§1 — Topological Data Analysis & Persistent Homology
Stable multiscale summaries of the telemetry state geometry, used as candidate regime features. Any link to a proprietary transition is an empirical model result — not a consequence of persistence theory alone.
[1] Carlsson, G. (2009). Topology and Data. Bulletin of the AMS.
[2] Edelsbrunner, H. & Harer, J. (2010). Computational Topology: An Introduction. AMS.
[3] Zomorodian, A. & Carlsson, G. (2005). Computing Persistent Homology. Discrete & Comp. Geom.
[4] Bubenik, P. (2015). Statistical Topological Data Analysis Using Persistence Landscapes. JMLR.
[5] Ghrist, R. (2008). Barcodes: The persistent topology of data. Bulletin of the AMS.
[6] Cohen-Steiner, D., Edelsbrunner, H. & Harer, J. (2007). Stability of Persistence Diagrams. Discrete & Comp. Geom.
§2 — Neural SDE & Stochastic Dynamics
The drift architecture is informed by Hamiltonian mechanics; its continuous-time formulation is modeled as a Neural SDE. Whether symplectic or port-Hamiltonian structure is preserved depends on the specific parameterization and integrator — it is not automatic.
[7] Arnold, V. I. (1989). Mathematical Methods of Classical Mechanics. Springer.
[8] Marsden, J. E. & Ratiu, T. S. (1999). Introduction to Mechanics and Symmetry. Springer.
[9] Di Persio, L., Ehrhardt, M. & Outaleb, Y. (2026). Stochastic Port-Hamiltonian Neural Networks: Universal Approximation with Passivity Guarantees.
arXiv:2603.10078
[10] Tzen, B. & Raginsky, M. (2019). Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit.
arXiv:1905.09883
[11] Greydanus, S., Dzamba, M. & Yosinski, J. (2019). Hamiltonian Neural Networks. NeurIPS.
[12] Chen, R. T. Q., Rubanova, Y., Bettencourt, J. & Duvenaud, D. (2018). Neural Ordinary Differential Equations.
NeurIPS. arXiv:1806.07366
[13] Li, X., Wong, T.-K. L., Chen, R. T. Q. & Duvenaud, D. (2020). Scalable Gradients for Stochastic Differential Equations.
AISTATS. arXiv:2001.01328
[14] Kidger, P., Foster, J., Li, X. & Lyons, T. (2021). Neural SDEs as Infinite-Dimensional GANs.
ICML. arXiv:2102.03657
[48] Milstein, G. N., Repin, Yu. M. & Tretyakov, M. V. (2002). Symplectic Integration of Hamiltonian Systems with Additive Noise. SIAM J. Numer. Anal.
§3 — Empirical Functional Decomposition & Dependence-Aware Attribution
Under correlated inputs the engine computes an exact empirical least-squares projection onto a selected dictionary, then allocates interaction effects. Sensitivity decomposition is not causal identification, and the allocation is not conditional SHAP unless the cooperative game is stated explicitly — the references below bound each claim.
[15] Pearl, J. (2009). Causality. 2nd Ed. Cambridge.
[16] Hooker, G. (2004). Discovering Additive Structure in Black Box Functions. KDD.
[17] Sobol, I. M. (2001). Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates. Math. & Comp. in Simulation.
[18] Spirtes, P., Glymour, C. & Scheines, R. (2000). Causation, Prediction, and Search. MIT Press.
[19] Peters, J., Janzing, D. & Schölkopf, B. (2017). Elements of Causal Inference. MIT Press.
[20] Owen, A. B. (2013). Variance Components and Generalized Sobol' Indices. SIAM/ASA J. Uncert. Quant.
[49] Chastaing, G., Gamboa, F. & Prieur, C. (2012). Generalized Hoeffding-Sobol Decomposition for Dependent Variables. Electron. J. Statist.
[50] Owen, A. B. (2014). Sobol' Indices and Shapley Value. SIAM/ASA J. Uncert. Quant.
[51] Song, E., Nelson, B. L. & Staum, J. (2016). Shapley Effects for Global Sensitivity Analysis: Theory and Computation. SIAM/ASA J. Uncert. Quant.
[52] Harbrecht, H., Peters, M. & Schneider, R. (2012). On the Low-Rank Approximation by the Pivoted Cholesky Decomposition. Appl. Numer. Math.
§4 — Chaos Theory & Dynamical Systems
Delay-coordinate reconstruction and local-instability (Lyapunov) estimates used as regime diagnostics. A positive exponent in noisy, nonstationary market data is a diagnostic — not proof of a deterministic attractor; surrogate-data and embedding checks are required.
[21] Takens, F. (1981). Detecting Strange Attractors in Turbulence. Dynamical Systems and Turbulence, Warwick 1980, LNM 898, Springer.
[22] Eckmann, J.-P. & Ruelle, D. (1985). Ergodic Theory of Chaos and Strange Attractors. Rev. Mod. Phys.
[23] Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. (1985). Determining Lyapunov Exponents from a Time Series. Physica D.
[24] Kantz, H. & Schreiber, T. (2004). Nonlinear Time Series Analysis. Cambridge.
[25] Packard, N. H., Crutchfield, J. P., Farmer, J. D. & Shaw, R. S. (1980). Geometry from a Time Series. Phys. Rev. Lett.
§5 — Non-Markovian Dynamics & Rough Path Theory
Rough-path and fractional models for non-Markovian structure. Roughness (low Hurst, H<½) and long-range memory (typically H>½) are distinct — and non-Markovian structure does not by itself imply persistent directional alpha.
[26] Mandelbrot, B. B. & Van Ness, J. W. (1968). Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review.
[27] Lyons, T. (1998). Differential equations driven by rough signals. Rev. Mat. Iberoamericana.
[28] Friz, P. K. & Hairer, M. (2014). A Course on Rough Paths: With an Introduction to Regularity Structures. Springer.
[29] Gatheral, J., Jaisson, T. & Rosenbaum, M. (2018). Volatility is Rough. Quantitative Finance.
[30] Biagini, F., Hu, Y., Øksendal, B. & Zhang, T. (2008). Stochastic Calculus for Fractional Brownian Motion and Applications. Springer.
§6 — Geometric Loop Features Inspired by Gauge Theory
Holonomy-style geometric features over the asset covariance manifold, inspired by gauge theory. The correspondence to executable mispricing is a modeling analogy — not a theorem from the cited physics literature.
[31] Yang, C. N. & Mills, R. L. (1954). Conservation of Isotopic Spin and Isotopic Gauge Invariance. Physical Review.
[32] Connes, A. (1994). Noncommutative Geometry. Academic Press.
[33] Baez, J. C. & Muniain, J. P. (1994). Gauge Fields, Knots and Gravity. World Scientific.
[34] Witten, E. (1989). Quantum Field Theory and the Jones Polynomial. Commun. Math. Phys.
[35] Donaldson, S. K. (1983). An Application of Gauge Theory to Four-Dimensional Topology. J. Diff. Geom.
§7 — Subdifferential Mechanics & Non-Smooth Optimization
Generalized-gradient methods for optimization at non-differentiable points (locally Lipschitz functions). Modeling genuine market jumps additionally requires jump-diffusion, change-point, or regime-switching structure — the subdifferential handles kinks, not arbitrary discontinuities.
[36] Clarke, F. H. (1990). Optimization and Nonsmooth Analysis. SIAM.
[37] Rockafellar, R. T. (1970). Convex Analysis. Princeton.
[38] Moreau, J. J. (1962). Fonctions convexes duales et points proximaux dans un espace hilbertien. Comptes Rendus Acad. Sci.
[39] Shor, N. Z. (1985). Minimization Methods for Non-Differentiable Functions. Springer (Consultants Bureau transl.).
[40] Nesterov, Y. (2018). Lectures on Convex Optimization. Springer.
§8 — Stochastic Calculus & Measure Theory
Foundations for the stochastic forward pass and scoring. PSD of the Gram matrix Γ = ΦᵀΦ/M follows directly from vᵀΓv = ‖Φv‖²/M ≥ 0 — a linear-algebra fact certified by Cholesky, not by any single classical reference below.
[41] Risken, H. (1989). The Fokker-Planck Equation. Springer.
[42] Doléans-Dade, C. (1970). Quelques applications de la formule de changement de variables pour les semimartingales. Z. Wahrscheinlichkeitstheorie verw. Geb. 16, 181–194.
[43] Choquet, G. (1954). Theory of Capacities. Annales de l'Institut Fourier.
[44] Carathéodory, C. (1911). Über den Variabilitätsbereich der Fourierschen Konstanten. Rend. Circ. Mat. Palermo. (Toeplitz/positivity background — not the PSD certificate itself.)
[45] Øksendal, B. (2003). Stochastic Differential Equations. Springer.
[46] Karatzas, I. & Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus. Springer.
[47] Ruelle, D. (1989). Statistical Mechanics: Rigorous Results. World Scientific.
§9 — DePIN Incentive Design & Enforcement Capacity
Whether a protocol can deter a dishonest operator is a property of its published parameters. We implement only the publicly computable side of these conditions: stake, slash fraction, reward ladder, audit frequency. The deterrence ratio itself depends on an operator’s private cost saving and an audit’s detection gap, neither of which is public, so nothing here yields a compliance verdict on any named network.
[53] Milionis et al. (2025). Incentive-Compatible Recovery from Manipulated Signals, with Applications to Decentralized Physical Infrastructure.
arXiv:2503.07558
[54] Chitra et al. (2025). On Sybil-proofness in Restaking Networks.
arXiv:2509.18338 †
[55] Capitaine et al. (2026). Test-then-Punish: A Statistical Approach to Repeated Games.
arXiv:2603.05619
[56] Tian et al. (2026). TORCH: Characterizing Invalid Route Filtering via Tunnelled Observation.
arXiv:2603.29207
[57] Zhang et al. (2026). Distributed General-Purpose Agent Networks: Architecture, Key Mechanisms, and Prototypes.
arXiv:2606.17368
[58] Zhang & Liu (2026). Beyond Byzantine: An Organizational Consensus Algorithm for Self-Interested Agents Under Information Asymmetry.
arXiv:2607.28957
[59] Nechepurenko (2026). Axient: On-Chain Credit and Loss Allocation for Leveraged Event Markets: A Venue-Agnostic Protocol for Traders, Credit Providers, Market Makers, and Liquidation Backstops.
arXiv:2608.00647
[60] Shang et al. (2026). Repeated-Game Security for Restaking-Based Verifiable Inference.
arXiv:2608.09055
[61] Qazi (2026). A Repeated-Game Framework for Incentives in Decentralized Infrastructure Protocols.
arXiv:2608.12576 — we implement the publicly computable side of its Theorem 1; the deterrence ratio itself is not public.
[62] Kim & Chelikavada (2026). 0xPass: A Secure Protocol for Universal Cross-Chain Accounts.
arXiv:2608.18359
[63] Jiang et al. (2026). A Survey of Decentralized Physical Infrastructure Network,Research Directions, and Open Challenges.
IEEE Communications Surveys & Tutorials, 2026, Early Access.
arXiv:2609.02125
§10 — Network Measurement & Path Verification
Independent observation of who participates in a network and over what path. These are third-party measurement results; several require a vantage point inside the measured network or a per-node endpoint join that we do not hold, and are listed because they bound what outside observation can and cannot establish.
[64] Heimbach et al. (2024). Deanonymizing Ethereum Validators: The P2P Network Has a Privacy Issue.
arXiv:2409.04366
[65] Izhikevich et al. (2024). Rooting Out Incorrect RIPE Atlas Probe Geolocations.
arXiv:2409.19109 †
[66] Li et al. (2025). EGNInfoLeaker: Unveiling the Risks of Public Key Reuse and User Identity Leakage in Blockchain.
arXiv:2507.01635
[67] Kiffer et al. (2025). Multiple Sides of 36 Coins: Measuring Peer-to-Peer Infrastructure Across Cryptocurrencies.
arXiv:2511.15388 †
[68] Nosyk et al. (2025). Day in the Life of RIPE Atlas: Operational Insights and Applications in Network Measurements.
arXiv:2511.22474
[69] Kim (2026). Zero Knowledge Verification of Transaction Guides for P2P Energy Trading in Distribution Networks.
arXiv:2606.12085
[70] Chen et al. (2026). Understanding the Stealthy BGP Hijacking Risk in the ROV Era.
arXiv:2606.23071
[71] Klein et al. (2026). Overconfident Coordinates: Quantifying Confidence in Traceroute Geolocation.
arXiv:2606.24027 †
[72] Xiong et al. (2026). Can Trustless Agents Be Trusted? An Empirical Study of the ERC-8004 Decentralized AI Agent Ecosystem.
arXiv:2606.26028
[73] Liu et al. (2026). Beyond Sparse Supervision: Diffusion-Guided Learning for Few-Shot Graph Fraud Detection.
arXiv:2606.28134
[74] Villarrubia-Martin et al. (2026). Relational Multi-Agent Reinforcement Learning for Dynamic Pricing in High-Speed Railway Markets.
arXiv:2607.05179
[75] Hassan & Rouhani (2026). Layer 2 Coordinated Trusted Setup for Continuous CRS Generation.
arXiv:2607.05776
[76] Zheng et al. (2026). Wireless Decentralized Federated Learning via Device Clustering and Inter-Cluster Link Enhancement.
arXiv:2607.08797
[77] Taherpour & Wang (2026). Secure Decentralized Federated Learning via Gossip and Virtual Voting.
arXiv:2607.08651
[78] Ye et al. (2026). Duet: Co-Optimizing P2P Message Propagation and Rotating-Leader Consensus.
arXiv:2607.22209
[79] Muntaka et al. (2026). Bridging the Epistemic Gap in the Invisible Internet: Extended Mathematical Modeling and Empirical Characterization of I2P Topology.
arXiv:2607.23825
[80] Mathieu et al. (2026). Stream Learning: Partition-Fair Gossip Learning Without Tokens.
SSS 2026, 28th International Symposium on Stabilization, Safety, and Security of Distributed Systems, Oct 2026, Gothenburg, Sweden. arXiv:2608.06946
[81] Sadowy et al. (2026). BGPay: An Incentive-Compatible Mechanism for BGP Hijack Filtering.
arXiv:2608.25165
[82] Thiagarajan & Bustamante (2026). Who Resolves Your DNS? Measuring Resolver Opacity and Closing the Visibility Gap.
arXiv:2608.29371
[83] Paglieri et al. (2026). A Case Study on Emergent Cheating and Whistleblowing in Autonomous Research Swarms.
arXiv:2609.04170
§11 — Misreporting, Sybil & Collusion Detection
Methods for detecting fabricated or coordinated reporting. Entries marked † were evaluated against our own estate and rejected for our use — in most cases because the method needs a ground-truth oracle, per-node labels, or a participant’s view of the network, none of which a third-party observer has. They are kept because a rejected method is evidence too. No claim is made here about which techniques we run.
[84] Bates et al. (2021). Testing for Outliers with Conformal p-values.
Ann. Statist. 51(1): 149-178 (February 2023). arXiv:2104.08279 †
[85] Cong et al. (2021). Crypto Wash Trading.
arXiv:2108.10984 †
[86] Ding & Du (2022). Detection threshold for correlated Erdős-Rényi graphs via densest subgraphs.
arXiv:2203.14573
[87] Chen & Tsourakakis (2022). AntiBenford Subgraphs: Unsupervised Anomaly Detection in Financial Networks.
arXiv:2205.13426
[88] Shekhar et al. (2023). Risk-limiting Financial Audits via Weighted Sampling without Replacement.
arXiv:2305.06884
[89] Hohenfeld et al. (2025). Explaining Anomalies with Tensor Networks.
arXiv:2505.03911 †
[90] Cano-Rodriguez (2025). How much is too much? Measuring divergence from Benford's Law with the Equivalent Contamination Proportion (ECP).
arXiv:2506.09915
[91] Söderhäll et al. (2025). On the Impact of Sybil-based Attacks on Mobile Crowdsensing for Transportation.
arXiv:2506.20585
[92] Akgul et al. (2025). ZK-SenseLM: Verifiable Large-Model Wireless Sensing with Selective Abstention and Zero-Knowledge Attestation.
arXiv:2510.25677
[93] Bharti et al. (2026). Global Sequential Testing for Multi-Stream Auditing.
arXiv:2602.21479 †
[94] Kong & Chen (2026). CSI-RFF: Leveraging Micro-Signals on CSI for RF Fingerprinting of Commodity WiFi.
IEEE Transactions on Information Forensics and Security, vol. 19, pp. 5301-5315, 2024. arXiv:2602.22738
[95] Sornsaeng et al. (2026). SMT-AD: a scalable quantum-inspired anomaly detection approach.
arXiv:2604.06265 †
[96] Gil et al. (2026). Adaptive Conformal Anomaly Detection with Time Series Foundation Models for Signal Monitoring.
arXiv:2604.20122
[97] Yagiz et al. (2026). Lightweight Tamper-Evident Log Integrity Verification for IoT Edge Environments: A Merkle Tree Pipeline with Adaptive Chunking.
arXiv:2605.00065
[98] Alpay & Sarioglu (2026). Service-Cut Certificates for Aligned Eviction in Tiered Cache Networks.
arXiv:2606.22270
[99] Zhang & Venkatakrishnan (2026). Rethinking Collaborative Trust for Verifiably Decentralized Blockchain Systems.
arXiv:2606.29826
[100] Cerqueti & Ventura (2026). Manipulation testing based on Benford's Law for discrete scores.
arXiv:2607.13564
[101] Xu et al. (2026). Collusion with Competitive Marginals: Price-Level Audits Are Blind by Construction.
arXiv:2607.26385
[102] Zhu et al. (2026). Verifiable Random Sampling.
arXiv:2607.26734
[103] Bartnicki & Chudziak (2026). Compression-Based Behavioral Similarity for Open-World Sybil Discovery on Ethereum.
arXiv:2607.27370
[104] N et al. (2026). ZAPs: A Reward Attribution Framework for DeFi Ecosystems with Adversarial-Robust Scoring via Parallel Anomaly Ensemble Detection.
arXiv:2607.27859
[105] Catalano & Mantegna (2026). How null-model constraints affect statistical validation in projected bipartite networks.
arXiv:2607.29242 †
[106] Li (2026). Post-Hoc Trajectory-Risk Certification for Modular LLM-Based Security Agents.
arXiv:2608.05199
[107] Tomson et al. (2026). Toward Practical Decentralized Proof-of-Location via Physical Witnessing Zones.
arXiv:2608.04957
[108] Sarenche & Liu (2026). Towards Decentralized Searcher Competition in MEV Markets.
arXiv:2608.05011
[109] Zou et al. (2026). InterSAGE: The Secure and Verifiable Interoperability Protocol for An Internet of Agents.
arXiv:2608.13030
[110] Opoku & Banahene (2026). SynthGuard-ReleaseBench: Locked-Audit Evidence for Synthetic Tabular Data Releases.
arXiv:2608.14753
[111] Guo et al. (2026). IriSig-Spoof: A Real-World Benchmark for Time-Robust Satellite RF Fingerprinting and Spoofing Detection.
arXiv:2608.18642
[112] Han & Qu (2026). When the Martingale Never Stops Firing: Anytime-Valid Gating on Real Forecast Streams.
arXiv:2608.30502
[113] Yin et al. (2026). CRSF: Collusion-Resilient Privacy-Preserving Sensor Fusion with Byzantine-Robust Participation.
arXiv:2609.01096
[114] Shi et al. (2026). Otter: A Provably MEV-Resilient Automated Market Maker via Surplus Redistribution.
arXiv:2609.03474
[115] Diop & Plantevit (2026). Differentiable Interval Bottlenecks for Interpretable Anomaly Detection in Numerical Data.
arXiv:2609.03878
§12 — Attestation, Provenance & Verifiable Records
Tamper-evidence, transparency logs and authenticated data structures — the machinery under signed receipts and inclusion proofs. Inclusion here describes the literature we work from, not a claim that every mechanism is deployed in our stack.
[116] Eisler et al. (2007). Fluctuation scaling in complex systems: Taylor's law and beyond.
Advances in Physics 57, 89-142 (2008). arXiv:0708.2053
[117] Buhrman et al. (2010). Position-Based Quantum Cryptography: Impossibility and Constructions.
arXiv:1009.2490
[118] Wolfe et al. (2016). The Inflation Technique for Causal Inference with Latent Variables.
J. Causal Inference 7(2), 2019. arXiv:1609.00672 †
[119] Navascues & Wolfe (2017). The Inflation Technique Completely Solves the Causal Compatibility Problem.
J. Causal Inference 8(1), 2019. arXiv:1707.06476 †
[120] Miccichè & Mantegna (2019). A primer on statistically validated networks.
Proceedings of the International School of Physics "Enrico Fermi", Volume 203: Computational Social Science and Complex Systems, (2019). arXiv:1902.07074
[121] Burrell & Schoenebeck (2021). Measurement Integrity in Peer Prediction: A Peer Assessment Case Study.
arXiv:2108.05521
[122] Aizpurua et al. (2023). Tensor Networks for Explainable Machine Learning in Cybersecurity.
Neurocomputing, Volume 639, 28 July 2025, Article 130211. arXiv:2401.00867 †
[123] Ovezik et al. (2025). SoK: Measuring Blockchain Decentralization.
arXiv:2501.18279
[124] Liu et al. (2025). Certified randomness using a trapped-ion quantum processor.
Nature (2025). arXiv:2503.20498
[125] Mallick et al. (2025). Quantum Disruption: An SOK of How Post-Quantum Attackers Reshape Blockchain Security and Performance.
arXiv:2512.13333
[126] Cao et al. (2026). Early Rug Pull Warning for BSC Meme Tokens via Multi-Granularity Wash-Trading Pattern Profiling.
arXiv:2603.13830
[127] Chung et al. (2026). Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment.
arXiv:2608.23691
[128] Zhang et al. (2026). More Criticism Does Not Make a Better Review: EquiReview-R.
arXiv:2609.03943
§13 — Foundations
Primary sources underneath the modern work above. Every citation here was checked against a bibliographic record on 2026-09-04, and every link was fetched and confirmed to name the work at that date — a full-text or scan link delivers the work itself, a record link a catalogue, DOI or Crossref entry for it — rather than a paywall or bot-challenge page. Two entries (Benford 1938, Hakimi 1962) carry no link because no copy we could verify is openly hosted — the citation is given instead of a link we could not stand behind.
[129] Newcomb, S. (1881). Note on the Frequency of Use of the Different Digits in Natural Numbers.
American Journal of Mathematics 4(1), 39–40.
scan — First statement of the leading-digit law.
[130] Yule, G. U. (1925). A Mathematical Theory of Evolution, Based on the Conclusions of Dr. J. C. Willis, F.R.S.
Philosophical Transactions of the Royal Society of London, Series B 213, 21–87.
full text ·
full text (mirror) ·
record — Origin of the Yule process: species multiply within a genus at a rate proportional to genus size while new genera arise at a constant rate, giving a genus-size distribution that is straight on log–log axes (Sections I–II, pp. 25–40) — the size-proportional growth mechanism later called preferential attachment, which we apply to heavy-tailed node and stake distributions.
[131] Gibrat, R. (1931).
Les Inégalités économiques. Librairie du Recueil Sirey, Paris.
scan ·
full text ·
record — Law of proportional effect (growth independent of size), from which he derives the log-normal size distribution, worked on firms by headcount (pp. 63–64, 75–77); our null model for node-count growth across networks.
[132] Benford, F. (1938). The Law of Anomalous Numbers. Proceedings of the American Philosophical Society 78(4), 551–572. — The digit law used in fraud screening. Its precondition — values spanning orders of magnitude — holds for only a minority of our series.
[133] Ville, J. (1939).
Étude critique de la notion de collectif. Gauthier-Villars, Paris.
thesis record ·
thesis scan — Introduces the martingale as a gambler’s betting system and shows that no countable family of von Mises–Wald selection rules can exclude every probability-zero property (Ch. II Th. 4; Ch. IV). Ville’s inequality (Ch. V Th. 1) is the guarantee behind the anytime-valid sequential tests we cite.
[134] Wald, A. (1945). Sequential Tests of Statistical Hypotheses.
Annals of Mathematical Statistics 16(2), 117–186.
record — The SPRT, ancestor of every anytime-valid audit.
[135] Shannon, C. E. (1948). A Mathematical Theory of Communication.
Bell System Technical Journal 27, 368–423 and 623–656.
full text
[136] Zipf, G. K. (1949).
Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology. Addison-Wesley Press, Cambridge, MA. xi + 573 pp.
record ·
scan ·
full text — Rank-frequency law for words (r × f = C, p. 24) and rank-size law for communities (r · Pq = K, p. 366): the regularity a reported node distribution can be screened against. That fabricated counts violate it is our hypothesis, untested here, not a claim of the book.
[137] Havel, V. (1955). Poznámka o existenci konečných grafů [A remark on the existence of finite graphs].
Časopis pro pěstování matematiky 80(4), 477–480.
record ·
full text ·
EuDML record ·
DOI — Degree-sequence realisability test for reported peer counts.
[138] Simon, H. A. (1955). On a Class of Skew Distribution Functions.
Biometrika 42(3/4), 425–440.
record ·
full text — Cumulative-advantage (Yule–Simon) process generating heavy-tailed size distributions, fitted in the paper to word counts, publications, city sizes, incomes and genera; our baseline for skewed DePIN operator sizes.
[139] Erdős, P. & Gallai, T. (1960). Gráfok előírt fokú pontokkal [Graphs with prescribed degrees of vertices].
Matematikai Lapok 11, 264–274.
full text — A claimed degree sequence is either realisable or it is not — decidable from published numbers alone.
[140] Taylor, L. R. (1961). Aggregation, Variance and the Mean.
Nature 189, 732–735.
record — Fluctuation scaling: real populations obey a variance–mean power law.
[141] Hakimi, S. L. (1962). On Realizability of a Set of Integers as Degrees of the Vertices of a Linear Graph. I. SIAM Journal on Applied Mathematics 10(3), 496–506. — Constructive counterpart to Erdős–Gallai.
[142] Kolmogorov, A. N. (1965). Three approaches to the quantitative definition of information.
Problems of Information Transmission 1(1), 1–7.
record (translation contents) ·
record (Russian original) ·
zbMATH record ·
full text (scan) ·
Russian original (PDF) — §3 (“An algorithmic approach”, transl. p. 4 ff.; definition and invariance theorem p. 5) defines the complexity of an object as the minimal length of a program that produces it — the quantity that compression-distance similarity methods (NCD) approximate with real compressors. Russian original: Problemy Peredachi Informatsii 1(1), 3–11; reprinted Int. J. Computer Mathematics 2(1–4), 157–168 (1968).
[143] Becker, G. S. (1968). Crime and Punishment: An Economic Approach.
Journal of Political Economy 76(2), 169–217.
record ·
full text — The deterrence condition arXiv:2608.12576 generalises.
[144] Akerlof, G. A. (1970). The Market for “Lemons”: Quality Uncertainty and the Market Mechanism.
Quarterly Journal of Economics 84(3), 488–500.
record — Why verifiable quality has value at all.
[145] Price, D. de S. (1976). A general theory of bibliometric and other cumulative advantage processes.
Journal of the American Society for Information Science 27(5), 292–306.
record ·
scan — Success-breeds-success (cumulative advantage) urn / pure-birth process after Yule, derived for citation counts and the Lotka, Bradford, Pareto and Zipf laws; our null model for operator and node concentration.
[146] Holmström, B. (1979). Moral Hazard and Observability.
Bell Journal of Economics 10(1), 74–91.
record — The informativeness principle: which observable signals can improve a contract.
[147] Merkle, R. C. (1979). Secrecy, Authentication, and Public Key Systems.
Ph.D. thesis, Department of Electrical Engineering, Stanford University; Information Systems Laboratory Technical Report No. 1979-1 (SEL 79-017), ch. V, §4 “Tree Authentication,” pp. 40–45.
full text ·
author’s listing ·
1982 UMI revision (record) ·
S&P 1980 full text ·
S&P 1980 record (Crossref) ·
CRYPTO ’87 record (Crossref) ·
US 4,309,569 (Google Patents) — Defines the authentication path (thesis p. 43) — the hash-tree inclusion proof our /v1/attest returns; anchoring the batch roots to Bitcoin is our construction, not Merkle’s.
[148] Lamport, L., Shostak, R. & Pease, M. (1982). The Byzantine Generals Problem.
ACM Transactions on Programming Languages and Systems 4(3), 382–401.
full text
[149] Shapiro, C. & Stiglitz, J. E. (1984). Equilibrium Unemployment as a Worker Discipline Device.
American Economic Review 74(3), 433–444.
record — No-shirking under imperfect monitoring; the reputation-ladder analogue.
[150] Haber, S. & Stornetta, W. S. (1991). How to time-stamp a digital document.
Journal of Cryptology 3, 99–111.
DOI — Back- and forward-dating infeasible even with collusion of the timestamping service.
[151] Dwork, C. & Naor, M. (1993). Pricing via Processing or Combatting Junk Mail.
Advances in Cryptology — CRYPTO ’92, LNCS 740, 139–147. Springer.
record ·
full text — Pricing functions: access to a shared resource must cost a moderately hard, not intractable, computation — the idea later called proof-of-work.
[152] Cilibrasi, R. & Vitányi, P. M. B. (2005). Clustering by compression.
IEEE Transactions on Information Theory 51(4), 1523–1545.
arXiv:cs/0312044 — Normalized compression distance; the primitive behind compression-based Sybil discovery.
§14 — Moment problems, prime-complex topology and reduced-model certificates
Added 2026-09-05. Sources read during the week’s research sessions: the Hankel-moment route to the Riemann hypothesis, persistent-homology descriptors of the crypto cross-section (the preregistered BETTI-v1 test; registered prediction null, result null), witnessed-obligation geometry over Akash escrow data, and the Navier–Stokes regularity notes. Each entry says whether it was used in a computation on our hardware or only read. Metadata was taken from the arXiv API or a resolving DOI on 2026-09-05. Nothing in this section is deployed, and none of it is a claim about our data products or trading.
[153] Bickel, K., Pascoe, J. E. & Sargent, M. (2021). Zero-free regions near a line. arXiv:2108.04807.
arXiv — Read in full 2026-09-05. Their N-HRRH hierarchy (Hankel positivity at every real basepoint, fixed N) is the other direction from the one we computed (all N, one basepoint); Theorem 1.1 and Corollaries 2.4–2.5 are what our finite positivity checks do and do not buy. Notes: research/riemann/NOTES.md.
[154] Platt, D. & Trudgian, T. (2021). The Riemann hypothesis is true up to 3·10
12.
Bull. London Math. Soc., doi:10.1112/blms.12460.
arXiv doi — Read. The verified-height bound quoted in the notes when stating what finite zero data can and cannot certify; not reproduced.
[155] Odlyzko, A. M. (2026). Tables of zeros of the Riemann zeta function. University of Minnesota, online tables.
tables — Used. The first 100,000 zeros (zeros1, 9 decimals) were fetched 2026-09-05 and fed the Hankel pivot, Gauss-node and Jacobi checks at 320-digit precision; agreement with prime-sum and ζ-derivative moments to 1e-10…1e-16.
[156] Helfgott, H. A. & Thompson, L. (2021). Summing μ(n): a faster elementary algorithm. arXiv:2101.08773.
arXiv — Read as the state of the art for computing the Mertens function, the object behind the M(x) reformulation discussed in the notes; not run.
[157] Björner, A. (2011). A cell complex in number theory.
Advances in Applied Mathematics, doi:10.1016/j.aam.2010.09.007.
arXiv doi — Read. The simplicial complex on square-free integers whose homology encodes the Mertens function — the precedent for reading arithmetic through topology that the obligation-geometry notes lean on.
[158] Pakianathan, J. & Winfree, T. (2011). Quota complexes, persistent homology and the Goldbach conjecture. arXiv:1104.4324.
arXiv — Read. Persistent homology over an arithmetic filtration; cited for the construction, not for any result we rely on.
[159] Cohen-Steiner, D., Edelsbrunner, H. & Harer, J. (2007). Stability of persistence diagrams.
Discrete & Computational Geometry 37, 103–120.
doi — Read. The bottleneck-stability theorem is why the preregistered BETTI-v1 test could use total persistence of a Vietoris–Rips filtration as a well-posed feature; the test's registered null prediction held (pipeline/betti_flow_test).
[160] Cohen-Steiner, D., Edelsbrunner, H., Harer, J. & Morozov, D. (2009). Persistent homology for kernels, images, and cokernels.
Proc. SODA 2009, 1011–1020.
doi — Read for the relative-persistence machinery in the witnessed-obligation notes; not implemented.
[161] Loiseaux, D., Scoccola, L., Carrière, M., Botnan, M. B. & Oudot, S. (2023). Stable vectorization of multiparameter persistent homology using signed barcodes as measures. arXiv:2306.03801.
arXiv — Read. Candidate vectorization if a two-parameter (time × scale) persistence descriptor is ever tested; nothing built.
[162] Balle, B., Panangaden, P. & Precup, D. (2019). Singular value automata and approximate minimization.
Math. Struct. Comp. Sci. 29, 1444–1478.
arXiv doi — Read. Approximate minimization with an error certificate — the shape of “reduced model plus bound” the obligation-geometry notes ask for; not applied to our data.
[163] Baez, J. C. & Master, J. (2020). Open Petri nets.
Math. Struct. Comp. Sci. 30, 314–341.
arXiv doi — Read. Compositional semantics for open networks of places and transitions; the language the witnessed-obligation graph (WOG/COG) drafts are written in.
[164] Picard, J.-C. (1976). Maximal closure of a graph and applications to combinatorial problems.
Management Science 22(11), 1268–1272.
doi — Read. Maximal closure via minimum cut — the reduction the obligation-geometry notes use to make a closure computable; not run on estate data.
[165] Baker, G. & Chatterjee, A. (2025). Minimal solutions to the Skorokhod reflection problem driven by jump processes and an application to reinsurance. arXiv:2512.24491.
arXiv — Read. Reflected jump dynamics as a model for escrow replenishment (deposits arriving as jumps against a continuous drain); relevant to the Akash escrow collector that began 2026-09-05, no model fitted yet.
[166] Furuya, T. & Kratsios, A. (2024). Polynomial scaling is possible for neural operator approximations of structured families of BSDEs. arXiv:2410.14788.
arXiv — Read. Cited on the Green’s-function card above; an approximation-rate result, not a claim about the encoder.
[167] Chernyshenko, S. I., Constantin, P., Robinson, J. C. & Titi, E. S. (2007). A posteriori regularity of the three-dimensional Navier–Stokes equations from numerical computations.
J. Math. Phys., doi:10.1063/1.2372512.
arXiv doi — Read. A numerical computation can certify regularity of a nearby exact solution — the “certificate” template the Navier–Stokes notes borrow; nothing computed.
[168] Constantin, P. & Iyer, G. (2008). A stochastic Lagrangian representation of the 3-dimensional incompressible Navier–Stokes equations.
Comm. Pure Appl. Math. 61(3), 330–345.
arXiv doi — Read. The transported-metric formulation behind the “retained geometry plus memory” note.
[169] Constantin, P. & Iyer, G. (2006). Stochastic Lagrangian transport and generalized relative entropies.
Commun. Math. Sci. 4(4), 767–777.
arXiv — Read. Companion to the previous entry.
[170] Miller, E. (2020). A regularity criterion for the Navier–Stokes equation involving only the middle eigenvalue of the strain tensor.
Arch. Rational Mech. Anal. 235, doi:10.1007/s00205-019-01419-z.
arXiv doi — Read. The strain-eigenvalue criterion our notes compare the trace-mass bound against; the open step in the notes is exactly the borderline this criterion does not close.
[171] Miller, E. (2026). On the interaction of strain and vorticity for solutions of the Navier–Stokes equation.
Pure Appl. Analysis 8, 247–270.
arXiv doi — Read. Strain–vorticity interaction; same role as the previous entry.
[172] Tao, T. (2016). Finite time blowup for an averaged three-dimensional Navier–Stokes equation. arXiv:1402.0290.
arXiv — Read. The obstruction any energy-only argument must clear; the notes' verdict that the transported-metric route is not a proof rests on it.
[173] Hasanalizade, E., Shen, Q. & Wong, P.-J. (2021). Counting zeros of the Riemann zeta function. arXiv:2107.06506 (J. Number Theory 235 (2022), 219–241 per the citing note; the journal reference is not in the arXiv record).
arXiv — Read. The explicit zero-count estimate behind the tail bound tl ≤ CR(log(l+1)/l)2 used in the fixed-node convergence rate of the 2026-09-05 Gauss–Jacobi note; only N(T) = O(T log T) is used.
[174] Berezansky, Y. & Shmoish, M. (1994). Nonisospectral flows on semi-infinite Jacobi matrices.
J. Nonlinear Math. Phys. 1, 116–146.
doi — Read. The established theory that the basepoint flow of the Riemann Jacobi coefficients specialises; the displayed equations were derived directly and verified here to 10−32 relative on a 3,000-zero measure (research/riemann/session3).
[175] NIST Digital Library of Mathematical Functions (2026). §3.5 (Gaussian quadrature), §5.11 (gamma asymptotics), §18.2 (general orthogonal polynomials), §18.5 (Chebyshev polynomials). Release 1.2.x, online.
18.2 3.5 18.5 — Used. Recurrence, Jacobi-matrix and third-kind Chebyshev formulas used in the verification script; the large-basepoint limit R·an → 1/2, R·bn → 1/4 was checked against §18.5.
[176] He, Y. & Tang, Q. (2026). An Erdős–Trotter problem on antichains with multiplicity r on each occurring level. arXiv:2602.09803v2 (preprint, 21 March 2026).
arXiv — Read in full (PDF, 2026-09-05). Definition 1.3 (strict n > n0 convention), Theorem 1.4 (n0(r) ≥ 2r+2), Proposition 4.1 (g(n,r) = n−3 for n ≥ 2r + 2log2r + log2log2r + 15), exact values n0(2)=3, n0(3)=8. Our Kruskal–Katona profile computation for r = 5, 6, 11 uses its Proposition 4.1 for the infinite tail.
[177] Thiim, M. (operator; ChatGPT 5.6 Pro, Claude Fable 5, Codex as provers) (2026). A Leanified proof of Erdős Problem 776: n
0(r) = 2r+4 for 4 ≤ r ≤ 10 and 2r+5 for r ≥ 11. Erdős-problems proof claim #78, 17 July 2026; GitHub tag v0.4.1-proof-claim. The forum assigns no review status to a proof claim; its header states that appearing there is no guarantee of correctness.
claim package — Used. Built on our box 2026-09-05 (Lean 4.30.0, Mathlib v4.30.0): 1,064 targets, exit 0; the axiom audit reproduces the documented allowlist (three native-evaluation certificate axioms plus propext, choice, Quot.sound; no sorry). Our three parameter cases n0(5)=14, n0(6)=16, n0(11)=27 are corollaries of its endpoint theorem and were compiled as such; this package has priority over our 2026-09-05 note by seven weeks, by the same method.
§15 — Record Linkage and Entity Resolution
Kairos sells normalisation with provenance. The verify_url proves a VALUE is real; it does nothing to prove the value belongs to the network you asked about. Right now /v1/network/NODE hands a paying customer NodelyAI's catalog entry stapled to NodeOps' fee and GitHub telemetry, and "Sentinel" is counted twice in the headline coverage figure under two symbols with no marker on either. Both are one Added 2026-09-06; every link below was fetched and confirmed to name the work at that date.
[178] Newcombe, H. B.; Kennedy, J. M.; Axford, S. J.; James, A. P. (1959). "Automatic Linkage of Vital Records." Science 130(3381): 954–959.
record Establishes: The original mechanised linkage procedure: identity between two records can be decided by accumulating odds-weights over several independently compared partial identifiers, rather than by matching on one key that neither file reliably carries. Does not establish: No decision theory, no error-rate control, and nothing about non-person entities or identifiers that an adversary or a rebrand can change at will. Fetched the Crossref record (a catalogue entry naming the work); no open full text was located.
[179] Fellegi, I. P.; Sunter, A. B. (1969). "A Theory for Record Linkage." Journal of the American Statistical Association 64(328): 1183–1210.
record Establishes: The formal model we do not have: a comparison vector γ over field-by-field agreement, the two conditional distributions m(γ)=P(γ|match) and u(γ)=P(γ|non-match), and the optimality result that ranking on the likelihood ratio m/u with TWO thresholds — MATCH / CLERICAL REVIEW / NON-MATCH — minimises the size of the human-review region for a fixed pair of error rates (μ false-match, λ false-non-match). The named review region is the key idea for us: it makes "Dan decides" a bounded, measured queue rather than an unbounded backlog. Does not establish: It does not supply m and u for OUR features; it assumes conditional independence across comparison fields (shared homepage and shared contract address are plainly not independent for us); it says nothing about making the pair space tractable; and it decides PAIRS, not clusters — closing pairwise decisions transitively is an extra assumption it never licenses. Fetched the Crossref record; the tandfonline landing page returned HTTP 403 and no open full text was found, so a record link is given rather than a paywall link.
[180] Winkler, W. E. (1990). "String Comparator Metrics and Enhanced Decision Rules in the Fellegi-Sunter Model of Record Linkage." Proceedings of the Section on Survey Research Methods, American Statistical Association. ERIC document ED325505.
record Establishes: How PARTIAL string agreement becomes a weight inside Fellegi-Sunter: the paper extends the Jaro comparator (the extension now called Jaro-Winkler), gives a formal method for adjusting a matching weight between pure agreement and pure disagreement, and shows the Fellegi-Sunter decision rules remain valid under that adjustment. This is the licence for treating "Green Power Network" vs "GreenPower Network" as a graded, not binary, agreement. Does not establish: It is calibrated to TYPOGRAPHIC variation in person names on 1990 census lists. Nothing in it licenses assuming that a one-character difference between two DePIN project names is a typo rather than two genuinely different projects — in our catalog HNT/IOT/MOBILE are three real, distinct Helium tokens whose names are near-identical. It also offers no comparator for contract addresses, chain ids or URLs, which are our highest-value fields. Link check: WebFetch's summariser could not read the compressed PDF stream, so I extracted the text locally with pypdf; the title page reads exactly "Winkler, William E. / String Comparator Metrics and Enhanced Decision Rules in the Fellegi-Sunter Model of Record Linkage", ED 325 505, PUB DATE 90, 8p. Full text delivered.
[181] Winkler, W. E. (2006). "Overview of Record Linkage and Current Research Directions." U.S. Census Bureau, Statistical Research Division, Research Report Series (Statistics #2006-2), issued 8 February 2006.
record Establishes: The practitioner's account of running Fellegi-Sunter in production: EM estimation of m and u WITHOUT labelled training pairs, blocking as the standard means of making the pair space tractable, and the warning that error rates estimated from an unsupervised model are themselves unreliable in the absence of truth data. Does not establish: It is a survey by the field's leading practitioner, not a new result, and it gives no per-feature parameterisation we could copy. Its caution about unverified error rates bites us directly: we could not publish a false-match rate for our catalog without hand-labelled truth, and under house rules we must therefore not publish one. Link check: WebFetch's summariser could not read the PDF stream; I extracted it locally with pypdf — 44 pages, title page verbatim as cited. Full text delivered.
[182] McCallum, A.; Nigam, K.; Ungar, L. H. (2000). "Efficient clustering of high-dimensional data sets with application to reference matching." Proceedings of the sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM, pp. 169–178.
record Establishes: Canopies: use a cheap approximate similarity to place records into OVERLAPPING subsets, then score only within-subset pairs. Overlap is the point — a hard partition silently destroys recall at every boundary, whereas overlapping canopies do not. This is why a record may sit in a name-block, a contract-block and a host-block at once. Does not establish: Blocking says nothing about whether a candidate pair IS a match, and gives no error-rate guarantee. Its cheap metric is a TEXT metric; our single most decisive cheap key — two catalog rows served by the same non-aggregator first-party endpoint host — is not text similarity at all, so we get that key for free from provenance rather than from this paper. Fetched the Crossref record; the widely cited open PDF at kamalnigam.com refused the connection (ECONNREFUSED 66.39.80.162:443), so no full-text link is offered.
[183] Bhattacharya, I.; Getoor, L. (2007). "Collective entity resolution in relational data." ACM Transactions on Knowledge Discovery from Data 1(1), Article 5.
record Establishes: Resolving references JOINTLY over the graph that connects them beats resolving each pair in isolation: evidence propagates, so one resolved link raises the odds on its neighbours. Our evidence is exactly relational — shared contract address, shared homepage host, shared first-party endpoint, shared GitHub org. Does not establish: It assumes a reasonably dense co-occurrence graph (citations, co-authorship). Ours is sparse to the point of being mostly absent: 467 of 731 catalog rows carry NO token_address, 633 carry no website, and 424 carry neither (restamped daily from the catalog table) — for those rows the name is the only evidence there is, and collective ER has nothing to propagate. The paper offers no calibration for that regime. Fetched the Crossref record; the UMD copy did not resolve (ENOTFOUND www2.cs.umd.edu) and no other open full text was located.
[184] Enamorado, T.; Fifield, B.; Imai, K. (2019). "Using a Probabilistic Model to Assist Merging of Large-Scale Administrative Records." American Political Science Review 113(2): 353–371.
record Establishes: A scalable EM implementation of Fellegi-Sunter for large administrative files, and — the part that matters most here — that the UNCERTAINTY in the linkage must be carried into whatever is computed from the merged file. Merging on a point-estimate match set and then counting produces biased downstream estimates. Every headline number we publish is a count over a merged file. Does not establish: It treats a fixed, closed pair of files whose entities have stable identity. It does not address entities that rename themselves (ATOR → ANyONe), wrap themselves onto another chain (Sentinel's native DVPN vs its Osmosis IBC denom), or split into sub-tokens (HNT/IOT/MOBILE) — which is our normal case, not our edge case. Fetched the Crossref record; no open full text was located.
§16 — Data Lineage and Computational Provenance
The product's entire pitch is that a buyer never has to trust us — every value carries a verify_url and a daily batch is Bitcoin-anchored. That promise holds for raw rows and, via the derivation ledger, for single-source collector-derived rows. It does not hold for the derived numbers on the two most expensive engine endpoints, and one of them ($9.99 gpu-supply-demand) publishes cross-source sums with no source or verify_url at all, which contradicts the "provenance or silence" rule stated in our own API header. That is a live accuracy defect on a paid surface, not a missing feature, which is why this is ship-now rather than next. The fix is cheap and asymmetric: the engines already receive `as_of`, `source`, and `verify_url` on every input record and simply discard them, so closing the gap is a recorder plus five call sites, with no schema change and no new collection. The replay test is what converts it from documentation into a claim — a lineage block that cannot reproduce its own published number fails the build, which is the same mechanical-divergence standard the derivation ledger already sets for collectors. Added 2026-09-06; every link below was fetched and confirmed to name the work at that date.
[185] Peter Buneman, Sanjeev Khanna, Wang-Chiew Tan (2001). "Why and Where: A Characterization of Data Provenance." Database Theory — ICDT 2001, LNCS 1973, pp. 316–330. DOI 10.1007/3-540-44503-X_20.
record Establishes: The primary split we are missing: why-provenance (the witness set of source records whose presence justified an output) is a different object from where-provenance (the source location a value was copied from), and a system can supply one while supplying nothing of the other. Does not establish: It is defined over deterministic relational/tree queries; it says nothing about the arithmetic transforms our collectors and engines actually perform (ratios, sums across heterogeneous fleets), and offers no wire format.
[186] James Cheney, Laura Chiticariu, Wang-Chiew Tan (2009). "Provenance in Databases: Why, How, and Where." Foundations and Trends in Databases, Vol. 1, No. 4 (2007), pp. 368–474. DOI 10.1561/1900000006.
record Establishes: The three-way taxonomy and, critically for us, the eager-vs-lazy axis: provenance can be materialised at write time or reconstructed at query time from a pinned input plus a pinned transform. Our derivation ledger is the lazy form; the engines have neither. Does not establish: It is a survey, not a construction, and its scope is database query languages — it does not cover provenance for a service that computes derived values in application code outside any query engine, which is exactly where our engines sit.
[187] Todd J. Green, Grigoris Karvounarakis, Val Tannen (2007). "Provenance Semirings." PODS 2007: Proceedings of the 26th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 31–40. DOI 10.1145/1265530.1265535.
record Establishes: How-provenance as an algebraic object: annotate each source tuple and propagate through the query, so the output carries a polynomial recording which inputs were combined and in what multiplicity — the standard against which a bare list of input records is a strict weakening. Does not establish: The semiring construction is defined for positive relational algebra and does not extend to aggregation (the authors' own later work says so). Every derived number we publish is an aggregate or a ratio, so this framework does not directly apply to a single Kairos utilisation figure.
[188] Yael Amsterdamer, Daniel Deutch, Val Tannen (2011). "Provenance for Aggregate Queries." PODS 2011: Proceedings of the 30th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 153–164. DOI 10.1145/1989284.1989302.
record Establishes: That semiring tuple-annotation provably fails for aggregation, and that the repair is to annotate individual VALUES inside tuples, not just tuple membership. This is the exact shape of our problem: a utilisation percent is an aggregate over values, so per-row provenance would not have sufficed even if we had it. Does not establish: It is a theory paper about query evaluation with symbolic annotations; it gives no serialisation, no cost model for a live HTTP service, and does not address multi-source freshness skew (inputs observed at different times), which is our largest practical hazard.
[189] Yingwei Cui, Jennifer Widom, Janet L. Wiener (2000). "Tracing the lineage of view data in a warehousing environment." ACM Transactions on Database Systems 25(2), pp. 179–227. DOI 10.1145/357775.357777.
record Establishes: The engineering precedent closest to us: lineage for materialised views WITH aggregation over multiple independent sources, and the point that lineage tracing must be generated at view-definition time rather than reconstructed afterwards. Fetched as a Crossref record; the ACM full-text PDF (dl.acm.org/doi/pdf/10.1145/357775.357777) returned HTTP 403 bot-challenge, so it is not cited as a link. Does not establish: Its lineage is defined relative to base tables the warehouse controls and can re-read. Our 'base tables' are third-party HTTP endpoints that restate their own history (we have caught this: default.depin_revision_ledger), so recomputing lineage on demand is not available to us the way it is to a warehouse.
[190] Timothy Lebo, Satya Sahoo, Deborah McGuinness (eds.) (2013). "PROV-O: The PROV Ontology." W3C Recommendation, 30 April 2013.
record Establishes: A stable, standardised vocabulary for the edges we would emit — prov:Entity for a published value, prov:Activity for the computation, prov:used for each input, prov:wasDerivedFrom between value and input, prov:generatedAtTime — so a customer's audit tooling can consume our lineage without a Kairos-specific parser. Does not establish: PROV-O is a vocabulary, not a semantics of correctness: it can express that a value was derived from three inputs but cannot express the arithmetic, cannot be checked for arithmetic consistency, and asserts nothing about whether the inputs were fresh, comparable, or correctly denominated.
§17 — Bitemporal data modelling
Kairos sells provenance, and the one claim that separates us from every aggregator is "you can check what we said, when we said it." Point-in-time reconstruction is the paid product: `/v1/attest`, `/v1/attestations`, the batch archive and the Design Partner brief all rest on it. A test run today showed the table underneath cannot support that claim — the past is editable, and 2,148 rows have in fact been edited out. This is the one gap in the estate where a customer-facing sentence ("retained, never deleted") is currently ahead of the schema, which is the exact failure mode this house treats as unacceptable in either direction. It is also unusually cheap to close. The table is 14.66 MiB. The model is already written and tested in `research/point_in_time_eval.py`. The anchoring is already correct and needs no change. The 70 collectors need no change. What is missing is two columns and the discipline to stop calling DELETE — and the fix converts our strongest audit finding from an embarrassment into the thing we publish. Added 2026-09-06; every link below was fetched and confirmed to name the work at that date.
[191] Richard T. Snodgrass and Ilsoo Ahn, "A Taxonomy of Time in Databases," in Proceedings of the ACM-SIGMOD International Conference on Management of Data, Austin, TX, May 1985, pp. 236–246.
record Establishes: Fetched HTTP 200, application/pdf, 976,619 bytes; page 1 reads "A Taxonomy of Time in Databases / March, 1985 / Richard Snodgrass, Ilsoo Ahn, Department of Computer Science, University of North Carolina." It is the origin of the three-times taxonomy and of the classification of a relation by WHICH times it carries — a database that records only one time cannot express the other, and the paper's stated motivation is exactly the terminological confusion we are in. Does not establish: It predates and does not use the later standard terms "valid time"/"transaction time" (it says historical/rollback/temporal); it prescribes no storage layout, no ClickHouse mapping, and nothing about using a content hash as a surrogate observation key.
[192] Christian S. Jensen, James Clifford, Ramez Elmasri, Shashi K. Gadia, Pat Hayes and Sushil Jajodia (editors), with Curtis Dyreson, Fabio Grandi, Wolfgang Käfer, Nick Kline, Nikos Lorentzos, Yannis Mitsopoulos, Angelo Montanari, Daniel Nonen, Elisa Peressi, Barbara Pernici et al., "A Consensus Glossary of Temporal Database Concepts," ACM SIGMOD Record 23(1), March 1994, special section "Temporal Database Infrastructure" (R. T. Snodgrass, section editor).
record Establishes: Fetched HTTP 200, application/postscript, 199,710 bytes; the text stream contains the exact title and editor list. It gives the normative definitions we should adopt verbatim, quoted from the fetched file: "The valid time of a fact is the time when the fact is true in the modeled reality"; "The transaction time of a database fact is the time when the fact is current in the database and may be retrieved … Transaction-time values cannot be later than the current transaction time. Also, as it is impossible to change the past, transaction times cannot be changed. Transaction times … are system-generated and -supplied"; "A bitemporal relation is a relation with exactly one system supported valid time and exactly one system-supported transaction time." The "cannot be changed" clause is precisely the property our prefix-invariance test measured and found violated. Does not establish: It says nothing about how to timestamp a fact whose upstream supplies no time at all — that stays a per-collector judgment we must make and document — and nothing about late-arriving data policy, physical storage, or how to make a violation of the model externally detectable. It is a glossary, not a design.
[193] Richard T. Snodgrass, "The Temporal Query Language TQuel," ACM Transactions on Database Systems (TODS) 12(2), June 1987, pp. 247–298.
record Establishes: Fetched HTTP 200, application/pdf, 4,116,328 bytes; page 1 carries the title, "RICHARD SNODGRASS, University of North Carolina," and the abstract, whose keyword list includes "rollback database" and "historical database." It supplies the first full tuple-relational-calculus semantics for querying valid time and transaction time together, including rollback ("as-of") retrieval — the semantics an /v1/as-of endpoint has to implement rather than improvise. Does not establish: Its semantics assume a DBMS-supplied transaction time, which is exactly the thing we do not have; it is Quel-based, not SQL, and offers no guidance on reconciling multiple upstream sources that disagree about the valid time of the same fact.
[194] Richard T. Snodgrass, Developing Time-Oriented Database Applications in SQL, Morgan Kaufmann Series in Data Management Systems, Morgan Kaufmann, 1999.
record Establishes: Fetched HTTP 200, application/pdf, 5,003,142 bytes; the title page reads "Developing Time-Oriented Database Applications in SQL … Richard T. Snodgrass" in the Morgan Kaufmann series list. This is the engineering source for the pattern we should copy in plain SQL on an engine with no temporal support: transaction-time tables as (start, stop) column pairs with a now/forever sentinel, deletion implemented as closing the stop time rather than removing the row, and the current/sequenced/nonsequenced distinction that tells you which of the three a given query is asking for. Does not establish: It targets 1990s SQL DBMSs with UPDATE and referential integrity; ClickHouse has neither in the assumed form (mutations rewrite parts asynchronously), so the (start, stop) pattern transfers but its concurrency and integrity arguments do not. It also says nothing about proving to a third party that the history was not rewritten.
[195] Krishna Kulkarni and Jan-Eike Michels, "Temporal features in SQL:2011," ACM SIGMOD Record 41(3), September 2012, pp. 34–43.
record Establishes: Fetched HTTP 200, application/pdf, 219,916 bytes; page 1 carries the exact title, both IBM authors and the abstract ("the ability to create and manipulate temporal tables"), and the PDF's own page numbers run 34 to 43. It fixes the standardised vocabulary we should use in customer-facing docs — application-time period tables (valid time), system-versioned tables (transaction time, system-maintained, where DELETE closes a row version rather than removing it), and FOR SYSTEM_TIME AS OF <t> — so our endpoint can name a standard instead of inventing a term. Does not establish: None of it is available to us: ClickHouse 26.4.2.10 (measured on this box) has no SYSTEM_TIME, no period tables and no automatic row-version closure, so the paper gives us the contract to imitate, not an implementation. It also does not cover application-time semantics for point observations, only for periods.
[196] Dean Croushore and Tom Stark, "A Real-Time Data Set for Macroeconomists," Federal Reserve Bank of Philadelphia Research Department Working Paper No. 99-4, June 1999.
record Establishes: Fetched HTTP 200, application/pdf, 1,520,821 bytes; the cover page names the working paper, both authors and the date, and the abstract states the data set "consists of vintages, or snapshots, of the major macroeconomic data available at quarterly intervals in real time," and that the paper "examines key empirical papers in macroeconomics and investigates their robustness to different vintages." This is the demand-side argument for our product: a vintage (as-first-published) series is a distinct, separately valuable artifact from a latest-revision series, and it exists because analysts needed to reproduce what was knowable at a decision time. It is why a fund's compliance team asks us for this at all. Does not establish: It is macroeconomic statistics, not DePIN telemetry; it does not show that OUR revisions are material. We have measured that 110 (symbol, metric) series lost observations and that AR BLOCKS moved -14%, but we have run no analogue of their robustness study on our own data, and must not imply we have.
§18 — Schema evolution and upstream drift
The product's entire claim is "every value carries a verify_url; if a metric isn't flowing, it's absent — not zero." A silent upstream field rename breaks the second half of that sentence in the one direction we cannot detect: absence looks identical to "this network legitimately has no max supply." We already ship the mirror-image defect (`total_volume_usd` zero-filled through a paid engine, confirmed 2026-09-06: 0 rows against 104,118 for the real name), so the failure class has a proven cost here, not a hypothetical one. Worse, `anchoring/anchor_batch.py` would Merkle-root and Bitcoin-anchor the day a metric disappeared, attesting cryptographically to an incomplete batch — we would be selling a tamper-proof record of a gap we never noticed. 997 (source, metric) pairs across 134 sources are currently asserted by nothing. Added 2026-09-06; every link below was fetched and confirmed to name the work at that date.
[197] Sebastian Schelter, Dustin Lange, Philipp Schmidt, Meltem Celikel, Felix Biessmann, Andreas Grafberger (2018). "Automating Large-Scale Data Quality Verification." Proceedings of the VLDB Endowment 11(12), 1781-1794. DOI 10.14778/3229863.3229867. (Deequ / Amazon Research.)
record Establishes: That data-quality constraints can be declared as 'unit tests for data' and executed cheaply by compiling them into aggregation queries over the dataset, with incremental validation on growing datasets and anomaly detection over the HISTORY of computed quality metrics rather than over single snapshots. Does not establish: It says nothing about our specific failure — a producer field silently vanishing from a JSON feed. Its constraints are declared against a known column set; it does not tell you how to decide which (source, metric) pairs should exist, and its Spark/incremental machinery is irrelevant at our scale (997 pairs, one ClickHouse GROUP BY).
[198] Eric Breck, Neoklis Polyzotis, Sudip Roy, Steven Euijong Whang, Martin Zinkevich (2019). "Data Validation for Machine Learning." Proceedings of the 2nd SysML Conference, Palo Alto, CA, USA.
record Establishes: The closest published analogue of our gap: a versioned, human-curated SCHEMA is kept as a production artefact and each incoming batch is validated against it, with 'missing feature column (in schema but not in data)' as an explicit named anomaly class. Their Table 1 (30-day production sample) shows missing-feature-column firing on 6% of pipelines with 66% of those subsequently fixed, and new-feature-column as the most common anomaly at 10% — i.e. a rename presents as a missing-column alert plus a noisy new-column alert, and the missing half is the one worth paging on. Does not establish: It is measured on Google's internal ML pipelines with a human operator in the loop and an expectation that engineers curate the schema; it offers no evidence about provenance/telemetry feeds, no treatment of per-value verify_url or point-in-time semantics, and its anomaly rates are not transferable as thresholds to us.
[199] Sergey Redyuk, Zoi Kaoudi, Volker Markl, Sebastian Schelter (2021). "Automating Data Quality Validation for Dynamic Data Ingestion." Proceedings of the 24th International Conference on Extending Database Technology (EDBT 2021), Nicosia, Cyprus, pages 61-72. DOI 10.5441/002/edbt.2021.07.
record Establishes: That in the regime we are actually in — batches of EXTERNAL data regularly ingested into a schema-less store, where an error corrupts a large fraction of a batch — thresholds for quality constraints can be derived from the history of prior batches instead of hand-set, and that hand-tuned thresholds are the baseline this must beat. It is explicit that this regime is different from fine-grained row-level error detection. Does not establish: Its six injected error types are value-level (missing values, wrong encoding, and so on), not field renames; it assumes a stable column set and asks whether the VALUES in it went bad. It gives no method for asserting that a column still exists, which is the half we need first.
[200] Dezhan Tu, Yeye He, Weiwei Cui, Song Ge, Haidong Zhang, Han Shi, Dongmei Zhang, Surajit Chaudhuri (2023). "Auto-Validate by-History: Auto-Program Data Quality Constraints to Validate Recurring Data Pipelines." KDD 2023. arXiv:2306.02421.
record Establishes: Names our exact hazard as 'schema drift' — 'a newly arrived batch of input data may have a schema change compared to previous input (e.g., missing columns)' — in RECURRING pipelines, and shows constraints for it can be auto-programmed from the statistics of historical executions, evaluated on 2,000 production pipelines at Microsoft, with schema-change among the issue types the method is effective against. Does not establish: It operates on single-column statistics inside a tabular pipeline with a real column list; our store is key-value-shaped (symbol, metric, value, ...) so 'a column disappeared' is for us 'a (source, metric) pair stopped producing rows' — a translation the paper does not make. Its approximation guarantees are about constraint selection, not about whether the underlying feed is honest.
[201] Stephan Rabanser, Stephan Günnemann, Zachary C. Lipton (2019). "Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift." Advances in Neural Information Processing Systems 32 (NeurIPS 2019). arXiv:1810.11953.
record Establishes: That the credible way to detect distributional shift is two-sample testing on a dimensionality-reduced representation, and that characterising whether a shift is harmful is a separate step from detecting it. Cited here as the reason NOT to reach for distribution tests first: the failure we must catch is a presence failure, and presence is decidable exactly. Does not establish: Nothing about schemas, field names, or metadata. Its perturbations are applied to image/ML feature matrices with large sample counts; it gives no basis for a claim about 24 metrics per source per day, and no method that would notice a renamed field at all.
[202] Great Expectations (GX Core), open-source data-validation library, maintained by Fivetran. Software, repository README consulted 2026-09-06.
record Establishes: The engineering-practice half: 'Expectations' as expressive, extensible unit tests for data expressed in shared language across a team, with automatically generated documentation of each set of validation results — i.e. the convention that a data contract is a checked artefact a non-author can read, not tribal knowledge in a collector. Does not establish: It is a library, not evidence. It supplies no measurement, and adopting it here would mean a Python/Spark validation layer over a store we already query directly in SQL — the pattern is worth copying, the dependency is not. The README text consulted does not itself document expectation suites or column-set expectations; those claims are not made here.
§19 — Change-point and stale detection
We sell this exact sentence on the homepage — index.html:218, "whose published dashboard has quietly stopped updating" — and on pricing.html:57 as "stale-dashboard catches". Today the evidence behind it is a keyword match on a value that did not change, and I measured that ~94% of what the rule calls frozen (1,147 of 1,218) is a quantity that has never moved in our entire observation history. Publishing IO devices_a100_80g_pcie_spot_active "frozen 10 days at 0" as a stale-dashboard catch, when the honest reading is "that GPU model has no active devices", is the same class of error this estate has repeatedly caught in itself: a guard checking the wrong evidence. A design partner who spot-checks two of the twelve published findings and discovers they are protocol constants loses the segment, not just the finding — the house's own note on why we advertise "no alpha" applies directly. The fix costs one new pure module, ~40 changed lines in partner_brief.py, 16 seconds of daily cron time, no schema change and no restart, and it converts an unbacked assertion into a number with a stated false-alarm budget that a customer can check. It also strictly increases sensitivity where it counts: a 7-poll freeze in a block height is conclusive today and invisible to the current 5-day floor. Added 2026-09-06; every link below was fetched and confirmed to name the work at that date.
[203] Page, E. S. (1954). Continuous Inspection Schemes. Biometrika 41(1/2), 100-115. DOI 10.1093/biomet/41.1-2.100.
record Establishes: The CUSUM recursion S_n = max(0, S_{n-1} + z_n) with an alarm at S_n > h: the original sequential scheme for detecting that a process changed while it is still running, rather than testing a fixed batch after the fact. Does not establish: Nothing about our setting directly - Page assumes i.i.d. observations from a KNOWN pre-change distribution and a known post-change shift. Our pre-change 'how often does this feed normally change' rate is estimated from the feed's own history, and our polls are irregularly spaced. Fetched Crossref record only; I found no openly hosted full text or scan of the 1954 Biometrika paper, so the record link is given instead of a link I could not stand behind.
[204] Lorden, G. (1971). Procedures for Reacting to a Change in Distribution. The Annals of Mathematical Statistics 42(6), 1897-1908. DOI 10.1214/aoms/1177693055.
record Establishes: The criterion under which a stale-feed detector can be called good rather than merely loud: minimise worst-case expected DETECTION DELAY subject to a floor on the mean time between false alarms - and the bound tying the CUSUM threshold h to that floor. Does not establish: Any finite-sample guarantee once the pre-change rate is estimated rather than known, which is exactly our case. The link is the Project Euclid RECORD page, which I fetched and which names the work, author, volume, issue and page range; the .pdf URL on the same host returns a NOINDEX/NOFOLLOW bot-challenge interstitial (HTTP 200, 1,062 bytes of HTML, tested with curl), so it is deliberately not linked.
[205] Moustakides, G. V. (1986). Optimal Stopping Times for Detecting Changes in Distributions. The Annals of Statistics 14(4), 1379-1387. DOI 10.1214/aos/1176350164.
record Establishes: That Page's CUSUM is EXACTLY optimal for Lorden's criterion (not merely asymptotically), when the pre- and post-change distributions are both known. This is why the restart-on-change form is the right shape for our detector rather than an arbitrary heuristic. Does not establish: Optimality when the post-change parameter is unknown. We do not know how far a stopped feed's change rate drops - a partially stalled feed is not the same as a dead one - so we get the shape from this result, not the guarantee. Record page fetched and confirmed to name the work; its .pdf URL is bot-challenged like Lorden's and is not linked.
[206] Lai, T. L. (1995). Sequential Changepoint Detection in Quality Control and Dynamical Systems. Journal of the Royal Statistical Society Series B 57(4), 613-644. DOI 10.1111/j.2517-6161.1995.tb02052.x.
record Establishes: The unified treatment of changepoint detection with UNKNOWN post-change parameters, and window-limited GLR rules with bounded per-step computation - the property that matters when the detector must rescan every series in the estate every day forever. Does not establish: Finite-sample false-alarm control. Lai's optimality is asymptotic in the false-alarm constraint, so a number derived from it is not the number we could honestly quote a customer as 'the chance we falsely accuse your feed'. I first guessed this paper's DOI as ...tb02051.x; fetching that record returned a DIFFERENT paper (Pena & Yohai, influential subsets in linear regression), and the correct DOI and the 613-644 page range came from a Crossref bibliographic query. Fetched Crossref record only; no open full text located.
[207] Howard, S. R., Ramdas, A., McAuliffe, J., Sekhon, J. (2021). Time-uniform, nonparametric, nonasymptotic confidence sequences. The Annals of Statistics 49(2), 1055-1080. DOI 10.1214/20-AOS1991.
record Establishes: Nonasymptotic, time-uniform bounds built from nonnegative supermartingales and Ville's inequality: a bound that holds simultaneously at ALL sample sizes and stopping times. This is the property that lets a daily rescan of ~11,000 series pay no multiplicity penalty for repeated looking - the exact failure mode our own memory file records as 'repeated peeking is p-hacking'. Does not establish: A changepoint procedure. This supplies the estimation guarantee, not the detection rule; the rule has to be built on top and its own error budget stated separately. arXiv abstract page fetched; it carries the journal reference Ann. Statist. 49(2): 1055-1080 (April 2021) and the DOI above.
[208] Shekhar, S., Ramdas, A. (2023). Sequential change detection via backward confidence sequences. arXiv:2302.02544 [math.ST]. DOI 10.48550/arXiv.2302.02544.
record Establishes: The reduction from sequential ESTIMATION to sequential CHANGEPOINT DETECTION - run confidence sequences backward from each candidate changepoint - giving a nonparametric detector with explicit false-alarm and delay control. This is the modern, e-value-native answer to the same question Page asked in 1954. Does not establish: Our specific test. Their guarantees are for a change in a functional theta under their stated conditions; the one-sided Bernoulli drop we actually need (change rate falls toward zero) has to be instantiated and its conditions checked, not inherited. Preprint cited as a preprint: the abstract page I fetched showed no journal-ref field.
[209] Ramdas, A., Grunwald, P., Vovk, V., Shafer, G. (2022). Game-theoretic statistics and safe anytime-valid inference. arXiv:2210.01948. DOI 10.48550/arXiv.2210.01948.
record Establishes: e-processes and test martingales as the currency of anytime-valid evidence, resting on Ville's inequality - P(sup_n M_n >= 1/alpha) <= alpha - which is already citation [133] in our own bibliography. A single published number can be updated continuously with no alpha spending. Does not establish: That an e-value is a p-value, or that it controls anything across NETWORKS. The number we would publish is a betting score against one series' own baseline; the estate-wide budget is alpha times the number of epochs tested and must be stated as its own figure. Preprint cited as a preprint: the abstract page I fetched showed no journal-ref field (a /v4 suffixed fetch 404'd; the base abs URL is the one verified).
§20 — Missing-Data Mechanism and Selection Bias in Cross-Network Aggregates
Kairos sells provenance, and a percentile is a claim about a population the customer cannot see. Right now /v1/network/<sym> serves percentile_rank and /v1/grades serves sector averages and a worst_10 list over 421 and 426 rows frozen on 2026-08-20, with no as-of and no definition of who is in the denominator — while depin_intel_engines.py:1577 puts our own collection success inside the health score being ranked. The coverage map already proves we know how to name the edge of the map for raw values; the aggregates re-cross that edge one layer up. Meanwhile 16 networks left the supply-telemetry panel in the last week and no surface says so, and derivation_ledger has 32,566 rows without a single failure record, so we cannot yet distinguish "they stopped publishing" from "we stopped asking" anywhere except the frozen-feed detector. Naming the population and counting the leavers costs two scalar queries and one brief section, needs no schema change, and is the only version of this fix that does not require us to model something we have not measured. Added 2026-09-06; every link below was fetched and confirmed to name the work at that date.
[210] Rubin, D. B. (1976). "Inference and missing data." Biometrika 63(3), 581–592.
record Establishes: Treats the missing-data mechanism as a formal object with its own distribution, and gives the conditions under which inference may ignore it rather than model it — the reason "which projects still publish" is a modelling assumption we are making silently, not a data-cleaning detail. Does not establish: It is a record link (Crossref entry), not the full text; and the three-label MCAR/MAR/MNAR vocabulary as we use it is the later Little–Rubin refinement, not this paper's own naming. It supplies no way to tell from observed data which regime DePIN coverage sits in.
[211] Little, R. J. A. (1988). "A Test of Missing Completely at Random for Multivariate Data with Missing Values." Journal of the American Statistical Association 83(404), 1198–1202.
record Establishes: That the MCAR null is testable — a computable statistic on multivariate data with missing entries, i.e. the one part of the taxonomy that is empirically checkable rather than assumed. Does not establish: Record link only. Rejecting MCAR does not distinguish MAR from MNAR, and failing to reject it does not license imputation; neither outcome would tell us whether our dropped networks are the failing ones.
[212] Heckman, J. J. (1979). "Sample Selection Bias as a Specification Error." Econometrica 47(1), 153–161.
record Establishes: That selection into the observed sample is formally an omitted-variable problem, so any correction requires an explicit model of the selection process itself, not a better estimator on the observed rows. Does not establish: Record link only. Its two-step correction needs a selection equation with an exclusion restriction — a variable driving whether a project publishes but not its supply level. We have no such variable, so this citation tells us what we cannot do here as much as what we could.
[213] Horvitz, D. G. and Thompson, D. J. (1952). "A Generalization of Sampling Without Replacement from a Finite Universe." Journal of the American Statistical Association 47(260), 663–685.
record Establishes: That a finite-population total is estimated without bias by weighting each observed unit by the inverse of its known, strictly positive inclusion probability — the canonical machinery for reweighting an unequally-observed population. Does not establish: Record link only. It gives nothing when inclusion probabilities are unknown or zero, which is exactly the not_covered set: for the 43 projects named at depin_intel_api.py:233 the probability of observation is zero, so no weighting scheme can recover them.
[214] Manski, C. F. (1990). "Nonparametric Bounds on Treatment Effects." American Economic Review (Papers and Proceedings) 80(2), 319–323.
record Establishes: Full-text scan, verified by reading pages 319–320: when the outcome is known to lie in a bounded interval, the sampling process identifies an interval for the target under NO assumption about the selection mechanism, with width equal to the outcome range times the missing share (his eq. 5). This is the only correction in this list that survives our refusal to model why projects go dark. Does not establish: The bound is uninformative when the outcome is unbounded — node counts and fee totals have no natural ceiling, so a bound is only publishable per-metric where we can state a defensible range. It yields an interval, never a point estimate, and never a ranking.
[215] Brown, S. J., Goetzmann, W., Ibbotson, R. G. and Ross, S. A. (1992). "Survivorship Bias in Performance Studies." The Review of Financial Studies 5(4), 553–580.
record Establishes: The direct financial analogue: conditioning a cross-sectional performance sample on survival distorts the surviving cross-section in a characterisable way — the same shape as ranking only the networks that still publish. Does not establish: Record link only. Their setting is fund returns with a known, dated survival criterion; no magnitude from it transfers to DePIN telemetry, and citing it would not license any numeric adjustment on our side.
[216] Hernán, M. A., Hernández-Díaz, S. and Robins, J. M. (2004). "A Structural Approach to Selection Bias." Epidemiology 15(5), 615–625.
record Establishes: That selection bias arises structurally from conditioning on a common effect — which supplies a criterion for deciding whether a particular selection (here: "still publishes") can bias a particular comparison, rather than assuming it always does or never does. Does not establish: Record link only — the publisher full text at journals.lww.com returned HTTP 402 when fetched, so I did not read it. The criterion needs the actual causal structure of why a DePIN project stops publishing, which we have never measured; it gives us the vocabulary for the direction, not the direction.
§21 — Multiple Testing Across the Estate
Kairos sells provenance, and the anchoring stack proves only that a published number was not altered afterwards — it says nothing about whether the number deserved publication. A daily brief over 11,294 series as measured on 2026-09-06 (11,907 at the 2026-09-19 restamp) with no false-discovery accounting is the one place where the product's own standard ("provenance or silence", "no estimates, no zero-fill") is not being met by its most visible output. The whale-netflow section is the sharpest instance: I measured that its 5%/95% band manufactures ~4.4 flags a day across 44 assets by construction, and the last four briefs published 7, 4, 3 and 1. Those rows are not distinguishable from noise, and they sit in a document whose entire pitch is that every other vendor's dashboard is stale. Worse, `/v1/correlations/lead-lag` — a paid SKU — told agents until 2026-09-26 that thousands of relationships were "FDR-corrected significant" when that count pooled 648 hourly re-tests of 128 hypotheses (measured 2026-09-06); 49 of those 128 pairs had passed in at least one run, which is what unadjusted repeated looking buys. That was a live overstatement for twenty days after this section named it, and the house rule is that overstatement and understatement are equally wrong. Since 2026-09-26 the endpoint counts significance within its latest hourly run only and labels same-hour correlation as co-movement, not a lead. The fix is small, needs no ClickHouse schema change, and turns the weakest section of the brief into the strongest: a q-value attached to every flag is precisely the credential a competitor scraping the same aggregators cannot produce. Added 2026-09-06; every link below was fetched and confirmed to name the work at that date.
[217] Yoav Benjamini and Yosef Hochberg (1995). "Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing." Journal of the Royal Statistical Society, Series B, 57(1), 289–300. DOI 10.1111/j.2517-6161.1995.tb02031.x
record Establishes: The step-up procedure that, for m independent (or PRDS) tests, guarantees E[FDP] ≤ (m0/m)·α — the exact primitive our daily brief needs to convert a pile of per-series flags into a bounded expected false-discovery proportion, and the procedure already implemented correctly at cross_asset_correlation.py:137. Does not establish: It gives no guarantee for a family that is re-tested every day: BH controls FDR within ONE family, and repeating it on 648 hourly or 365 daily families gives no control over the union of what we published. It also says nothing about detectors that emit no p-value at all, which is what our frozen-feed, supply-mover and whale-netflow rules do.
[218] Yoav Benjamini and Daniel Yekutieli (2001). "The control of the false discovery rate in multiple testing under dependency." The Annals of Statistics, 29(4), 1165–1188. DOI 10.1214/aos/1013699998
record Establishes: That plain BH still controls FDR under positive regression dependency, and that under ARBITRARY dependence FDR control is recovered by dividing α by the harmonic sum Σ(1/i) — directly relevant because our 11,294 series as measured on 2026-09-06 (11,907 at the 2026-09-19 restamp) are heavily dependent (many metrics per network, several sources per metric, a shared upstream aggregator). Does not establish: The BY log-factor is a worst-case bound, not a measurement of OUR dependence structure; applied to 11,294 series (2026-09-06 measure) it costs a factor of ~9.7 in power and would suppress genuine findings. It does not tell us which regime the estate is actually in, and it is still a single-family result. Note: Project Euclid's copy of this paper is a paywall page (fetched and confirmed), so this is a Crossref record link, not full text.
[219] John D. Storey (2002). "A direct approach to false discovery rates." Journal of the Royal Statistical Society, Series B, 64(3), 479–498. DOI 10.1111/1467-9868.00346
record Establishes: The q-value as the FDR analogue of a p-value — a per-finding number that can be published beside each flag without fixing α in advance — and the π0 estimator that recovers the power BH gives away when, as here, the overwhelming majority of the 11,294 series (2026-09-06 measure) are null on any given day. Verified by extracting page 1 of the fetched PDF: it carries the JRSS-B 64(3) 479–498 masthead, Storey's name and the q-value abstract. Does not establish: π0 estimation is itself unstable when the p-value histogram is not well behaved, and our empirical-null p-values will be coarse (a 90-point history gives resolution no finer than ~1/91). It also inherits BH's single-family scope: a q-value is not a statement about the alert stream over time.
[220] Dean P. Foster and Robert A. Stine (2008). "α-Investing: a Procedure for Sequential Control of Expected False Discoveries." Journal of the Royal Statistical Society, Series B, 70(2), 429–444. DOI 10.1111/j.1467-9868.2007.00643.x
record Establishes: The alpha-wealth mechanism: a testing budget that is spent when you test and partially refunded when you reject, giving control of expected false discoveries over an UNBOUNDED sequence of hypotheses arriving one at a time. This is the correct frame for a subscription alert product where the hypothesis stream never ends. Does not establish: α-investing as originally stated controls mFDR (a ratio of expectations), not FDR itself, and the guarantee assumes p-values that are valid and — in the base result — independent of the past. Our whale-flow p-values are computed from an overlapping trailing window, so successive days are not independent; that has to be handled, not assumed away.
[221] Adel Javanmard and Andrea Montanari (2018). "Online rules for control of false discovery rate and false discovery exceedance." The Annals of Statistics, 46(2). DOI 10.1214/17-AOS1559. Preprint arXiv:1603.09000.
record Establishes: The LORD family of online rules, which set each test's threshold from the times of PREVIOUS rejections and control FDR (not just mFDR) over an infinite stream, plus control of false discovery exceedance. This is the named method for our exact situation: a fixed detector re-fired every day forever. Journal record confirmed separately via Crossref (Ann. Statist. 46(2), DOI 10.1214/17-AOS1559); the arXiv page carries the full text and states 'To appear in Annals of Statistics'. Does not establish: The arXiv record does not give page numbers and the Crossref record does not list them either, so I do not assert them. LORD's guarantee requires independent (or suitably super-uniform) p-values; it does not repair a detector that emits no p-value, and it does not tell us how to build the empirical null for a 90-day exchange-balance series.
[222] Aaditya Ramdas, Tijana Zrnic, Martin Wainwright and Michael Jordan (2018). "SAFFRON: an adaptive algorithm for online control of the false discovery rate." arXiv:1802.09098 (submitted 2018-02-25, revised 2019-07-10).
record Establishes: An adaptive online procedure that estimates the proportion of nulls as it goes — the online analogue of Storey-BH — and demonstrably beats LORD in power. Matters here because a daily scan of the full live-series panel is close to all-null, which is precisely where the non-adaptive alpha-wealth rules waste their budget. Does not establish: I fetched the arXiv record, which lists the venue as arXiv (stat.ME); it does not on that page assert a peer-reviewed venue, so I make no ICML/PMLR claim. SAFFRON adds a user-chosen candidate threshold λ whose misspecification costs power, and like every entry above it presumes valid p-values we do not currently produce.
[223] Aaditya Ramdas, Fanny Yang, Martin J. Wainwright and Michael I. Jordan (2017). "Online control of the false discovery rate with decaying memory." NIPS 2017. arXiv:1710.00499.
record Establishes: Decaying-memory FDR (mem-FDR): a discounted error criterion under which recent errors count more than old ones, and 'alpha-death' — a procedure that goes permanently broke after a long null run — is avoided. This is the criterion a paying subscriber actually cares about: whether THIS quarter's alerts are mostly real, not the estate's cumulative FDR since 2026-08. Does not establish: mem-FDR is a different, weaker target than FDR over the whole stream; a page quoting it must say so, or we would be selling a discounted guarantee as an absolute one. The paper does not address our detectors' calibration problem, only the accounting on top of valid p-values.
[224] Jonathan B. Hill (2026). "A High Dimensional Wild Bootstrap Max-Test for Detecting the Presence of Significant Predictors." arXiv:2604.27813 (submitted 2026-04-30).
record Establishes: The wild-bootstrap max-statistic test that gives FWER control under arbitrary cross-feature dependence without estimating a covariance matrix. Cited here because ~/propintel/depin_significance.py already implements it, and I fetched the arXiv record to confirm the identifier resolves and names this work — the in-code citation is accurate, not fabricated. Does not establish: FWER is the wrong error rate for this gap: controlling the probability of even ONE false flag across the full daily panel would silence the product entirely. It is also inert as shipped — POST /v1/significance returns 404 (probed on the live service), so no customer can reach it.
§22 — Index Methodology and Benchmark Governance
This is the one gap where a live sales claim runs ahead of the code. Everywhere else the estate errs toward understatement; pricing.html:79 sells "index/ETF methodology use" at $2,000/mo, and the artefact that phrase implies — a versioned methodology with constituent rules, a weight definition, a rebalancing calendar and a restatement policy — does not exist in any form. The redistribution buyer is the only buyer who will ask for it, and it is the first thing they ask for. It is also the cheapest credibility we can buy, because the hard half is already built and the missing half is paperwork with a hash on it. We already anchor the daily input batch to Bitcoin, already keep a before/after ledger of upstream restatements, already hold a correct as-of/vintage primitive, and already refuse to publish a claim our auditor cannot verify. A benchmark methodology is that same discipline pointed at our own derived numbers instead of at other people's — and OTS-stamping the methodology file makes "the rules predate the numbers" a checkable fact rather than a promise, which is the only version of this argument our product is entitled to make. And the gap is not hypothetical drift: three sector tables that disagree on five symbols, a weight denominator that silently varies by symbol, and a published sector ratio nobody can reproduce for a past date are exactly the failure mode we sell against. With zero paying customers today the blast radius is zero, which is the cheapest moment this fix will ever be available. Added 2026-09-06; every link below was fetched and confirmed to name the work at that date.
[225] The Board of the International Organization of Securities Commissions, "Principles for Financial Benchmarks: Final Report", FR07/13, July 2013.
record Establishes: The nineteen Principles a benchmark administrator is expected to meet, verbatim: Principle 8 Hierarchy of Data Inputs, 9 Transparency of Benchmark Determinations, 10 Periodic Review, 11 Content of the Methodology (whose minimum contents (a)-(h) include input-selection criteria, the guidelines controlling discretion, the procedures for periods when data sources are absent, and (e) 'the procedures for dealing with error reports, including when a revision of a Benchmark would be applicable'), and 12 Changes to the Methodology (publish the rationale of any material change, define what counts as material, and state notice timing). Does not establish: It is a supervisory principles document addressed to benchmark administrators. It does not make Kairos an administrator, confer any compliance or assurance status, or say anything about DePIN supply telemetry or whether our sector aggregates are fit for index use. Fetched via the SEC's hosted copy because the canonical iosco.org URL (https://www.iosco.org/library/pubdocs/pdf/IOSCOPD415.pdf) returns HTTP 403 to non-browser clients — I confirmed the SEC copy is the work itself by rendering its title page (FR07/13, July 2013, OICU-IOSCO) and the Principle 8-12 pages.
[226] European Parliament and Council, Regulation (EU) 2016/1011 of 8 June 2016 on indices used as benchmarks in financial instruments and financial contracts or to measure the performance of investment funds, OJ L 171, 29.6.2016, pp. 1-65.
record Establishes: The binding EU regime that turns the IOSCO principles into obligations. Article 12 'Methodology' requires a methodology that is robust and reliable and that 'has clear rules identifying how and when discretion may be exercised'; Article 13 'Transparency of methodology' requires the administrator to develop, operate and administer the benchmark and methodology transparently and to publish or make it available. Does not establish: It binds administrators of benchmarks used in the EU, not upstream data vendors. Supplying input data into someone else's index does not make us an administrator, and nothing in it certifies our data as eligible BMR input. The EUR-Lex landing page (…/TXT/?uri=…) truncates after Article 5; the /TXT/HTML/ URL above delivers the full text and is the one I fetched.
[227] S&P Dow Jones Indices, "S&P Float Adjustment Methodology" (Index Methodology), April 2024.
record Establishes: What a free-float rule looks like when it is actually operational: an Investable Weight Factor per constituent (available float / shares outstanding), a 5% minimum strategic-block threshold with worked examples (IWF 1.00 where officers+directors hold 3% and no other 5%+ holder; 0.93 at 7%; 0.77 where strategic holdings total 23%), IWFs reported to the nearest percentage point, reviewed annually and applied at a named moment (open of the Monday after the third Friday of September, per index family), with a reference-date cutoff five weeks before the third Friday of March/June/September/December. Does not establish: It is an equity rule set resting on a share register and regulatory ownership filings. A token's 'circulating supply' has no equivalent registry, so this gives us the shape and precision a float rule must have, not a rule we can copy. The canonical S&P URL (https://www.spglobal.com/spdji/en/documents/index-policies/methodology-sp-float-adjustment.pdf) returns HTTP 403 to non-browser clients, so I fetched this third-party mirror and confirmed locally with pdftotext that the cover reads 'S&P Float Adjustment Methodology / April 2024 / S&P Dow Jones Indices: Index Methodology' and that the IWF definition and maintenance schedule are present. Being a mirror, it pins the April 2024 edition, not the current one.
[228] Darrell Duffie and Jeremy C. Stein, "Reforming LIBOR and Other Financial Market Benchmarks", Journal of Economic Perspectives 29(2), 2015, pp. 191-212.
record Establishes: That benchmark failure is a governance failure rather than a mathematical one: benchmark users are locked in, which makes an administrator's undisclosed discretion economically exploitable, and reform therefore runs through rules, disclosure and transition planning. Does not establish: It concerns submission-based interest-rate benchmarks. It prescribes no methodology for a supply-side asset-class aggregate, and it does not claim that a provenance-first vendor is immune to the incentive problem. The link is the AEA record page for the article, which names the work and offers the complimentary full-text PDF.
[229] Dean Croushore and Tom Stark, "A Real-Time Data Set for Macroeconomists", Federal Reserve Bank of Philadelphia Working Paper No. 99-4, June 1999 (published as Journal of Econometrics 105, 2001, pp. 111-130).
record Establishes: The vintage discipline: data must be stored as dated snapshots ('we refer to the data available as of a date as a vintage, and the collection of such vintages as a real-time data set'), because results computed on the latest vintage differ from results computed on the vintage that was actually available at the time. Does not establish: Nothing about index construction, weighting or benchmark rules — it is macroeconomic data, and it makes no claim about whether our snapshot table is fit for purpose. I fetched and text-extracted the working-paper PDF; I did not fetch the published Journal of Econometrics version, so the page range above is from the bibliographic record, not from a copy I opened.
[230] Antti Petajisto, "The index premium and its hidden cost for index funds", Journal of Empirical Finance 18(3), 2011, pp. 271-288.
record Establishes: That membership and rebalancing rules are priced, not editorial: price impact from announcement to effective day averaged +8.8% (S&P 500) and +4.7% (Russell 2000) for additions and -15.1% and -4.6% for deletions, 1990-2005, and the reconstitution rule itself imposes a measurable 'index turnover cost' on trackers. Does not establish: US equities over a specific window; it says nothing about DePIN tokens, and does not imply any Kairos aggregate would show a premium. It is evidence that 'which constituents, and when they change' must be a published rule — not evidence about our data.
§23 — Regime Identification and Empirical Alpha Validation
A regime is not inferred merely because a feature clusters observations, a topology changes, a Lyapunov estimate moves, or a latent-state model returns two labels. Here a regime means a statistically supported difference in the data-generating process across time or state, plus evidence that the distinction is useful on information unavailable when the state was fitted. Two forms of evidence count: structural change (the stability null that parameters are constant, rejected at unknown break points [232], [233]) and latent state (an unobserved Markov state with state-specific observation distributions [231]). A candidate state is promoted to a supported regime only when its distributions are distinguishable, occupancy is nondegenerate, transitions persist over the stated horizon, the result is not retrospective relabelling, and the definition reproduces on unseen data. The stronger designation, predictive regime, requires that the state improve an out-of-sample forecast of a prespecified quantity relative to a stated no-regime benchmark [234]–[237]. Alpha is benchmark-relative empirical performance, not a mathematical property of a signal: net return after fees, spread, slippage, impact and funding, relative to a benchmark or risk model declared before the decisive evaluation [238], surviving the correction for however many signals, horizons and parameters were searched [239]–[242], and clearing a stated cost and capacity assumption [243]. The promotion ladder is therefore: candidate feature; regime feature; predictive regime; candidate alpha; validated net alpha; prospective evidence. The words regime, predictive regime and alpha are used on this site only at the corresponding stage. Persistent homology, rough-path statistics, Neural-SDE embeddings, nonlinear-dynamics diagnostics, order-flow variables and network telemetry (§1–§8) enter this chain as candidate features; none is a regime certificate by itself. The required chain for a trading claim is therefore: telemetry → feature → supported regime → out-of-sample forecast advantage → locked trade rule → net benchmark-relative return → search-adjusted inference → prospective confirmation. Three conditions govern how that chain may be tested here. First, the inferential regime must be declared and not mixed. Our referee is a capped sequential probability ratio test with a pre-registered boundary, so its sample is a stopped one; a fixed-sample t-statistic, Sharpe ratio, Reality Check or SPA p-value computed on that stopped sample is not valid, because the stopping rule changes the sampling distribution. Either the pre-registered sequential test governs, with its own error spending, or a fixed-sample evaluation is run on a frozen holdout — never one reported as the other. Second, a prospective observation counts only if the locked rule could have produced it. A sequential test can be decided by a single extreme observation, so an execution failure, a venue outage or a stop that never fired can end a policy on evidence that is not about edge. The exclusion criterion for non-executable observations must therefore be registered in advance; reaching in afterwards to remove the observation that decided the test is not a correction, it is an escape hatch, and it is worse than counting the observation. Third, the benchmark must be named before it is used. Stages 3 and 4 are both benchmark-relative, so until Bt is written down the quantity At is undefined. It is now declared, because for a perpetual-futures book zero is not the honest default: funding carry and basis exposure account for a large part of what is casually called crypto alpha. Bt = β̄ · (Runiverse + Cuniverse), taken over the trader’s own 33-asset opportunity set rather than an index it did not trade, priced and funded on a single venue, where β̄ is the book’s realised net directional exposure and C the funding carry a passive position of that sign would have paid. The specification was frozen and hash-sealed before any At, β̄ or Bt was computed against it, and a script recomputes it rather than a person restating it. What makes the choice consequential rather than ceremonial is that this book is currently net short: against a zero benchmark, a falling market would be booked as alpha. Naming it is a precondition of stage 4, not a formality — and it removes one blocker, not both. Where the estate stands, graded against its own referee on the date added: stage 1 is present; no hypothesis has reached stage 2 under the registered rules; the capped SPRT referee returned KILL on the current paper policy at stage 4; stage 5 cannot be measured because the paper-trade table carries no cost column; the declined-forecast ledger that stages 3 and 6 need was built on 2026-09-16 and wrote nothing for three days — its table-creation call existed and was invoked by nothing, so every insert was refused and spooled to disk. It was repaired on 2026-09-19 and now records each declined evaluation with the reason it was declined. Most rows so far are evaluations the scoring loop never reached rather than genuine abstentions, and no taken trade has been recorded against them yet, so the denominator stage 3 requires is only beginning to accumulate. No figure on this page claims alpha. Added 2026-09-19 from a proposal Dan brought to the estate; every reference below was checked against its Crossref record on that date and the DOI link is the record link.
[231] Hamilton, J. D. (1989). "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle." Econometrica 57(2), 357–384. DOI 10.2307/1912559.
record Establishes: A probabilistic Markov-switching framework for inferring unobserved discrete shifts in time-series dynamics from observed behaviour: an unobserved state S_t following a Markov chain, with the observable drawn from a state-specific distribution. It is the canonical latent-state construction, and the one this section means by "state model". Does not establish: That an inferred state is a unique physical market state, or that it forecasts profitable trades. A fitted hidden state is model-relative: two inferred states are not proof that the market has two objectively real regimes. Crossref record fetched 2026-09-19 and confirmed to name the work.
[232] Andrews, D. W. K. (1993). "Tests for Parameter Instability and Structural Change with Unknown Change Point." Econometrica 61(4), 821–856. DOI 10.2307/2951764.
record Establishes: Formal testing of parameter stability against structural change at an unknown break point over a broad class of parametric and GMM models, so that "the process changed" can be a rejected null rather than an eyeballed chart. Does not establish: Tradability or the economic meaning of a detected break. Rejecting stability under an appropriate specification is evidence the modelled process changed; it says nothing about whether the change is persistent, uniquely identified or worth a position. Crossref record fetched 2026-09-19.
[233] Bai, J. & Perron, P. (1998). "Estimating and Testing Linear Models with Multiple Structural Changes." Econometrica 66(1), 47–78. DOI 10.2307/2998540.
record Establishes: Inference for the presence, number and locations of multiple structural breaks in regression models, which is the structural-change route to regime evidence when more than one break is plausible. Does not establish: That the resulting segments are stable latent regimes or possess predictive alpha. A segmentation is a description of the past; the prospective test below is a separate step. Crossref record fetched 2026-09-19.
[234] Diebold, F. X. & Mariano, R. S. (1995). "Comparing Predictive Accuracy." Journal of Business & Economic Statistics 13(3), 253–263. DOI 10.1080/07350015.1995.10524599.
record Establishes: Tests of equal predictive accuracy for competing forecasts under broad loss functions and serially correlated forecast errors: the primitive for "the regime-conditioned forecast beats the no-regime benchmark out of sample". Does not establish: That a superior statistical forecast is economically profitable after execution costs; the evaluated object is forecast loss, not net strategy return. Crossref record fetched 2026-09-19.
[235] Giacomini, R. & White, H. (2006). "Tests of Conditional Predictive Ability." Econometrica 74(6), 1545–1578. DOI 10.1111/j.1468-0262.2006.00718.x.
record Establishes: An out-of-sample framework for testing conditional predictive ability, allowing for model misspecification and estimation error, and asking whether the relative performance of two forecasts can be predicted from information available at the time. This is the test that turns "supported regime" into "predictive regime". Does not establish: Alpha. It evaluates forecasts, not executable returns net of costs. Crossref record fetched 2026-09-19.
[236] Clark, T. E. & West, K. D. (2007). "Approximately Normal Tests for Equal Predictive Accuracy in Nested Models." Journal of Econometrics 138(1), 291–311. DOI 10.1016/j.jeconom.2006.05.023.
record Establishes: A correction for the bias in forecast comparison when the candidate model nests the benchmark, which is our case whenever the regime-conditioned model reduces to the unconditional one by switching the state off. Does not establish: Economic profitability or protection against unrestricted model search. Crossref record fetched 2026-09-19.
[237] Giacomini, R. & Rossi, B. (2010). "Forecast Comparisons in Unstable Environments." Journal of Applied Econometrics 25(4), 595–620. DOI 10.1002/jae.1177.
record Establishes: Tests of whether relative out-of-sample forecast performance is itself stable through time, so a forecast advantage that held in one stretch and vanished in the next is detected as such rather than averaged away. Does not establish: That instability in relative performance corresponds to a discrete market regime, or to alpha. Crossref record fetched 2026-09-19.
[238] Jensen, M. C. (1968). "The Performance of Mutual Funds in the Period 1945–1964." Journal of Finance 23(2), 389–416. DOI 10.1111/j.1540-6261.1968.tb00815.x.
record Establishes: The classical risk-adjusted framework: performance is the return in excess of what the portfolio's systematic risk exposure would have earned, measured as an intercept against a stated benchmark, not as raw return. Does not establish: That CAPM is the correct benchmark for DePIN or crypto assets, or that any positive estimated intercept is permanent. The benchmark and risk model used here must be declared and fixed before the decisive evaluation; Jensen's particular specification is not adopted. Crossref record fetched 2026-09-19.
[239] White, H. (2000). "A Reality Check for Data Snooping." Econometrica 68(5), 1097–1126. DOI 10.1111/1468-0262.00152.
record Establishes: A test of whether the best model encountered during a specification search has genuine predictive superiority over a benchmark, accounting for the fact that it was selected from many. This is the correction the ladder requires at stage 5. Does not establish: Economic implementability, or immunity to research choices made outside the model universe that was tested. Crossref record fetched 2026-09-19.
[240] Hansen, P. R. (2005). "A Test for Superior Predictive Ability." Journal of Business & Economic Statistics 23(4), 365–380. DOI 10.1198/073500105000000063.
record Establishes: A more powerful predictive-ability test than the Reality Check, with reduced sensitivity to poor and irrelevant alternatives in the search set. Does not establish: Net trading alpha, unless the quantity tested is the properly specified benchmark-relative net strategy outcome. Crossref record fetched 2026-09-19.
[241] Harvey, C. R., Liu, Y. & Zhu, H. (2016). "… and the Cross-Section of Expected Returns." Review of Financial Studies 29(1), 5–68 (online 2015). DOI 10.1093/rfs/hhv059.
record Establishes: Why large-scale factor search requires substantially stronger multiple-testing control than single-hypothesis inference: the size of the search space must enter the evidentiary standard. Does not establish: A universal t-statistic threshold for every strategy, asset class or Kairos experiment. Their numerical cutoff is specific to their factor-research setting and is not adopted here. Crossref record fetched 2026-09-19.
[242] Bailey, D. H. & López de Prado, M. (2014). "The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting and Non-Normality." Journal of Portfolio Management 40(5), 94–107. DOI 10.3905/jpm.2014.40.5.094.
record Establishes: A Sharpe-based diagnostic that adjusts apparent Sharpe evidence for selection bias, backtest overfitting and non-normal returns. Does not establish: That a strategy will remain profitable prospectively, or that its execution assumptions are realistic. Crossref record fetched 2026-09-19.
[243] Novy-Marx, R. & Velikov, M. (2016). "A Taxonomy of Anomalies and Their Trading Costs." Review of Financial Studies 29(1), 104–147 (online 2015). DOI 10.1093/rfs/hhv063.
record Establishes: Empirically, that trading costs and turnover materially change the profitability and capacity of many documented anomalies, which is why economic significance is a separate requirement from statistical predictability. Does not establish: Any particular cost schedule or capacity limit for Kairos assets; those must be measured from the actual venue and strategy. Crossref record fetched 2026-09-19.
† Evaluated for use by a third-party observer with public data only, and rejected on that basis — typically because the method requires an oracle, labels, or a participant’s view. A dagger is not a criticism of the paper. Inclusion in this
bibliography records what we read and tested; it is not a claim that a method is deployed,
nor an endorsement of its applicability to our estate. Full-text PDFs and per-paper
evaluation notes are retained internally.
