, "words": 6457, "doi": "10.5281/zenodo.18910386", "status": "draft", "status_label": "Draft", "review_status": "unreviewed", "is_safe": false, "summary": "A 200-tree Random Forest has 126,074 parameters. Its knowledge? Three numbers and a basis.\n\nWe introduce the **Knowledge Artifact** — a portable representation of what any ML model has learned — and the **Knowledge Algebra** — provably exact arithmetic on these artifacts.", "url": "https://thalens.org/papers/ml_knowledge_artifacts_algebra/", "pdf": "", "created": "", "updated": ""}, {"id": "phy_fundamental_constants_as_grade_ratios", "title": "Fundamental Constants as Grade-Ratio Hypotheses", "domain": "physics", "lean": true, "words": 9506, "doi": "10.5281/zenodo.19183139", "status": "draft", "status_label": "Draft", "review_status": "math_verified", "is_safe": true, "summary": "A speculative grade-ratio model for fundamental constants, with formalized arithmetic components and explicit physical assumptions.", "url": "https://thalens.org/papers/phy_fundamental_constants_as_grade_ratios/", "pdf": "https://thalens.org/papers/phy_fundamental_constants_as_grade_ratios/paper.pdf", "created": "", "updated": ""}]