{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:AIXTNJ526XSS25VGMFVJU723VY","short_pith_number":"pith:AIXTNJ52","canonical_record":{"source":{"id":"2501.17042","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-01-28T16:07:41Z","cross_cats_sorted":["cond-mat.dis-nn","cs.DM","cs.SI","math.CO"],"title_canon_sha256":"70698f635b6b1aea5a9eae5dc7cedb73114240c3224beaecbc7a1cb73b80c5e2","abstract_canon_sha256":"716e3de7a2bc55294aaecdcf03bf095519e2276f24cc4b88e74abe939d6ad7c4"},"schema_version":"1.0"},"canonical_sha256":"022f36a7baf5e52d76a6616a9a7f5bae3c35bde464bedc5e0b247e8d590a9ea3","source":{"kind":"arxiv","id":"2501.17042","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.17042","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"2501.17042v4","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.17042","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"AIXTNJ526XSS","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"pith_short_16","alias_value":"AIXTNJ526XSS25VG","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"pith_short_8","alias_value":"AIXTNJ52","created_at":"2026-07-05T11:29:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:AIXTNJ526XSS25VGMFVJU723VY","target":"record","payload":{"canonical_record":{"source":{"id":"2501.17042","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-01-28T16:07:41Z","cross_cats_sorted":["cond-mat.dis-nn","cs.DM","cs.SI","math.CO"],"title_canon_sha256":"70698f635b6b1aea5a9eae5dc7cedb73114240c3224beaecbc7a1cb73b80c5e2","abstract_canon_sha256":"716e3de7a2bc55294aaecdcf03bf095519e2276f24cc4b88e74abe939d6ad7c4"},"schema_version":"1.0"},"canonical_sha256":"022f36a7baf5e52d76a6616a9a7f5bae3c35bde464bedc5e0b247e8d590a9ea3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:06.103652Z","signature_b64":"rY/5qeFZMxC+GKfInoC8ZESvxvZSbx1P3mrUwtK+MNEyeAopV5/zl6stRzxY0Zjx7ad0SmNXhGvLBwHUV857Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"022f36a7baf5e52d76a6616a9a7f5bae3c35bde464bedc5e0b247e8d590a9ea3","last_reissued_at":"2026-07-05T11:29:06.103120Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:06.103120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.17042","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:29:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cre6JYj+cDQZ0OvXrg3DRgj2R00bqZV+NFnIc/2z5Gf0dOOVOi3XSbUXK/tSihh7oS57eu7okyPRD7Xn33bDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:05:25.733144Z"},"content_sha256":"bc24464096457d64e8d8c9da94e7aabef464defc87aece39671f58d56e6a83b0","schema_version":"1.0","event_id":"sha256:bc24464096457d64e8d8c9da94e7aabef464defc87aece39671f58d56e6a83b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:AIXTNJ526XSS25VGMFVJU723VY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Emergence of network communities driven by local rules","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.DM","cs.SI","math.CO"],"primary_cat":"physics.soc-ph","authors_text":"Alexei Vazquez","submitted_at":"2025-01-28T16:07:41Z","abstract_excerpt":"Natural systems are modeled by networks with nodes and links. Often the nodes are segregated into communities with different connectivity patterns. Node heterogeneity such as political affiliation in social networks or biological function in gene networks are highlighted as key factors driving the segregation of nodes into communities. Here, by means of numerical simulations, I show that node heterogeneity is not a necessary requirement. To this end I introduce the Ramsey community number, $r_ \\kappa$, the minimum graph size that warranties the emergence of network communities with almost cert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.17042","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.17042/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:29:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gQs5Kr4dVVVdNy83wxCbMrAIegpSImQwjy8WuPaADgYGLoPb1v9B2/r/W+v2XJ9/m+nttp8fxtelgkZi5OmoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:05:25.734245Z"},"content_sha256":"90387d2348e09ef84fda37fc1af720f4a1a9557cb6c8480de40228b6a406ad5c","schema_version":"1.0","event_id":"sha256:90387d2348e09ef84fda37fc1af720f4a1a9557cb6c8480de40228b6a406ad5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AIXTNJ526XSS25VGMFVJU723VY/bundle.json","state_url":"https://pith.science/pith/AIXTNJ526XSS25VGMFVJU723VY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AIXTNJ526XSS25VGMFVJU723VY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T09:05:25Z","links":{"resolver":"https://pith.science/pith/AIXTNJ526XSS25VGMFVJU723VY","bundle":"https://pith.science/pith/AIXTNJ526XSS25VGMFVJU723VY/bundle.json","state":"https://pith.science/pith/AIXTNJ526XSS25VGMFVJU723VY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AIXTNJ526XSS25VGMFVJU723VY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AIXTNJ526XSS25VGMFVJU723VY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"716e3de7a2bc55294aaecdcf03bf095519e2276f24cc4b88e74abe939d6ad7c4","cross_cats_sorted":["cond-mat.dis-nn","cs.DM","cs.SI","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-01-28T16:07:41Z","title_canon_sha256":"70698f635b6b1aea5a9eae5dc7cedb73114240c3224beaecbc7a1cb73b80c5e2"},"schema_version":"1.0","source":{"id":"2501.17042","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.17042","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"2501.17042v4","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.17042","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"AIXTNJ526XSS","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"pith_short_16","alias_value":"AIXTNJ526XSS25VG","created_at":"2026-07-05T11:29:06Z"},{"alias_kind":"pith_short_8","alias_value":"AIXTNJ52","created_at":"2026-07-05T11:29:06Z"}],"graph_snapshots":[{"event_id":"sha256:90387d2348e09ef84fda37fc1af720f4a1a9557cb6c8480de40228b6a406ad5c","target":"graph","created_at":"2026-07-05T11:29:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.17042/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Natural systems are modeled by networks with nodes and links. Often the nodes are segregated into communities with different connectivity patterns. Node heterogeneity such as political affiliation in social networks or biological function in gene networks are highlighted as key factors driving the segregation of nodes into communities. Here, by means of numerical simulations, I show that node heterogeneity is not a necessary requirement. To this end I introduce the Ramsey community number, $r_ \\kappa$, the minimum graph size that warranties the emergence of network communities with almost cert","authors_text":"Alexei Vazquez","cross_cats":["cond-mat.dis-nn","cs.DM","cs.SI","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-01-28T16:07:41Z","title":"Emergence of network communities driven by local rules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.17042","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bc24464096457d64e8d8c9da94e7aabef464defc87aece39671f58d56e6a83b0","target":"record","created_at":"2026-07-05T11:29:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"716e3de7a2bc55294aaecdcf03bf095519e2276f24cc4b88e74abe939d6ad7c4","cross_cats_sorted":["cond-mat.dis-nn","cs.DM","cs.SI","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2025-01-28T16:07:41Z","title_canon_sha256":"70698f635b6b1aea5a9eae5dc7cedb73114240c3224beaecbc7a1cb73b80c5e2"},"schema_version":"1.0","source":{"id":"2501.17042","kind":"arxiv","version":4}},"canonical_sha256":"022f36a7baf5e52d76a6616a9a7f5bae3c35bde464bedc5e0b247e8d590a9ea3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"022f36a7baf5e52d76a6616a9a7f5bae3c35bde464bedc5e0b247e8d590a9ea3","first_computed_at":"2026-07-05T11:29:06.103120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:29:06.103120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rY/5qeFZMxC+GKfInoC8ZESvxvZSbx1P3mrUwtK+MNEyeAopV5/zl6stRzxY0Zjx7ad0SmNXhGvLBwHUV857Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:29:06.103652Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.17042","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc24464096457d64e8d8c9da94e7aabef464defc87aece39671f58d56e6a83b0","sha256:90387d2348e09ef84fda37fc1af720f4a1a9557cb6c8480de40228b6a406ad5c"],"state_sha256":"a16569a4b277673c9c243d7ddad96075c8f25c2239439b2b4227a5156bebb847"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0hhtB0zAqrk07YQ0y/IlWKk1DtQMA8jLNH5MIno6IP6ET0x8LImGjLwFePxJtdqEnEkkSGmHKuy2AFEozmCcBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:05:25.758071Z","bundle_sha256":"15342321eeea1d161d10225fe7fe05663ee2776bad7fa4446958acaecaff8acf"}}