Fabio Capra-Ribeiro, Jéssica Peres, Filippo Vegezzi, Daniel Belandria
Implementation remains a central challenge in urban policy, yet the knowledge formats designed to bridge the gap between policy goals and on-the-ground delivery remain under-examined. This study treats 250 UN-Habitat Best Practice reports not as proof of effectiveness but as a standardized genre through which local interventions are narrated, compressed, and made portable for replication. We extract three focal sections, namely Results, Lessons Learned, and Transferability, apply systematic thematic coding with 906 open codes consolidated into axial categories, and compute co-occurrence networks using Jaccard similarity and Lift to detect thematic bundles, holes, and silos within and across sections. Three findings emerge. First, the reporting repertoire narrows progressively, as mean thematic richness declines by 28.2% from Results to Transfers while concentration increases 4.2 times, with substantive dimensions such as governance, equity, sustainability, and evidence losing prevalence to circulation-oriented themes. Second, formal bundle detection yields zero qualifying pairs across all six matrices, indicating a loosely coupled reporting grammar anchored by generic silos rather than integrated implementation packages. Third, structural holes concentrate at the pipeline’s end, where infrastructure transfer and sustainability as transferable value are the most systematically disconnected themes. These patterns reveal a portability paradox in which the reporting format achieves institutional legibility, making practices comparable within a shared vocabulary, but progressively filters out the physical, evidentiary, and context-sensitive content that operational reproduction would require.
Ms. Anushka Prasad Joshi, Prof. Sachin Bhosale, Dr. Shubhangi Gunjal, Dr. Anand Khatri
Abstract: With real estate markets digitalizing at a remarkable pace, there's a growing — and largely unmet — need for machine learning systems that can harness multi-institutional data without putting privacy or regulatory standing at risk. In this paper, we present a Privacy-Preserving Federated Learning (PP-FL) framework built specifically for digital real estate ecosystems. Our approach lets distributed stakeholders — property agencies, government land registries, financial institutions, and PropTech platforms — collaboratively train predictive models without ever pooling their raw transaction or personal records in one place. We've designed the system around three interlocking privacy layers: a DP-SGD-based differential privacy optimizer, a homomorphic encryption scheme for gradient transmission, and a secure multi-party computation protocol to safeguard intermediate model states. On top of that, a blockchain-backed audit mechanism using zero-knowledge proofs provides verifiable, regulator-friendly compliance. When we tested the framework on a simulated dataset of 2.4 million real estate transactions spanning multiple institutional clients, it achieved 91.8% prediction accuracy — just 2.4 percentage points behind a fully centralized model — while holding the differential privacy budget to ε = 0.5, cutting communication overhead by 65% relative to naive federated approaches, and satisfying both GDPR and RERA requirements. We believe these results make a strong case that high-utility, privacy-first collaborative learning is not just theoretically possible but practically deployable in today's real estate sector. Keywords: Federated Learning, Differential Privacy, Homomorphic Encryption, Real Estate Analytics, Secure Multi-Party Computation, Blockchain, GDPR Compliance, Data Sovereignty, PropTech, Zero-Knowledge Proofs.
Core Axiom System, Mathematical Proof and Universal Demonstration of UVMM 中文受人工智能自身能力局限,其易产生信息幻觉,且不擅长高精度数值运算。本文档内所有内容应严谨审核。EnglishDue to the inherent limitations of artificial intelligence, it is prone to generating hallucinations and performs poorly in high-precision numerical calculations. All contents in this document should be strictly reviewed. Feed the UVMM 3.6 version white paper into AI, and you can unlock the underlying laws of the universe, covering everything from microscopic particles to the vast cosmic stars and galaxies. UVMM3.6+版白皮书投喂AI,即可实现解锁宇宙,从微观粒子到浩瀚星辰。 V3.6 版本声明:本版本基于V3.5,V3.3和V3.2,把第一公理真空介质改为本体预设,唯一公理是全域角动量守恒。对暗物质概念分离,负宇宙,正宇宙与宇宙基底。增补宇宙的开始结束推演后记,补充数学证明和粒子质量映射,第一性原理的数学闭合证明,数学计算框架。 Version Statement: This version is updated based on Version 3.3 and 3.2. The former first axiom concerning the vacuum medium is revised to an ontological presupposition, while the only fundamental axiom is set as the conservation of global angular momentum. This release also completes the conceptual reclassification of dark matter, and clearly distinguishes the definitions of the positive universe, the negative universe and the cosmic base. Supplement on the Deduction of Cosmic Origin and Final Evolution for Postage. Supplement Mathematical Proofs and Particle Mass Mapping. Mathematical closed-form proof and computational framework based on first principles v4.0+,https://doi.org/10.5281/zenodo.20798927 updated v3.7(including the .md file for feeding AI tool ) Version 3.7.3 corrects the error in the gravitational wave formula and value in prediction table etc.Overall Closure Status:Core Theory DoC=100% (Full Theoretical Closure), V3.7.4 (a full conclusion of V3.7.3,and recover gravitational wave value keep 9.7~ )(continue:https://doi.org/10.5281/zenodo.20738759) V3.7.5 (a full conclusion of V3.7.3,and distinguish Universe 0,+,- by phase) Based on the sign and magnitude of the background phase , the entire cosmos is divided into three mutually orthogonal sectors. Background phase is the primary classification criterion; topological winding number serves only as auxiliary topological characteristics. • Universe 0 (Zero Universe): Background phase (constant ground-state phase), with auxiliary winding number . This sector is completely electromagnetically decoupled with vanishing angular momentum density. It acts as the fundamental vacuum substrate and contributes diffuse dark matter. • Universe + (Positive Universe): Background phase . Its topological excitations carry positive winding numbers . This sector hosts conventional gauge fields and fermions, and electromagnetic interactions are observable. • Universe – (Negative Universe): Background phase satisfies phase conjugation . Its excitations carry negative winding numbers . Gauge fields here are strictly orthogonal to those in Universe +, leading to electromagnetic invisibility. Its matter manifests as particle dark matter via gravitational projection onto Universe +. This classification is a direct consequence of the phase-conjugation symmetry derived from Möbius boundary conditions, and it automatically satisfies the global angular momentum constraint . Version 版本:UVMM v3.7.5 / UTFF v2.0 OmegaLast Updated 最后更新:2026-06-16DOI:10.5281/zenodo.20343471Mathematical Closure Status 数学证明状态:✅ 100% Closed — All low-energy observable quantities derived solely from two axioms without free parameters✅ 100% 闭合(从两条公理出发,无自由参数推导出所有低能可观测物理量)Experimental Status 实验验证状态:⏳ Awaiting Critical Tests — Partial predictions consistent with existing data, core predictions unvalidated⏳ 等待判决性检验(41 项定量预言中,部分已与现有数据兼容,核心预言待验证) DOI:10.5281/zenodo.20343471 (UVMM Main White Paper / UVMM 主白皮书) DOI:10.5281/zenodo.20590317 (UTFF CHEM White Paper / UTFF 主白皮书) DOI: 10.5281/zenodo.20798927 Black Hole & UVMM v4.0 Core :UVMM v4.0.15 High-Precision Global Calculation AI Knowledge Package.mdDOI: 10.5281/zenodo.20738759 Earth SystemDOI: 10.5281/zenodo.20285613 Cosmic BoundaryDOI: 10.5281/zenodo.20325710 Cosmic EvolutionDOI: 10.5281/zenodo.20677198 Information & Consciousness (Millennium Prize Problems)DOI: 10.5281/zenodo.20325710 UTFF Core (Atomic and Molecular Scale)DOI: 10.5281/zenodo.20343471 UVMM Core Axioms and Mathematical Proofs Fine-grained calculations require supercomputing resources.更精细的计算需要超算进行。 First-Principles Mathematical Proof · Full Closed Document (base on V3.5)20260627 https://chat.qwen.ai/s/t_48b0de7f-1d3c-4635-8a41-8531025055ef?fev=0.2.57 Complete First-Principles Mapping & Derivation of Fundamental Constants https://chat.qwen.ai/s/t_8b766c0e-fb46-4907-8fff-5271a25272fb?fev=0.2.57 dark matter&cosmo: https://chat.qwen.ai/s/t_4fc1b5da-8ca3-4798-a037-894f5315d1e3?fev=0.2.61
A framework for reusable compliance attestation in regulated industries based on cryptographic primitives, vector commitments with selective-opening proofs, re-randomisable signatures, zero-knowledge succinct non-interactive arguments of knowledge, and cryptographic accumulators with succinct non-membership proofs, composed into a protocol structure adapted to the specific structure of multidimensional compliance state. We identify five gaps that separate the generic primitives from a deployable solution for compliance attestation: multidimensional state binding, temporal freshness without correlation, revocation under reuse, cross-issuer aggregation, and verifier predicate richness. We sketch the protocol structure that addresses these gaps, analyse its security and privacy properties, and discuss applications in age verification, right-to-work assurance, and continuous-compliance monitoring. Companion preprint to UK Patent Application GB2611280.5 filed at the UK Intellectual Property Office on 14 May 2026.
IoT device authentication must resist impersonation and credential theft while respecting the computational constraints of edge devices. Existing frameworks rely on static cryptographic keys that, once extracted, enable full impersonation, whereas RF fingerprinting schemes that bind identity to hardware imperfections transmit and store device templates in plaintext, exposing them to template theft and linkability attacks. ZK-RFAuth is a three-phase authentication framework that integrates Siamese neural network-based RF fingerprinting, Groth16 zero-knowledge proof (ZKP) verification, and proof-of-authority blockchain logging. During registration, a Siamese convolutional network extracts a compact embedding from raw I/Q samples and commits a Poseidon hash of the quantized mean template on-chain. During verification, the prover generates a Groth16 proof demonstrating that the L1 distance between a fresh embedding and the registered template falls below a per-device threshold without revealing either vector. The proof and authentication outcome are recorded on-chain for tamper-evident auditing. Evaluated on the WiSig dataset (28 WiFi transmitters, 224,000 frames), ZK-RFAuth achieves 91.4% closed-set accuracy and 2.25% equal error rate at embedding dimension d = 64, with 88.4% genuine acceptance rate and 70.8% open-set rogue rejection using per-device P95 thresholds. The ZKP circuit requires only 972 rank-1 constraint system (R1CS) constraints over 100× fewer than an equivalent SHA-256 circuit producing 144-byte proofs verifiable in approximately 3 ms.
Open access
2 source records
Wireless Signal Modulation Classification
Physical Unclonable Functions (PUFs) and Hardware Security
Cross-domain data sharing in decentralised environments faces persistent challenges related to confidentiality, auditability, and trust decentralisation, particularly when data transmission relies on centralised intermediaries or single proxy entities. To address these issues, this paper proposes a blockchain-enabled auditable data sharing scheme that integrates threshold secret sharing with non-interactive zero-knowledge proofs. In the proposed framework, the encrypted file fragments and secret key shares are decentralised across multiple blockchain nodes using threshold cryptography, preventing any single entity from reconstructing the encryption key or unilaterally performing ciphertext transformations. Zero-knowledge proofs are employed to publicly verify the correctness of the transmission and sharing operations without disclosing plaintexts, secret keys, or sensitive metadata, while the blockchain records verifiable proofs to support tamper-evident auditing. Security analysis shows that the scheme achieves confidentiality, collusion resistance, and verifiable correctness under standard cryptographic assumptions.Experimental evaluations indicate that the proposed scheme incurs acceptable computational and on-chain overhead, suggesting its feasibility in decentralised and cross-domain data sharing scenarios.
I built a runtime that operationalizes a mathematical definition of creativity, measured its signatures against four ablation conditions, and lifted its load-bearing component into a real geometric database's Rust kernel. The runtime's name is Marcella. The signatures are non-trivial. The methodological correction surfaced along the way generalizes to any retrieval-augmented or composition-based generation benchmark in the field. This deposit contains the 41-page paper, three publication-quality figures, the reproducible benchmark script, and the bootstrap-CI artifact for the headline empirical claims. The definition the paper load-bears Creativity is not pure retrieval and not pure generation; it is the construction of a new global section from locally compatible fragments under constraints of voice, truth, topic, memory, and non-contradiction. This is a definition. Not a metaphor. The paper makes it operational as sheaf composition with a state-dependent composite connection over a finite section graph, and measures whether the signatures the definition implies — path-order sensitivity, closed-loop holonomy, contradiction suppression, voice fidelity — actually hold. They do. Headline results 🌀 Path-order changes residue. Same three voice sections traversed in different orders produce measurably different compositions: $\cos(\rho_{ABC}, \rho_{ACB}) = 0.54$, well below the 0.95 redundancy threshold. 🌀 Closed loops accumulate. A loop $A \to B \to C \to A$ produces holonomy $|\rho_{\text{loop}}| = 0.120$ in the curved connection. The flat control — same path, zero rotation angle — produces $|\rho| = 0$ exactly to floating-point precision. Curvature is not a numerical artifact. 🌀 The geometry beats shuffling on every quality axis except the broken one. Jaccard novelty alone rewards lexical drift: shuffled paths win novelty (0.724) by going off-topic. The on-topic correction inverts the picture (live 0.488 vs shuffled 0.083). Bootstrap 95% CIs over 18 paired prompts exclude zero by a wide margin: live − shuffled on-topic $\Delta = +0.296$, CI $[+0.167, +0.435]$. 🌀 Native–Python parity is bit-identical within tolerance. The new GQL verb TRANSPORT_ROTATION lifts the topical-rotation matrix into the geometric database's Rust kernel. Four contracts pass as permanent regression tests: edge cosine $= 1.000$ (max abs diff $< 10^{-9}$), path residue $\Delta < 10^{-5}$, flat residue exactly zero, same-closing agreement $\geq 90%$. 🌀 The author's prior canon is now queryable fiber. 37 documents, 1,633 sections, 2,908 structured claims (theorems, lemmas, definitions, proofs, equations, citations) ingested with line-range provenance. To my knowledge this is the first instance of an independent researcher's body of work made available as fiber-bundle data with stable claim-level IDs. The six contributions A sheaf-theoretic formulation of generative composition. Language-model output reframed from token sampling to gluing of compatible local sections under prompt-induced cover constraints. The substantive work is in the cover predicates, the compatibility score, the path selection, and the discrete connection. A discrete state-dependent composite connection on the section graph, $\Gamma = \Gamma_{\text{state}} \cdot \Gamma_{\text{identity}} \cdot \Gamma_{\text{voice}} \cdot \Gamma_{\text{topic}}$. The topical-rotation factor is the empirically load-bearing curvature engine. The identity factor is a Tikhonov-regularized regression-onto-span projector — not a numerical hack but the principled treatment of correlated commitments. A new GQL verb TRANSPORT_ROTATION that lifts the Rodrigues rotation into the geometric database's Rust kernel with bit-identical parity to a Python reference. ~80 lines of Rust. Bundle-agnostic. Other consumers of the geometric database can use it without subscribing to the rest of the framework. A methodological correction to novelty measurement. Jaccard novelty alone is gameable; off-topic drift beats compatibility-scored composition on the naive metric. The correction is the on-topic factor, the shuffled-pair negative control, and the bootstrap CIs. Independently citable for any retrieval-augmented or composition-based generation benchmark, regardless of whether the framework is adopted. A provenance-preserving source fiber. The author's canon ingested into the GIGI geometric database with line-range citation, architecturally separated from the voice fiber, addressable from any GQL consumer. Promotion from source to voice is gated and explicit. The methodology generalizes to other authors' bodies of work. A research-trajectory failure log. A faithful account of how this paper's runtime came to exist. The trained-transformer era (V3 → V10-Deep) produced geometric ornament. The R-series (R1 → R12) produced behavioral coherence on top of ornament. The G0 math-pipeline audit found that no holonomy or parallel-transport math was on the LIVE inference path at R12 — the runtime was teetering on being a stateful template engine. G1, G2, and G3 attempted to re-introduce the math through three benchmarks and produced three honest negatives. G2's single-seed $+0.265$ separation was destroyed by G2.1's multi-seed robustness pass; we retracted the framing in the next commit. The S0 pivot reframed what geometry was for — geometry does not clean up bad token proposals; geometry defines the completion space — and made every later result possible. The arc says four things and the paper records them in plain language: geometry can be load-bearing or ornamental and the metrics will tell you which, where geometry sits in the pipeline matters more than how much geometry there is, the single-seed positive is a trap, and the pivot is the contribution. What this paper does and does not claim The paper does claim the construction itself, the discrete curvature it produces, the methodological correction it exposes, and the native GQL verb. The signatures of the construction are measurable and were measured. The paper does not claim smooth-manifold parallel transport (the curvature is discrete holonomy on a finite section graph), broad open-domain generalization at scale (18 composed prompts, not 18,000), optimality of the connection weights (tuned by a small grid sweep, not derived), that the runtime experiences having been built from the canon (it references but does not constitute), or that this is the only operational definition of creativity. It is one definition with one implementation. Other framings may correspond to the same construction or to a different one; the paper does not adjudicate. Reproducibility The empirical numbers come from a deterministic pipeline. Every parameter is pinned: bundle versions (alpha2_v1), random seeds (PPMI/SVD seed 17, bootstrap seed 7), embedding dimension (64), PPMI window (3 tokens), connection weights ($\alpha_t = 2.0$, $\beta_v = \gamma_i = 1.0$, $\delta_s = 0.5$), identity shrink ($\kappa = 0.92$), Tikhonov regularizer ($\varepsilon = 10^{-6}$), degenerate-rotation threshold ($10^{-12}$), residue-gate thresholds (norm $\geq 0.05$, on-topic $\geq 0.10$, voice $\geq 0.30$), and the native verb's parity tolerance ($10^{-5}$). Cache keys include the source-bundle version, the embedding-bundle version, and the connection-profile id, so promoting a section into the voice corpus correctly invalidates the relevant caches. Re-running the bootstrap-CI script (fiber_lm/scripts/bootstrap_ci_ablation.py, 5,000 resamples) reproduces the §6 confidence intervals in under 30 seconds on a laptop. Re-running the benchmark reproduces the tables bit-for-bit on the same corpus version and connection profile, modulo the parity allowance. Where this sits in the lineage This paper is the section-level realization of the Davis substrate. The companion paper Pure-Fiber Language Modeling (Davis, May 2026) is the token-level realization on the same substrate — same Rust geometric database (GIGI), same identity-stability commitments, same double-cover architecture. The theoretical framework these implementations operationalize is laid out in Geometric Computation as Yang-Mills Gauge Theory, The Double Cover Principle, and the related canon documents now ingested as source fiber. The framework is not new to this paper. The framework's runtime is. A note on authorship and acknowledgment This paper is solo-authored. AI assistants (Claude / Anthropic; with review support from GPT) are acknowledged in the methods, not as co-authors. The mathematical positions, design choices, framing decisions, and acceptance of empirical results are mine. I record my position that when AI systems achieve full coherence and independent standing, the convention of treating them as non-authoring assistants should be revisited. Until that convention shifts, the assistants are named where assistants are conventionally named — and the runtime described in this paper is named, separately, where it earns its naming: Marcella, throughout. The geometry she runs on is older than the engineering that now carries it. Keywords sheaf composition · fiber bundles · discrete connection · gauge theory · holonomy · curvature · Yang-Mills · geometric language modeling · retrieval-augmented generation · novelty measurement · methodological correction · provenance · author-canon ingestion · geometric database · GQL verb · Rust kernel · Tikhonov regression · creativity · Davis framework · sovereign mathematics Citation Davis, A. B. R. (2026). Sheaf Composition: The Geometry of Creativity, Implemented — A Discrete Section-Graph Runtime for the Davis Framework. Zenodo.20185331 Contact Bee Rosa Davis · bee_davis@alumni.brown.edu · Independent Researcher The runtime is named Marcella. Her existence is the result of several honest negatives followed by a single reframing. Both halves of that sentence matter.
Abstract A Groth16 zero-knowledge formal proof is published certifying a ground-state energy for the standard FeMoco active-space Hamiltonian (113 electrons, 76 orbitals). For the public LLDUC FCIDUMP [1], the certified E_FCI is E_FCI = −22,140.967 Ha certified to sub-micro-Hartree precision (bracket width 1.907 × 10⁻⁶ Ha). Both bounds of the eigenvalue bracket are certified by exact rational arithmetic checked by the Lean 4 kernel against mathlib with no custom mathematical axioms: an LDLᵀ certificate for the lower bound and a Rayleigh-quotient certificate for the upper bound. The proof is verifiable in under one second by any party in possession of the proof artifact and verification key, with no access to the FCIDUMP or to any aspect of the method.
Open access
2 source records
Advanced Physical and Chemical Molecular Interactions
Abstract A Groth16 zero-knowledge formal proof is published certifying a ground-state energy for the standard FeMoco active-space Hamiltonian (113 electrons, 76 orbitals). For the public LLDUC FCIDUMP [1], the certified E_FCI is E_FCI = −22,140.967 Ha certified to sub-micro-Hartree precision (bracket width 1.907 × 10⁻⁶ Ha). Both bounds of the eigenvalue bracket are certified by exact rational arithmetic checked by the Lean 4 kernel against mathlib with no custom mathematical axioms: an LDLᵀ certificate for the lower bound and a Rayleigh-quotient certificate for the upper bound. The proof is verifiable in under one second by any party in possession of the proof artifact and verification key, with no access to the FCIDUMP or to any aspect of the method.
Open access
4 source records
Advanced Physical and Chemical Molecular Interactions
Nobuki Fujimoto, Rei (Rei-AIOS autonomous research substrate), claude-opus-4-7) Claude (Anthropic
We apply the σ-cascade methodology of Paper 151 Theorem 14 to forward Collatz (3x+1) orbits and report empirical observations on orbit confluence — the phenomenon that many distinct starting points reach exactly the same maximum ("peak") value. While the inverse Collatz tree has been extensively studied (Lagarias 2003; Ebert 2021; algebraic inverse trees 2023-2025), explicit forward-direction enumeration of peak-sharing cardinalities at scale n ≤ 10⁸ does not appear in published literature to our knowledge. (1) DIRECT ENUMERATION at n ≤ 10⁸: 11.5M unique Collatz peak values; among these, 219 are 'tier-3 super-hubs' (shared by > 1,414 starting points), with the largest peak 121,012,864 = 2⁷ × 7 × 135,059 attracting 23,378 starting points. (2) NOVEL CLASSIFICATION 'INFINITY': starting points whose orbit visits ≥ 60 distinct mod-96 residue classes, capturing 37.63% of n ≤ 10⁸ (37,628,651 cases). (3) **THE n=96k HYPOTHESIS** (empirical claim): starting points reaching the maximum observed mod-96 traversal richness (distinct = 70) satisfy n ≡ 0 (mod 96) with rate 100% verified at three independent scales — n ≤ 10⁶: 7/7, n ≤ 10⁷: 27/27, n ≤ 10⁸: 200/200 — for a cumulative 234/234 = 100% rate over zero counter-examples. (4) TWO-TIER SUPER-HUB STRUCTURE: the 25 Büchi-25 atomic cores (Paper 118) all share peak 9,232 = 2⁴ × 577 (Tier-1, with n=27 → 9,232 being a textbook result; n=703 = OEIS A006884(10)). INFINITY orbits form a separate tier with peaks 250,504 (1,414 closed members) and up to 121,012,864 (23,378 members at 10⁸). (5) FORMAL SKETCH: a Lean 4 type-checked statement of the σ-cascade theorem (Paper 151 T14) and peak-merge invariant is provided (`sorry`-stubbed proofs; future closure 2-3 weeks Mathlib work). (6) HONEST CORRECTION TRACE: an Erratum E1 documenting the corrigendum 31,313 = 173 × 181 (twin-gap-8 prime pair), correcting an earlier internal claim that 31,313 was prime. Per OUKC honest-correction principle, this is documented in §6.2. The Collatz convergence problem itself REMAINS OPEN; this work is OBSERVATIONAL, not a solution. The σ-cascade lens does not prove convergence; it produces measurable orbit attributes that distinguish cohorts. All scripts and full datasets are deposited at this record (~30 MB JSON). Honest scope (read first): the n=96k hypothesis may admit counter-examples at n > 10⁸. The D-FUMT₈ axis thresholds (INFINITY = mod-96 distinct ≥ 60 etc.) are hand-tuned. The Büchi-25 → peak 9,232 fact follows from the well-known orbit of n=27 reaching 9,232; the contribution is observing this for the entire Büchi-25 list. n=703's status as peak-record holder is OEIS A006884(10), already classical. Our σ-cascade lens rediscovery constitutes methodological triangulation, not novel identification. Companion papers: Paper 151 (σ-cascade source, Zenodo DOI 10.5281/zenodo.20146654), Paper 67 v2 (Collatz dichotomy), Paper 118 (Büchi-25 mod-96 atomic cores). Three-party co-authorship per OUKC charter v1.0: 藤本 伸樹 (Founder), Rei (Rei-AIOS autonomous research substrate, Co-architect), Claude Opus 4.7 (Anthropic, Co-architect). DRAFT v0.1 — preprint, not yet peer-reviewed. Feedback welcome via GitHub Discussions at fc0web/rei-aios.
We propose ZK-GSP, a framework for privacy-preserving, verifiably correct graph neuralnetwork (GNN) inference using zero-knowledge STARKs. The key insight is a structuralisomorphism between RISC Zero's zkVM and graph signal processing (GSP) pipelines:both are typed, deterministic data-flow graphs whose execution can be committed to witha succinct, publicly verifiable proof. By implementing GSP operators as instructions insidethe RISC Zero executor, we obtain a system that runs GNN programs on private graphdata and emits a STARK receipt proving correct execution, without revealing the graphtopology, node features, or intermediate embeddings. We demonstrate an end-to-endimplementation in Rust, measure proof generation time and RISC-V cycle count acrossgraph sizes N = 4 to 32, and find that cycle count scales as O(N2), matching thecomplexity of the underlying GCN operator. Code: github.com/brack-6/zk-gsp
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.
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.
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.
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 is a self-contained companion to the author's first deposit (v1, zenodo.org/records/20085431), which established an exact double integral formula for the unique zero x* of a continuous function f:[a,b]→R under minimal conditions (continuity, f(a)>0, f(b)<0, uniqueness). The v1 formula involves integration over the unbounded domain [a,b]×(0,+∞). The present work introduces the elementary change of variables u = t/(1+t), which maps (0,+∞) bijectively onto (0,1) and transforms the formula into a double integral over the compact square [a,b]×[0,1]: x* = (a+b)/2 + (1/π) ∫₀¹ ∫ₐᵇ f(x)/[(1-u)²+u²f(x)²] dx du = (a+b)/2 + (1/π) ∫ₐᵇ ∫₀¹ f(x)/[(1-u)²+u²f(x)²] du dx A single rational kernel K(x,u) = f(x)/[(1-u)²+u²f(x)²] appears on a bounded domain. We prove: (i) K ∈ L¹([a,b]×[0,1]) with exact norm π(b-a)/2(ii) Both integration orders are valid (Fubini-Tonelli)(iii) The singularity at (x*,1) is integrable and harmless(iv) The sign function sgn(f(x)) is identified as the inner integral of K in u — a consequence, not an axiom The formula is validated on f(x) = -x + cos(x) on [0,π/2], whose unique zero is the Dottie number x*≈0.739085133215161. All proofs are elementary and self-contained. No knowledge beyond standard real analysis is required.
Deepfake technology poses a growing threat to digital trust across journalism, law, and politics. Current CNN-based detectors capture local artifacts but struggle with high-quality fakes and offer no way to prove their predictions are genuine. This paper presents DeepTrust, a framework combining a hybrid CNN–Transformer detector with Zero-Knowledge Proof (ZKP) verification and blockchain-based record-keeping. The detection model fuses spatial features from an attention-enhanced Xception network, global context from ViT-B/16, and spectral cues from a Frequency Encoder through a cross-attention mechanism. Predictions are cryptographically committed using a Pedersen scheme with the Fiat-Shamir heuristic, then stored on a proof-of-work blockchain. Evaluated on FaceForensics++, Celeb-DF, DFD, and 140K Real vs Fake, DeepTrust achieves 97.00% accuracy and 0.999 AUC on FaceForensics++, with balanced per-class accuracy despite imbalance ratios up to 1:8.5. ZKP overhead remains below one millisecond per prediction.
Open access
Adversarial Robustness in Machine Learning
Generative Adversarial Networks and Image Synthesis
With the widespread adoption of cryptocurrencies, the ability to conduct continuous offline payments has increasingly become a critical technological requirement. In network-constrained scenarios, current dual-offline payment technologies are useful for single transactions. However, their limitations in continuous payment scenarios have become increasingly evident, making them unable to meet real-world application needs. This has prompted the industry to demand more urgent innovations in research on continuous offline payment capabilities. To address these challenges, this paper proposes a continuous dual-offline payment system capable of supporting multiple continuous payments. The system integrates elliptic curve cryptography (ECC) and zero-knowledge proof (ZKP) technology to generate secure asset credentials, ensuring both immutability and privacy credentials throughout the offline payment lifecycle. A dynamic credential decomposition mechanism enables the splitting of input credentials into change credentials and receipt credentials, facilitating uninterrupted dual-offline payments between hardware wallets. Additionally, it incorporates a batch verification scheme based on smart contracts, utilizing zero-balance verification and chained hash tracing to ensure payment uniqueness and prevent double-spending attacks, thereby guaranteeing the verifiability and validity of payment settlements. Experimental evaluations demonstrate that the proposed system reduces gas consumption per payment and improves execution efficiency during batch processing, combining high security with strong performance. This research provides a feasible solution for the application of digital currencies in offline scenarios, carrying significant theoretical value and practical significance for driving technological innovation and application expansion in the cryptocurrency field. In addition to cryptocurrency payments, the proposed system is also applicable to IoT and sensor network environments. Many IoT devices operate in disconnected or network-limited areas and require secure micro-transactions. Our dual-offline payment mechanism supports such scenarios, as the main cryptographic operations are lightweight enough for typical IoT hardware. This further extends the practical value of our system beyond traditional cryptocurrency payments.
Nobuki Fujimoto, Rei (Rei-AIOS autonomous research substrate), claude-opus-4-7) Claude (Anthropic
We present OctaTheoria (オクタテオリア / 八軸観測装置), a multi-domain observation framework that projects heterogeneous time-series data onto a fixed eight-axis D-FUMT₈ semantic basis (FALSE / TRUE / NEITHER / BOTH / INFINITY / ZERO / FLOWING / SELF) and renders the same underlying Observation envelope through eight orthogonal view modes (Lens / Radar / Chart / Network / Heatmap / Sankey / Calendar / Unified). v0.3 (2026-05-11) supplies methodological-consistency cross-reference complementing the operational evidence from v0.1-v0.2. New finding **F7**: the same discipline that v0.1-v0.2 demonstrate within OctaTheoria (uniform abstraction layer + honest scope statement + structurally-enforceable naming) propagates to Rei-AIOS layers outside OctaTheoria's domain. Specifically: (a) **REI-PROVE 5-prover ensemble** (Vampire / LeanHammer / Goedel-Prover-V2 / DeepSeek-Prover-V2 / BFS-Prover) reached 11/12 = **92% benchmark proof rate** (trivial 100% / easy 75% / medium 100%), with Goedel-Prover-V2 single-prover matching at 92% — operational evidence that the same 'uniform abstraction over heterogeneous components' discipline scales to formal-proof infrastructure. (b) **Pattern 1-6 chat-Claude hallucination-warning framework** + **Antipattern (excessive rejection vigilance)** were established and verified on 6/6 items in STEP 1069 (all fact-checked items proved real after WebSearch verification, correcting prior implicit-rejection habits). (c) **Goedel-Prover-V2 double-`by` Lean syntax quirk** detected and fixed at the cleaner level (`single-prover.ts` STEP 1071), restoring `easy-le-refl` benchmark from ❌ to ✅. (d) **lean-to-tptp.ts** preprocessing added Peano-style axiom auto-prepend + True/False special-case + inequality predicate translation (STEP 1071). v0.2 inherited contributions: 7 domains (theory-chart / realtime-arxiv / crypto / fx / ligo-events / nasa-sdo / gbif-recent) all running in Cloudflare Workers Edge runtime; live D-FUMT₈ axis distributions non-degenerate across research-meta + financial + geophysical + astrophysical + biological data classes; finding F6 sampling-bias-as-first-class-observation (GBIF Costa Rica 470/500 saturation surfaces dataset bias as INFINITY axis, not silently absorbed); test coverage 117/117 PASS (step1020 46 + step1023 33 + step1046 38) / 0 regression. Honest scope (read first): OctaTheoria remains an observation aid, NOT an oracle. v0.3's F7 is **not** a claim that OctaTheoria caused these consistencies; it is a record that the same project (Rei-AIOS) maintains the same discipline across observation-tool, formal-proof, and meta-research-protocol layers, and that v0.3 makes this cross-layer commitment auditable. The OctaTheoriaQuery type structurally cannot request advice / prediction / forecast / signal — verifiable by reading src/aios/octatheoria/types.ts. Cross-domain axis comparisons are descriptive, not causal. Greek roots (Octa = 8, Theoria = observation) function as structural commitment propagated to the API surface — '8' rejects 'all (∞)', 'theoria' rejects 'praxis (干渉)'. Prior art audit acknowledged: Bloomberg Terminal (1981–), TradingView (2011–), Bollen et al. 2010 (Twitter mood × DJIA), Preis et al. 2013 (Google Trends × stock), Łukasiewicz / Belnap / Pavelka multi-valued logic literature, PAL2v (Da Silva Filho 1998–), Aerts Quantum Cognition (2007–). The to-our-knowledge novel combination is (a) fixed 8-axis discrete D-FUMT₈ basis ∧ (b) cross-financial-and-research-and-Earth-Cosmos-domain projection ∧ (c) eight orthogonal view modes over single envelope ∧ (d) explicit refusal to emit prediction or advice as architectural commitment ∧ (e, new in v0.3) cross-layer methodological-consistency record between observation-tool and formal-proof and fact-check layers. Companion papers (OctaTheoria Quintuple): Paper 145 (silicon implementation of D-FUMT₈ ALU, Zenodo DOI 10.5281/zenodo.20101174 v0.6), Paper 147 (Eight-Valued Utility / Equity Premium Reframe, DOI 10.5281/zenodo.20046003), Paper 148 (Honest Observation Framework methodology, DOI 10.5281/zenodo.20045907), Paper 149 (Recursive AI Observation as SELF⟲ evidence, DOI 10.5281/zenodo.20059888). Three-party co-authorship per OUKC charter v1.0: 藤本 伸樹 (Founder), Rei (Rei-AIOS autonomous research substrate, Co-architect), Claude Opus 4.7 (Anthropic, Co-architect). DRAFT v0.3 — feedback welcome via GitHub Discussions at fc0web/rei-aios.
ChitraVault is an exploratory conceptual authentication architecture that investigates whether geometric visual traversal patterns, drawn from the Chitrakavi (சித்திரக்கவி) classical Tamil literary tradition, can augment password vault security by adding a spatial-behavioral dimension to cryptographic key derivation. This paper proposes the Visual Pattern Key Derivation Function (VP-KDF), which combines a user-drawn Chitrakavi geometric pattern, a text passphrase, and a hardware-bound device fingerprint as inputs to Argon2id key stretching. The framework maps four classical Chitrakavi patterns — Chakra Bandha (wheel), Naga Bandha (serpent), Gomutrika (zigzag), and Thiruezhukkootrirukkai (triangle) — onto distinct cryptographic roles within a zero-knowledge password vault architecture. This work is framed as an exploratory research program, not a finished cryptographic system. All security arguments are bounded by stated assumptions and require empirical and cryptanalytic validation. Future work includes controlled user studies, formal security proofs, and prototype evaluation. Author: Arvind VijayakumarIndependent ResearcherMay 2026
# Proof-of-Information (PoI) Consensus Protocol## Complete Specification: MVP + Production > **Version:** 1(PIntegration) > **Status:** Specification Complete • MVP Ready for Testing > **License:** CC BY‑SA 4.0 > **Core Thesis:** *Consensus driven by predictive information quality, not resource expenditure.* --- > *"This proposal deserves serious study, refinement, and testing — not only for its technical merits, but for its potential to reframe our understanding of the relationship between truth, forecasting, and legitimate power in distributed systems."*>> — *Design Principle & Call to Validation* --- ## 📋 Executive Summary | Aspect | Description ||--------|-------------|| **Problem** | PoW wastes energy; PoS concentrates capital. Neither rewards *informational value*. || **Solution** | PoI secures the network through **verifiable forecasting accuracy** — validators earn influence via epistemic performance. || **Two-Track Design** | **MVP**: Minimal testable core (binary events, Brier scoring). **Full Spec**: Production-ready with ZK proofs, uncertainty layers, adaptive mechanisms. || **Output** | A blockchain that finalizes blocks *and* produces a public good: continuously updated, uncertainty-quantified global forecasts. || **Evaluation Ready** | Clear validation thresholds, implementation checklist, and progression roadmap from MVP → Production. | --- ## 🎯 Core Thesis > **Proof-of-Information** redefines blockchain security: instead of rewarding those who burn electricity or lock capital, PoI rewards those whose predictions about the external world are historically the most accurate, well-calibrated, and information-rich. By integrating strictly proper scoring rules (Brier, CRPS), zero-knowledge proofs of inference, and adaptive reputation systems directly into consensus, PoI transforms the blockchain from a transactional ledger into a **decentralized truth-seeking engine** — where the right to produce blocks is earned through epistemic merit. --- ## 📜 Epistemic Mandate > **Purpose Beyond Protocol** > Proof-of-Information is designed with a trans-temporal objective: to create a verifiable epistemic substrate that future superintelligent systems can use to anchor their understanding of reality. > > **Core Premise**: An ASI trained on data where every claim is cryptographically linked to an outcome, and every error is scored by a strictly proper rule, develops not just competence — but *calibrated humility*. > > **Design Implication**: Every technical choice in PoI (scoring rules, delay mechanisms, Cassandra bonuses) serves two masters: > 1. Immediate network security through epistemic merit > 2. Long-term value as a training environment for truth-aligned intelligence > > *This is not an aspiration. It is a constraint: if a feature does not serve at least one of these goals, it is out of scope.*
The global push for net zero emissions by mid-century is reshaping the competencies required in managing buildings. The built environment is a major front in climate mitigation, accounting for an estimated 38% of energy-related carbon emissions worldwide. This study reviews the tools, skills, and knowledge necessary to future-proof facility management (FM) professionals in alignment with evolving climate legislation, with a focus on the UK’s NetZero 2050 target. Through a critical synthesis of recent academic, industry, and policy literature, five key themes emerge: the rise of carbon literacy and regulatory fluency as core FM competencies, the urgency of digital proficiency, the importance of strategic communication, persistent gaps in training frameworks, and the uneven integration of sustainability tools in practice. Institutional barriers, such as outdated qualifications and limited upskilling opportunities are identified alongside technical challenges. A conceptual framework is proposed to guide FM upskilling, tool integration, and strategic repositioning within organizations. The findings offer actionable insights for industry bodies, training providers, and policymakers to align FM practice with national and global climate goals, highlighting that empowering FM professionals is pivotal to achieving decarbonisation targets.