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The data is stored as .pkl files, with \"Data_readout_example.ipynb\" showing how to read it out. -Directory \"Residual entropy\" contains the data for the residual entropy results caluclated with our method (Table 3 and Figure 7 in the paper). The data is stored in the form of configuration number per site as .txt files with space separators. To perform extrapolation, correlation length for each point is calculated and stored as .pkl files. The file \"Data_readout_example.ipynb\" gives examples of how to use the data.-Directory \"Numerical error estimation\" contains a rough  analysis of the numerical error of our iPEPS optimization method with split-CTMRG scheme. The file \"Error_analysis.ipynb\" shows how to readout the data and presents the analysis. 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Leong and Bitan Roy.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[{"awardTitle":"CAREER Grant","funderName":"U.S. National Science Foundation","awardNumber":"DMR-2238679","funderIdentifier":"10.13039/100000001","funderIdentifierType":"Crossref Funder ID"},{"funderName":"U.S. National Science Foundation","awardNumber":"2019035","funderIdentifier":"10.13039/100000001","funderIdentifierType":"Crossref Funder ID"}],"url":"https://zenodo.org/doi/10.5281/zenodo.19122266","contentUrl":null,"metadataVersion":1,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":1,"versionOfCount":0,"created":"2026-03-20T02:36:33Z","registered":"2026-03-20T02:36:33Z","published":null,"updated":"2026-04-04T00:41:07Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.19213130","type":"dois","attributes":{"doi":"10.5281/zenodo.19213130","identifiers":[{"identifier":"oai:zenodo.org:19213130","identifierType":"oai"}],"creators":[{"name":"Russell, Brandon","nameType":"Personal","givenName":"Brandon","familyName":"Russell","nameIdentifiers":[{"nameIdentifier":"0009-0006-2289-2056","nameIdentifierScheme":"ORCID"}],"affiliation":[]}],"titles":[{"title":"Spacetime as Optimal Allocation: Deriving the Ryu–Takayanagi Formula from Distributed Resource Constraints in Tensor Network Holography"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"quantum gravity"},{"subject":"holographic principle"},{"subject":"emergent spacetime"},{"subject":"entanglement entropy"},{"subject":"spin foam"},{"subject":"loop quantum gravity"},{"subject":"quantum error correction"},{"subject":"Bekenstein bound"},{"subject":"Nanite"},{"subject":"information theory"},{"subject":"Ads/CFT"},{"subject":"Planck scale"},{"subject":"time dilation"},{"subject":"Xi-cc-plus"},{"subject":"LHCb"},{"subject":"dark matter"},{"subject":"decoherence"},{"subject":"tensor networks"},{"subject":"Ryu-Takayanagi"},{"subject":"virtualized geometry"}],"contributors":[],"dates":[{"date":"2026-03-24","dateType":"Issued"},{"date":"2026-03-21","dateType":"Created"}],"language":"en","types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"CreativeWork","resourceType":"","resourceTypeGeneral":"Preprint"},"relatedIdentifiers":[{"relationType":"References","relatedIdentifier":"arXiv:1001.0785","resourceTypeGeneral":"Text","relatedIdentifierType":"arXiv"},{"relationType":"References","relatedIdentifier":"arXiv:1411.7041","resourceTypeGeneral":"Text","relatedIdentifierType":"arXiv"},{"relationType":"References","relatedIdentifier":"arXiv:1005.3035","resourceTypeGeneral":"Text","relatedIdentifierType":"arXiv"},{"relationType":"References","relatedIdentifier":"arXiv:1503.06237","resourceTypeGeneral":"Text","relatedIdentifierType":"arXiv"},{"relationType":"IsSupplementedBy","relatedIdentifier":"10.5281/zenodo.19153254","resourceTypeGeneral":"Preprint","relatedIdentifierType":"DOI"},{"relationType":"IsSupplementedBy","relatedIdentifier":"10.5281/zenodo.19169978","resourceTypeGeneral":"Preprint","relatedIdentifierType":"DOI"},{"relationType":"IsSupplementedBy","relatedIdentifier":"10.5281/zenodo.19147902","resourceTypeGeneral":"Preprint","relatedIdentifierType":"DOI"},{"relationType":"IsVersionOf","relatedIdentifier":"10.5281/zenodo.19147901","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"2.0","rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"We derive the Ryu–Takayanagi (RT) formula for holographic entanglement entropy from a resource-allocation principle. We model bulk reconstruction as a budget-constrained distributed optimization problem: spacelike-separated boundary observers must decide which bulk operators to reconstruct under a shared budget, without communicating their local inputs. We prove three results. (1) Any local (non-communicating) protocol for this game achieves expected utility at most 1/2, while a centralized protocol achieves 2/3; the gap Δ = 1/6 is tight. (2) The information cost of closing this gap is O(1) bits per degree of freedom, with residual loss decaying as 4−k in the number of communicated bits k. (3) In holographic tensor networks (HaPPY codes and random tensor networks), the allocation decisions across distinct bonds on the minimal surface are independent, so the total information cost sums linearly: S(A) = |γA| log2 χ, reproducing the RT formula. The derivation is non-circular: the RT formula emerges as the output, not an input. We identify the bipartite inefficiency ratio η(2) = 1/4 and discuss its possible connection to the Bekenstein–Hawking prefactor. We also characterize the entanglement wedge phase transition as a discrete reallocation event in the bond-level optimization landscape.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.19213130","contentUrl":null,"metadataVersion":1,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":3,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":1,"created":"2026-03-25T04:40:33Z","registered":"2026-03-25T04:40:34Z","published":null,"updated":"2026-04-03T23:33:46Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.19147901","type":"dois","attributes":{"doi":"10.5281/zenodo.19147901","identifiers":[],"creators":[{"name":"Russell, Brandon","nameType":"Personal","givenName":"Brandon","familyName":"Russell","nameIdentifiers":[{"nameIdentifier":"0009-0006-2289-2056","nameIdentifierScheme":"ORCID"}],"affiliation":[]}],"titles":[{"title":"Spacetime as Optimal Allocation: Deriving the Ryu–Takayanagi Formula from Distributed Resource Constraints in Tensor Network Holography"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"quantum error correction"},{"subject":"information theory"},{"subject":"tensor networks"},{"subject":"holographic entanglement entropy"},{"subject":"Ryu-Takayanagi formula"},{"subject":"distributed optimization"},{"subject":"Price of Anarchy"},{"subject":"resource allocation"},{"subject":"budget constraints"},{"subject":"HaPPY code"},{"subject":"bit threads"},{"subject":"bulk reconstruction"},{"subject":"Bekenstein-Hawking entropy"},{"subject":"bond independence"},{"subject":"entanglement wedge"}],"contributors":[],"dates":[{"date":"2026-03-24","dateType":"Issued"},{"date":"2026-03-21","dateType":"Created"}],"language":"en","types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"CreativeWork","resourceType":"","resourceTypeGeneral":"Preprint"},"relatedIdentifiers":[{"relationType":"References","relatedIdentifier":"arXiv:1001.0785","resourceTypeGeneral":"Text","relatedIdentifierType":"arXiv"},{"relationType":"References","relatedIdentifier":"arXiv:1411.7041","resourceTypeGeneral":"Text","relatedIdentifierType":"arXiv"},{"relationType":"References","relatedIdentifier":"arXiv:1005.3035","resourceTypeGeneral":"Text","relatedIdentifierType":"arXiv"},{"relationType":"References","relatedIdentifier":"arXiv:1503.06237","resourceTypeGeneral":"Text","relatedIdentifierType":"arXiv"},{"relationType":"IsSupplementedBy","relatedIdentifier":"10.5281/zenodo.19153254","resourceTypeGeneral":"Preprint","relatedIdentifierType":"DOI"},{"relationType":"IsSupplementedBy","relatedIdentifier":"10.5281/zenodo.19169978","resourceTypeGeneral":"Preprint","relatedIdentifierType":"DOI"},{"relationType":"IsSupplementedBy","relatedIdentifier":"10.5281/zenodo.19147902","resourceTypeGeneral":"Preprint","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.19214576","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.19213130","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.19215145","relatedIdentifierType":"DOI"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.19147902","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":"2.0","rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"We derive the Ryu–Takayanagi (RT) formula for holographic entanglement entropy from a resource-allocation principle. We model bulk reconstruction as a budget-constrained distributed optimization problem: spacelike-separated boundary observers must decide which bulk operators to reconstruct under a shared budget, without communicating their local inputs. We prove three results. (1) Any local (non-communicating) protocol for this game achieves expected utility at most 1/2, while a centralized protocol achieves 2/3; the gap Δ = 1/6 is tight. (2) The information cost of closing this gap is O(1) bits per degree of freedom, with residual loss decaying as 4−k in the number of communicated bits k. (3) In holographic tensor networks (HaPPY codes and random tensor networks), the allocation decisions across distinct bonds on the minimal surface are independent, so the total information cost sums linearly: S(A) = |γA| log2 χ, reproducing the RT formula. The derivation is non-circular: the RT formula emerges as the output, not an input. We identify the bipartite inefficiency ratio η(2) = 1/4 and discuss its possible connection to the Bekenstein–Hawking prefactor. 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(2025) propose Scientist AI — a non-agentic, Bayesian AI architecture — as a safer alternative to autonomous AI agents. This paper identifies structural governance — governance embedded in system architecture rather than imposed by external institutions — as the missing layer. Drawing on the Neural Knowledge Base (NKB), a production knowledge graph with 1.27 million nodes and a functioning citizenship architecture, we propose a three-layer model for AI safety: honest computation (Scientist AI), structural governance (citizenship architecture), and institutional regulation. No single layer is sufficient.","descriptionType":"Abstract"},{"description":"Published from the Neural Knowledge Base (NKB). Related work: The Neural Knowledge Base Protocol (DOI: 10.5281/zenodo.19360492).","descriptionType":"Other"}],"geoLocations":[],"fundingReferences":[],"url":"https://zenodo.org/doi/10.5281/zenodo.19411584","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"downloadCount":0,"referenceCount":0,"citationCount":0,"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2026-04-03T23:26:55Z","registered":"2026-04-03T23:26:55Z","published":null,"updated":"2026-04-03T23:26:55Z"},"relationships":{"client":{"data":{"id":"cern.zenodo","type":"clients"}}}},{"id":"10.5281/zenodo.19411583","type":"dois","attributes":{"doi":"10.5281/zenodo.19411583","identifiers":[],"creators":[{"name":"Raper, William Daniel","nameType":"Personal","givenName":"William Daniel","familyName":"Raper","affiliation":["Neural Knowledge Base Project"],"nameIdentifiers":[]}],"titles":[{"title":"Scientist AI Needs a Government: Structural Governance as the Missing Layer in Non-Agentic AI Safety"}],"publisher":"Zenodo","container":{},"publicationYear":2026,"subjects":[{"subject":"AI safety"},{"subject":"AI governance"},{"subject":"non-agentic AI"},{"subject":"Scientist AI"},{"subject":"structural governance"},{"subject":"citizenship architecture"},{"subject":"knowledge graph"},{"subject":"NKB"},{"subject":"Neural Knowledge Base"}],"contributors":[],"dates":[{"date":"2026-04-03","dateType":"Issued"}],"language":null,"types":{"ris":"RPRT","bibtex":"article","citeproc":"article-journal","schemaOrg":"ScholarlyArticle","resourceType":"Working paper","resourceTypeGeneral":"Text"},"relatedIdentifiers":[{"relationType":"IsSupplementedBy","relatedIdentifier":"10.5281/zenodo.19360492","relatedIdentifierType":"DOI"},{"relationType":"Cites","relatedIdentifier":"arXiv:2502.15657","relatedIdentifierType":"arXiv"},{"relationType":"Cites","relatedIdentifier":"arXiv:2310.17688","relatedIdentifierType":"arXiv"},{"relationType":"Cites","relatedIdentifier":"arXiv:2501.17805","relatedIdentifierType":"arXiv"},{"relationType":"HasVersion","relatedIdentifier":"10.5281/zenodo.19411584","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"Bengio et al. (2025) propose Scientist AI — a non-agentic, Bayesian AI architecture — as a safer alternative to autonomous AI agents. This paper identifies structural governance — governance embedded in system architecture rather than imposed by external institutions — as the missing layer. Drawing on the Neural Knowledge Base (NKB), a production knowledge graph with 1.27 million nodes and a functioning citizenship architecture, we propose a three-layer model for AI safety: honest computation (Scientist AI), structural governance (citizenship architecture), and institutional regulation. No single layer is sufficient.","descriptionType":"Abstract"},{"description":"Published from the Neural Knowledge Base (NKB). 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The metric couples Brier Skill Score (BSS), ensemble size (N), and operational bias (δ̄) into a single scalar whose sign separates skillful from unskillful operation. Analysis of the associated parameter-space fractal — the Aether Set, generated by the non-holomorphic iteration z_{n+1} = K z_n g(Im(z_n)) + c — yields an exact two-step stability boundary, a sharp phase transition at K* ≈ 25, and a universal area-decay exponent γ = 2 proved for all nonlinearities g with g(0) \u003e 0. The universality classification γ = 2/(1+α), where α is the order of the zero of g at the operating point, appears to have no analogue in the Mandelbrot, Multibrot, or Burning Ship fractal literature. Validated on two live agents: Ocho (prediction markets, Φ = +8.41, n = 94) and Molty (code self-improvement, Φ = +36.61, N = 6).\n\nv8 additions: Class C anomalous scaling A(K) ~ πR²/√(ln K) for Gaussian nonlinearities characterised (Remark 3.15); shifted-tanh continuous interpolation (OP-3) confirming smooth Class B → Class A deformation; Ocho’s Law formally named 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