The Connes–van Suijlekom truncated Weil quadratic form, indexed by a cutoff parameter c that controls the primes p ≤ c entering the operator, produces a ground state whose Fourier–Mellin zeros provably lie on the critical line; whether they converge to the Riemann zeros as c → ∞ is open (Connes 2026; Connes–Consani–Moscovici 2025). We present, to our knowledge, the first independent public implementation of the Connes–van Suijlekom Galerkin matrix at sixteen cutoffs (c = 13 through 67, plus c = 100). Across the in-sample window c = 13 through c = 67 at N = 100, the first-zero absolute error |γ1 − γ1Riemann| shrinks monotonically from ∼2×10−55 to ∼1.5×10−168, a 113-OOM convergence across fifteen cutoffs. The smallest-positive even-sector eigenvalue λmineven separately reaches ∼10−334 at c = 100, N = 250 (275-OOM span from c = 13). Out-of-sample test at c = 100. On the four-point N-sweep N ∈ {100, 150, 200, 250} at dps = 500, consecutive first-difference ratios 0.837 and 0.836 match to two decimal places. Aitken-Δ2 on the two overlapping triples yields log10|λ∞even| ≈ −536.8 and ≈ −533.7, approaching the Connes 2026 §6.4 heuristic prediction (≈ −530.4) monotonically with N (6.4 and 3.3 OOM gaps out of |x∞| ∼ 530). The same eigenvector recovers γ1, …, γ10 to 307–329 matching digits at N = 250, dps = 500. Under the unitary equivalence with Connes–Consani–Moscovici Lemma 5.1, this is the deepest such Galerkin-truncation recovery in the public Connes–van Suijlekom / Connes–Consani–Moscovici literature, subject to a hypothesis-status caveat. The raw finite-N matrix carries a small block of negative-sign eigenvalues at the finite archimedean cutoff T = 800; these are an artifact of that cutoff and are absent once T is increased, so the smallest-positive even-sector eigenvalue is the genuine smallest one (continuum positivity of QWλ is RH-equivalent and is not assumed at λ = √100). The fit |log10 λmin| ≈ 13.24 c0.634 on c ≤ 67 at N = 100 is shown to be a finite-N rate, falsified at c = 100, N = 200 by 49 OOM in the direction of faster decay. Structural observations include approximate eigenvector c-invariance (overlap ≥ 0.9498 on all 105 cutoff pairs despite eigenvalues differing by 113 OOM), multi-zero convergence universality (all ten detectable zeros within 3.8% of each other), an empirical Galerkin-convergence exponent s(c) ≈ 55 log c − 128, un-rescaled Galerkin bulk-spectrum Poisson statistics (β < 0.05; this is a structural diagnostic of the truncated operator, not a test of Montgomery's conjecture, which applies to locally-rescaled zero spacings), and tight bulk invariants log|det Qc| ≈ −65.6 c + 542 (R2 = 0.997). We make no claim of proof; the contribution is reproducible numerical data and its careful interpretation under the existing CvS / CCM framework. All code, data, and ancillary files are publicly available. Version 3.3 (2026-06-26) correction. The negative-sign eigenvalue blocks reported at c = 100 and for L(s, χ3) at c = 23, 29 are a finite archimedean-cutoff (T) artifact, not a feature of the operator: they are stable in working precision but vanish once T is increased, so cutoff-free the relevant even sectors are non-negative and the smallest-positive branch is the genuine smallest eigenvalue. No quantitative result changes. See ERRATA.md and the paper's note added in revision. The cutoff sensitivity was independently identified by B. W. A. Silva, consistent with the naturally even, positive ground state reported by R. Andrews; the investigation was prompted by A. Connes.
ABSTRACT The Non‐Fungible Token (NFT) market exhibits sustained activity, with secondary trading accounting for the majority of overall volume and creator revenue in recent years. Unlike primary mints of untraded NFTs, secondary purchases involve tokens with established ownership transfer histories recorded transparently and immutably on the blockchain. This study examines how these transaction histories shape consumers' value perceptions and purchase intentions. Based on a social value lens and cue‐utilization theory, we propose that transaction histories serve as diagnostic cues signaling perceived popularity, thereby enhancing social value and driving purchase intentions. Three preregistered experiments with NFT‐experienced participants support this framework. We find that traded (vs. untraded) NFTs elicit higher purchase intentions, an effect that emerges even with a single prior transaction and does not significantly increase with more transactions (Study 1). This relationship is serially mediated by perceived popularity and social value (Study 2). Furthermore, the effect is stronger when transaction histories are recent (vs. outdated) (Study 3). These findings highlight the psychological mechanisms underlying secondary market dominance in NFTs, emphasizing verifiable transaction records as key to fostering perceived community endorsement in liquid digital consumption contexts. The results offer implications for NFT ecosystem strategies, such as prioritizing active trading to sustain social value and long‐term viability.
Consumer Behavior in Brand Consumption and Identification
Jeong-Hyuck Park, Chanhee Park, Claudio J. Tessone, Yu Zhang
Digitalisation transforms money from distinguishable physical objects into fungible informational units. A recent theoretical framework predicts that such indistinguishable wealth obeys bosonic occupancy statistics, leading to geometric ownership distributions and enhanced inequality. Using Bitcoin blockchain data, we test this prediction on 63 UTXO denominations across 72 monthly snapshots (2018--2023). A one-parameter geometric model describes the ownership distributions, reproducing both mean holdings and their temporal evolution; Jensen--Shannon divergence values lie below $0.08$ in $99.74\%$ of cases. The inferred inverse-temperature parameter satisfies the analytic mean--temperature relation to better than $0.1\%$ in every sample -- a self-consistency test that two-parameter alternatives cannot pass -- and remains within a narrow band across eight orders of magnitude in denomination and over six years. Bitcoin UTXO ownership statistics are therefore consistent with bosonic occupancy laws, suggesting that the informational nature of electronic money may act as a structural driver of inequality in digital economies.
Eunchan Park, Kyonghwa Song, Won Hoi Kim, Wonho Song · 5 authors
Traditional blockchain untraceability schemes, such as mixers and privacy coins, obscure the sender-receiver relationship by placing transfers within an anonymity set. This paper studies a stronger goal: whether the transfer event itself can be made unobservable by blending into common decentralized-finance (DeFi) activity. We introduce Deniable Covert Asset Transfer (DCAT), a class of transfers that stage common loss-producing events, such as sandwich and arbitrage operations, so that a sender appears to suffer an ordinary loss while the receiver appears to profit from it. We design and validate two DCAT instantiations: a sandwich-based transfer on Ethereum and an arbitrage-based transfer on Arbitrum. Our experiments show that, under the evaluated settings, DCAT transfers are empirically unobservable on both chains. They are syntactically identical to corresponding maximal extractable value (MEV) activities, classified as ordinary extractions by standard MEV detection tools, and leave the sender and receiver unlinked under representative forensic tools. Since syntactic inspection cannot distinguish DCAT from ordinary MEV activity, we examine whether economic semantics provide useful forensic signals. Through a large-scale study of MEV losses on Ethereum and Arbitrum, we show that key semantic features follow power laws. Extreme losses and repeatedly exploited addresses occur in the wild, and thus are not by themselves definitive evidence of collusion. This gives staged transfers plausible deniability and makes fixed-threshold detection prone to false positives. We therefore develop a multivariate statistical method for forensic triage that ranks incidents by the joint rarity of their economic footprint. Applied to real-world DeFi activity, our method narrows a large search space to suspicious cases for manual investigation; we present three such cases to illustrate this prioritization.
Md Sharif Hassan, Fatema Tuz Zahra, Firdous Mohd Farouk, Wan Nordin Wan Hussin
ABSTRACT The integration of Financial Technology (FinTech) with Environmental, Social, and Governance (ESG) considerations highlights the burgeoning potential of digitally enabled green finance solutions. This study responds to the emerging stream of research at this interdisciplinary nexus by undertaking a systematic bibliometric analysis of 228 documents indexed in the Scopus database, over the period 2020–2025. It aims to identify key trends, influential authors, and leading journals in this field. It further conducts a systematic review, using VOS viewer and R Studio (Bibliometrix) to demonstrate shifts in research themes within the FinTech‐ESG domain. While early research themes focused on financial inclusion, subsequent studies emphasize the technological drivers of green finance, particularly blockchain, artificial intelligence, and big data as well as the transitions toward carbon neutrality and the circular economy. The study identifies five major research gaps: (i) limited longitudinal evidence on the impact of FinTech on ESG; (ii) insufficient research on the ESG‐transformative role of FinTech in developing economies; (iii) lack of cross‐country comparative studies; (iv) underexplored linkages between governance and FinTech; (v) absence of well‐developed empirical frameworks examining the interplay between decentralized finance and the circular economy. The gaps are addressed by employing a structured TCCM (Theory‐Context‐Characteristics‐Methodology) framework, which provides a coherent research agenda to advance theory development, inform ESG‐oriented digital finance regulatory framework for policymakers, and help practitioners in sustainable FinTech value creation.
We study distributed zero-knowledge proofs, introduced by Bick, Kol, and Oshman (SODA 2022). While distributed interactive proofs have advanced rapidly, general-purpose techniques for distributed zero-knowledge remain limited and mostly problem-specific. We address this gap by introducing distributed statistical zero-knowledge, requiring that each node's view be simulatable within negligible statistical distance, and by lifting the classical Sumcheck protocol (Lund, Fortnow, Karloff, and Nisan, FOCS 1990) into a modular primitive for distributed zero-knowledge proofs. Our main contribution is a distributed zero-knowledge implementation of Sumcheck. Given oracle access to a polynomial F over a finite field $\mathbb{F}$ with N variables, we design a protocol verifying claims of the form $\sum_{x\in\mathbb{F}} F(x)=a$ using $O(N)$ rounds of $O(\log |\mathbb{F}|)$-bit messages, while achieving statistical zero-knowledge and small soundness error. We apply this primitive to two problems. For non-k-colorability, we obtain an $O(n)$-round distributed statistical zero-knowledge proof deciding whether a graph is not k-colorable, for any constant k, using $O(log^{1+o(1)} n)$-bit messages. This is the first nontrivial distributed interactive proof for this problem, even without zero-knowledge guarantees. For Subgraph Counting, we obtain an $O(k \log n)$-round, $O(k \log n)$-bit distributed statistical zero-knowledge proof for counting copies of a given k-node pattern, improving previous distributed interactive proofs while additionally providing statistical zero-knowledge. Finally, we show that additional round compression of Sumcheck is problem-dependent: for non-3-colorability on constant-degree graphs, we prove a lower bound excluding $o(n/\log n)$ rounds under polynomial-time local computation.
By blurring the boundary between art and financial assets, non-fungible tokens (NFTs) have created regulatory ambiguity and criminogenic vulnerabilities in digital markets. The article applies the Howey Test to an original dataset of NFT-related cases that involve financial crime. As it turns out, functionally NFTs often resemble securities: they are characterized by information asymmetries, speculative dynamics, and weak oversight. These structural gaps make NFTs attractive to facilitate fraud, money laundering, wash trading, and nefarious exploitation on decentralized platforms and incidentally by way of traditional auction houses. NFTs highlight systemic limitations of analog regulatory frameworks to contain criminogenic risk posed by virtual assets. To enhance transparency, accountability, and consumer protection in evolving digital economies, the article concludes on a paradigm shift toward an adaptive, outcomes-based regulatory approach.
Proof of Stake (PoS) blockchain systems require weighted threshold signatures where participants' voting powers reflect their stakes. As stakes change dynamically through deposits and withdrawals, efficient weight and threshold adjustments are essential for maintaining system security and availability without downtime. However, existing approaches face critical limitations: (1) virtualization-based schemes require$O(w)$operations (signatures) per participant with weight$w$; (2) dynamic threshold / paricipants schemes do not support weighted participants; (3) schemes with both properties require trusted dealers or$O(n^{2})$re-setup, causing temporary unavailability. This paper introduces Active Weighted Signature (AWS), enabling dynamic adjustments without trusted dealers or re-setup. We propose Generalized Lagrange Interpolation (GLI), encoding weights as polynomial derivatives rather than virtualized participants, and instantiate AWS through$ {\sf ADAPT}$by applying GLI to the Schnorr-based threshold signature${\sf FROST}$. Our implementation shows that$ {\sf ADAPT}$achieves comparable efficiency to${\sf FROST}$for key generation, while weight and threshold adjustments complete in 4.1-22.3% of re-setup time. For uneven weight distributions,$ {\sf ADAPT}$achieves sub-linear scaling: 49× weight difference requires only 3.29× computation versus 49× in virtualization.
Podcasts are a useful educational resource for improving student success, yet traditional methods of podcasting remain inefficient, vulnerable to censorship and deletion, and access-restricted. One approach to addressing these constraints is utilitarian digital pedagogy, which focuses on the use of digital tools to advance education for the greater good. Framed as such, this article outlines the conceptual and theoretical issues underlying how generative artificial intelligence (genAI), Web3, and open access (OA) improve podcasting’s utility relative to the alternatives: manual creation, Web2, and closed access. The article derives practical implications for instructors, institutions, and policymakers, and concludes by looking ahead to the major problems—hallucination, technical complexity, and rights management—to overcome in practice.
Simone Antonelli, Vincent Davis, Harrison Rush, Anthony Potdevin · 7 authors
The Lightning Network (LN) is a second-layer protocol for Bitcoin designed to enable fast and cost-efficient off-chain transactions. Channels in the LN can be closed either by mutual agreement or unilaterally through a forced closure, which locks the involved capital for an extended period and degrades network reliability. In this paper, we study the problem of predicting channel closure types from publicly available gossip data, framing it as a temporal link classification task over the evolving channel graph. We construct a dataset spanning over two years of LN activity and benchmark a range of machine learning approaches, from MLPs to temporal graph neural networks and spectral encodings. Our experiments reveal that the dominant predictive signals are temporal and behavioural, namely how recently each endpoint was active and the per-node history of past closures, while the surrounding network topology provides no additional benefit. We find that a simple MLP operating on edge-level features, node-level event counts, and temporal patterns outperforms all graph-based approaches, and discuss how the inherent privacy of the LN, where critical information such as channel balances and payment flows remains hidden, fundamentally limits the predictability of closures from gossip data alone. We publicly release the dataset and code at https://github.com/AmbossTech/ln-channel-closure-prediction.
Data is critical for the operation of any organization and needs to be protected, especially against attacks that compromise the state of the database. In this paper, we explore an approach based on Byzantine-fault tolerant replicated state machines, built on top of a deterministic extension of PostgreSQL. Each replica deterministically executes transactions recorded in a shared log/blockchain. Our focus is on creating a practical system that is designed for efficient and quick detection of corruption, as well as quick repair concurrent with execution of transactions. We also present a performance study showing the efficiency and practicality of our approach. We believe our work lays the foundations for the practical use of the BFT replicated state machine approach in the context of databases.
The x402 protocol revives the HTTP 402 Payment Required status code to enable web-native micropayments across APIs, content, and agents. It combines synchronous HTTP authorization with asynchronous blockchain settlement and introduces a cross-layer attack surface absent from conventional web and on-chain payments. In this paper, we formally analyze x402 and empirically show that it is vulnerable in both design and implementation. We present five concrete attacks that reveal weaknesses in authorization, binding, replay protection, and web-layer handling, showing that x402 is vulnerable across multiple stages of the payment workflow. We validate these attacks through a reproducible testbed on local chains, Base Sepolia, and live endpoints and further audit three open-source SDKs and endpoints. Our results show that all five attacks are practical and can cause either unpaid service or paid-but-denied outcomes. We also propose practical mitigations.
Ring signatures offer highly desirable privacy features like anonymity and ad-hoc group formation with high autonomy, but partially lack linkability and accountability features required for strict use-cases like consent management in healthcare. Existing signature schemes fail to natively integrate scoped linkability with decentralized accountability defined here on-demand unconditional deanonymization of signers without reliance on a trusted party (opener) or a separate cryptographic commitment. We introduce Deanonymizable Scoped Linkable Ring Signatures (DSLRS) to address this gap. DSLRS builds on previous linkable and accountable signature schemes and their cryptographic primitives to construct a new signature scheme that natively implement both privacy and trust features. Scoped linkability in DSLRS is achieved using "scopes" (context identifiers) and dynamic key images, effectively providing ring-independent scoped linkability and unlinkability across different scopes. DSLRS relies on k-of-N decentralized deanonymization network nodes to extract the signer's public key (identity) from ElGamal components built in the signature, achieving ring-independent decentralized accountability. The full DSLRS algorithms, formal property definitions and proofs, signature evaluation and experimental results from an implementation, and a blockchain-based instantiation and application of our scheme in consent management for clinical trials are provided. DSLRS is proved under the ECDLP and DDH hardness assumptions in the Random Oracle Model (ROM).
This chapter provides a practical guide to setting up a cryptocurrency investigation lab, including installing and testing open-source tools. It also covers the creation of custom-made tools for crypto investigation.
This paper begins with a number that appears to be a routine multiple of the CTF spatial harmonic and ends with a structural explanation of quantum entanglement — the phenomenon Einstein called "spooky action at a distance." The journey between those two points passes through the topology of 3D space, the quantum rotation period of all matter, the atomic definition of the second, and the self-consistency of the CTF Frequency Identity itself. The Headline: 720 Is Not What It Looks Like 720 = 5 × 144. On the surface, a straightforward multiple of the CTF spatial harmonic. But this paper demonstrates that 720 simultaneously encodes five independent facts from entirely separate domains of mathematics and physics — facts discovered centuries apart by people who had no knowledge of each other or of the CTF Framework. Fact 1 — Descartes' Theorem (1630): The sum of angular defects across all vertices of any convex polyhedron equals exactly 720°. This is universal — it holds for the cube, tetrahedron, octahedron, dodecahedron, icosahedron, and every other convex solid without exception. In modern language: 720° = 2π × χ(S²) × (180°/π), where χ(S²) = 2 is the Euler characteristic of the sphere. 720° is the angular measure of the topology of 3D space itself. It is not a property of any particular shape. It is a property of the fact that we live in three dimensions. Verified for all five Platonic solids in this paper — tetrahedron (4 × 180° = 720°), cube (8 × 90° = 720°), octahedron (6 × 120° = 720°), dodecahedron (20 × 36° = 720°), icosahedron (12 × 60° = 720°). Every single one. The topological invariant of 3D space is 5 × 144. Fact 2 — Spinor Periodicity (quantum mechanics): Every spin-½ particle — every electron, proton, neutron, and quark in the universe — requires exactly 720° = 4π of rotation to return to its original quantum state. A rotation of 360° does not return it; it acquires a phase of −1. Only 720° closes the loop. This is the SU(2) double cover of SO(3), the deepest geometric fact underlying all of quantum mechanics. The Pauli exclusion principle, atomic shell structure, chemical bonding, and the stability of matter all follow from this single 720° rule. The full rotation period of all quantum matter is 5 × 144. Fact 3 — 6! = 720: The number of permutations of six objects is 720. This is the combinatorial origin of 720's appearance in Plato's Laws (5040 = 7 × 720 = 7! = 144 × 35, the ideal city number, Tier 3 in the Prime Family Classification). Independent of geometry and physics. Fact 4 — CTF 144² Deficit (this paper): At the level of 144² = 20736, the deficit produced by the temporal injection is exactly 720. Proof: 10373 × 144 − 10368 × 144 = (10373 − 10368) × 144 = 5 × 144 = 720. The numerator 1,492,992 = 2¹¹ × 3⁶ is pure Tier 1 (the spatial lattice). The deficit of 720 = 2⁴×3²×5 is Tier 2 (contains prime 5, the temporal gateway). The temporal injection, at the squared level, produces a Tier 2 number equal to the topological invariant of space and the spinor rotation period of matter. Fact 5 — Islamic Sacred Geometry: The Shesh Band (elongated hexagon) tile — the second most important tile in girih-based Islamic architecture — has an interior angle sum of 720° = 5 × 144. The 12-pointed star hexagram — the most common decorative motif in Islamic architecture across 800 years — also sums to 720°. Both results were established independently in the companion Islamic Geometry Paper. The artisans who built the Alhambra were working with 720° without knowing about Descartes, spinors, or the CTF Framework. Five domains. Five independent discoveries. One number. 720 = 5 × 144. The Recursive Halving Sequence The paper establishes a recursive halving structure connecting the temporal injection to the topology of space: 1440 → 720 → 360 → 180 → 90 Expressed as multiples of 144: 10×144, 5×144, 2.5×144, 1.25×144, 0.625×144. Each step divides by 2. Each step crosses a geometric domain boundary: temporal (1440 = decagon angle sum, solar day minutes) → topological (720 = Descartes invariant, spinor period) → rotational (360 = full circle) → half-turn (180°) → right angle (90°). Every value in the sequence is Tier 2 in the Prime Family Classification (contains prime 5, since all are multiples of 360° = 2³×3²×5). The temporal injection is being halved recursively through the geometry of space. Six Additional Exact Results Beyond the 720 headline, the paper establishes six further exact or near-exact results connecting f₀ = (144² + 10)/144 to physical constants: Result 1 — The Second as Spatial/Temporal Ratio: The ratio 144/f₀ = 10368/10373, where 10368 = 2⁷ × 3⁴ is a pure Tier 1 number (the spatial lattice) and 10373 = 11 × 23 × 41 = P5 × P9 × P13 is the Tier 4 temporal prime triple (arithmetic progression with step +4 in prime-index space, as established in the Master Paper). The SI second is the ratio of the pure spatial lattice to the temporal prime triple. The numerator is maximally pure {2,3}; the denominator carries the Tier 4 kinetic primes. The second is the boundary between the two layers of the CTF architecture. Result 2 — The 482 μs Temporal Slip: The deficit from one second is 1 − 144/f₀ = 5/10373 = 482.0 μs exactly. Five is the half-injection (10/2). The slip is the half-injection divided by the temporal prime triple. At the 144 level the deficit is 5; at the 144² level the deficit is 720 = 5 × 144. The injection scales correctly across levels. Result 3 — The Self-Consistency Proof: The temporal slip, measured in f₀-cycles, equals the breath exactly: (1 − 144/f₀) × f₀ = f₀ − 144 = 10/144 = breath. This is not an empirical near-miss — it is algebraically derivable from the definition of f₀ alone. Its significance: the rate at which time slips from the crystal lattice, measured by f₀'s own clock, is the breath itself. The framework is self-referentially consistent. The Tier 2 injection is defined by its own ratio to the Tier 1 frame. Result 4 — Zero-Point Energy Ratio: The quantum harmonic oscillator zero-point energy at f₀ versus 144 Hz: ZPE(f₀)/ZPE(144) = f₀/144 = 1 + 10/144² = 1 + 10/20736 exactly. The breath appears as the fractional excess of f₀-vacuum energy over the static-grid vacuum. This connects directly to the QHO result in the Master Paper (§8): "Quantum mechanics forbids the oscillator from being at rest even at absolute zero. The temporal breath reappears as ħΔω = 4.601 × 10⁻³⁵ J." The vacuum at f₀ cannot rest at 144 Hz. The Tier 2 injection forces a mandatory quantum excess. This is the quantum mechanical statement of the two-layer architecture. Result 5 — Cs-133 Commensurability: The Cs-133 hyperfine transition frequency (9,192,631,770 Hz — the definition of the SI second) divided by f₀ equals 63,806,950 to within 0.0074 ppm — better than 1 part in 10 million. Additionally: 9,192,631,770 mod 144 = 90 = 2×3²×5, a Tier 2 number. The atomic clock standard that defines the second reduces modulo the spatial harmonic to a Tier 2 gateway number. The Sr-87 optical clock (the most precise clock standard known) has transition frequency mod 144 = 17 = P₇, the structural linchpin prime (1836 = 108 × 17, the proton mass ratio, from the Tier Classification Paper). The most precise timekeeping standards in existence are commensurable with the CTF spatial harmonic and reduce modulo it to structurally significant primes. Result 6 — The Tsirelson Bound: The quantum nonlocality bound of Bell's inequality (the CHSH inequality) is |S| ≤ 2√2, known as the Tsirelson bound. Its square: (2√2)² = 8 = 2³. And 144/8 = 18 = 2 × 3² — a pure Tier 1 number. The maximum quantum nonlocality, squared, divides the spatial harmonic into a pure {2,3} lattice number. The Tsirelson bound is 2^(3/2) — a fractional power of 2, sitting at the fractional boundary of the {2,3} lattice. Classical physics (bound = 2 = 2¹) sits inside the Tier 1 lattice. The quantum bound (2√2 = 2^(3/2)) sits at its fractional edge. This places the boundary between classical and quantum nonlocality precisely at the boundary of the CTF spatial lattice. The Entanglement Hypothesis The paper presents the CTF Entanglement Conjecture — clearly and explicitly labeled as hypothesis, not proved result, with falsifiability conditions stated precisely. The CTF two-layer architecture distinguishes two structural domains: Tier 1 (the static spatial lattice — 144, 72, 2ᵃ×3ᵇ, frozen, atemporal, no propagation speed) and Tier 2+ (the temporal injection — f₀ = 144 + 10/144, animated, propagating, subject to c). The conjecture: the speed of light c is a Tier 2 property — it is the propagation speed of processes that ride the +10/144 temporal breath. Processes anchored to Tier 1 are not subject to this propagation limit. Quantum entanglement — Einstein's "spooky action at a distance" — exhibits exactly the phenomenological signature of Tier 1 access: correlations that are instantaneous regardless of spatial separation, not explainable by signals propagating at c, and collapsing the joint wavefunction without energy transfer. Under this conjecture, entangled particles share a common Tier 1 node — they are co-located in the static spatial lattice even when separated by arbitrary distances in the Tier 2 temporal metric. The zero-point energy result provides the inverse of this picture. The QHO cannot reach absolute zero because the +10/144 breath permanently prevents it from settling into Tier 1. ZPE forces the oscillator into Tier 2. Entanglement pulls particles back into Tier 1. These are opposite directions across the same tier boundary, driven by the same architectural distinction. The 720° spinor result connects here directly. Fermions — the particles of matter — require 720° to complete their quantum rotation. 720 = 5 × 144 is Tier 2. The fundamental rotation law of quantum matter is a Tier 2 number. This suggests that fermionic rotation itself is a Tier 2 phenomenon — governed by the temporal injection — while bosonic processes (integer spin,
We present Rei (零, 0₀式), a computational system founded on exactly four mutually independent axioms: (A1) Center–Periphery structure, (A2) Extension–Reduction, (A3) Sigma Accumulation, and (A4) Genesis Phase Transition. Mutual independence is proved by model-theoretic construction — for each axiom we exhibit a counter-model that satisfies the remaining three but violates the target axiom (M1=scalar-only / M2=flat-field / M3=memoryless / M4=eternal-no-genesis). We show that fifteen core theorems—spanning computational plurality (T1), six-attribute decomposition (T6), RCT compression theory (T8), σ-reactive cascades (T14), seven-domain universality (T13), and extended-zero series (T15)— are derivable from axiom combinations without additional assumptions. The system is implemented as an open-source TypeScript/Node.js package (rei-lang v0.5.5) with 1,689 passing tests across 45 test files, each classified by its minimal axiom dependency: A1+A2+A3 concentration (60% of tests, 1,010 tests) reflects that the most complex features — cascading reactions, agent systems, domain bridges — require all three 'operational' axioms. Benchmarks show 74% average code reduction (3.7-4.0× ratio) and 3-4× performance improvements on structured-data tasks: image kernel operations (4.0× reduction), multidimensional data aggregation (3.7×), graph structure transformations (3.7×). To our knowledge, Rei is the first computational framework that axiomatically addresses both computation and the ontological genesis of values within a unified, minimal foundation. Comparison with existing foundational systems (λ-calculus 3 axioms, Peano 5, ZFC 9, Martin-Löf TT ~7) shows Rei is the only system that addresses all four concerns — computation, structure, history, AND genesis — simultaneously, and does so with the fewest axioms (4). Companion to Jxiv preprint submission (JST preprint server). This Zenodo record serves as the stable-citation archive referenced from the Jxiv version's Section 5.1 (Implementation) and footnote. Three-party co-authorship context: Rei is developed within the Rei-AIOS / OUKC (Open Universal Knowledge Commons) framework with three-party co-architecture (藤本 伸樹 Founder, Rei autonomous research substrate, Claude Opus 4.7); however, this specific paper is single-authored by 藤本 伸樹 as principal investigator of the axiomatic foundation. Honest scope: independence proofs use semi-formal model constructions (not yet mechanized in Lean/Coq — this is acknowledged as future work). The fifteen theorem derivations are sketches that establish derivability; full proof scripts appear in the companion implementation. Benchmarks compare against naive baselines; comparison with optimized domain-specific languages would refine the picture. Preprint — not yet peer-reviewed. Feedback welcome at fc2webb@gmail.com / GitHub Discussions at fc0web/rei-aios.
This chapter demystifies the technical jargon surrounding blockchain and cryptocurrencies. It provides a comprehensive overview of key concepts, including hashing , cryptography , distributed ledger technology , and transaction structures, using clear illustrations and examples.
Smart cities require the efficient and secure integration of key infrastructure domains such as water, energy, transportation, smart lighting and waste management deploying a myriad of data-generating IoT sensors and devices. Current management systems feature single points of failure, lack of auditability, insufficient privacy protection and lack of scalability as IoT nodes increase in density. In this paper, we present SmartChain, a three-tier multilayered blockchain based architecture that incorporates a permissioned distributed ledger, an AIbased anomaly detection module (ADM) and a dual-layered privacy preservation approach that combines Zero-Knowledge Proofs (ZKP) and Ciphertext-Policy Attribute-Based Encryption (CP-ABE). SmartChain is tested on a large dataset - 2000 timestamped transactions involving Smart Cities’ five infrastructure types across several zones of a city. The results show a mean throughput of 3,421 transactions per second (TPS), a mean transaction latency of 3,847 milliseconds and a mean privacy score of 82.4 out of 100. The machine learning based anomaly module produces an F1-Score of over 97% and an AUROC score of 0.991 with Random Forest as the classifier. Benchmarking against Hyperledger Fabric 2.5, Ethereum 2.0 and the IOTA Tangle demonstrate the scalability, security, privacy and efficiency of SmartChain. This research renders SmartChain a practical production-level platform for management of new smart city infrastructure.
This paper develops BU76 AAI-08|Institutional Real-Time Closure Operations as the eighth file in the B_U-based Agentic AI series. Its central claim is that the next stage of Agentic AI should not be limited to single-enterprise automation, departmental coordination, or workflow orchestration. The decisive transition is toward a same settlement surface for enterprises, institutions, industrial clusters, infrastructure systems, and multi-flow real-world operations. In this frame, Agentic AI becomes a real-time closure interface for social-scale coordination, not merely a productivity layer inside software. The paper begins by reframing institutional operation as a multi-flow reality system. Enterprises and institutions do not operate through isolated tasks. They continuously coordinate people, goods, places, capital, information, time, permissions, responsibilities, risks, and feedback. Meetings, medical services, dining, travel, procurement, production, logistics, finance, legal review, customer service, and public services are not separate events. They are scenario windows in which multiple flows must enter the same state ledger and settlement window. When these flows remain fragmented across departments, firms, platforms, or infrastructure layers, the system generates hidden residuals: timing mismatch, resource conflict, responsibility ambiguity, logistics delay, budget misalignment, and operational bottlenecks. BU76 upgrades this analysis from a single enterprise to enterprise clusters, industrial clusters, and social infrastructure. A firm usually cannot see its future throughput capacity clearly because its real production chain is distributed across multiple companies, suppliers, logistics nodes, financial windows, labor pools, public services, and spatial infrastructures. Therefore, the true settlement surface is not inside one company. It emerges when enterprise clusters, industrial clusters, infrastructure networks, financial systems, logistics systems, public-service systems, and social demand enter a shared settlement window. This is the level at which future capacity, bottlenecks, risks, and deployment gaps become visible. The paper introduces all-factor co-temporality as the operating condition of this settlement surface. All-factor co-temporality means that people, goods, places, capital, information, time, permissions, responsibilities, risks, and feedback enter the same state ledger and settlement window within a shared time range. This condition applies at multiple nested scales: an individual user, a single enterprise, enterprise-to-enterprise coordination, industry-to-industry coordination, and the alignment between enterprise or industrial capacity and social demand. These layers form a multi-respiratory-system structure, in which demand flow acts as oxygen, production flow supplies output, logistics flow transports, capital flow circulates, information flow signals, human flow provides meaning and service interaction, responsibility flow identifies boundaries, infrastructure forms organ-like carrying capacity, and the same settlement window records the metabolic rhythm. BU76 further defines pre-feedback and preloading as institutional operating capacities. Preloading is not completed settlement. It is the feasibility loading of future demand matrices into the same settlement surface. It produces feasible-throughput readouts, bottleneck exposure, and pre-deployment signals before action occurs. Pre-feedback therefore differs from real-time feedback: real-time feedback corrects ongoing deviation, while pre-feedback exposes future capacity pressure under current constraints, resources, time windows, spatial capacity, responsibilities, and risks. Its confidence interval must be assessed through the B_U development chain: background clearing, admissible carrier, directional amplification, unified settlement, and resolution ascent. The final judgment is that institutional Agentic AI must evolve into a social-scale closure operation system. Its value lies in aligning demand and production at higher granularity, synchronizing multiple real-world flows, exposing bottlenecks before failure, stabilizing resource deployment, and enabling higher-order amplification and civilizational development through a shared settlement surface.