{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:77GMBABMMTWOHATVCVIWJL3HNF","short_pith_number":"pith:77GMBABM","canonical_record":{"source":{"id":"1501.06835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-01-27T17:34:57Z","cross_cats_sorted":["cs.SI","physics.data-an","stat.AP"],"title_canon_sha256":"b789838804b38d04c845487fc7db81d344a88fa74b51b85a01ef476cd7c9d44a","abstract_canon_sha256":"c2ad3111ae9501dbdf4ebcda6f81f38703da18dcddbbd13449a6443ef068520d"},"schema_version":"1.0"},"canonical_sha256":"ffccc0802c64ece38275155164af67697d7bdc21e981268d8c1abdfab2abaf78","source":{"kind":"arxiv","id":"1501.06835","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06835","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06835v1","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06835","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"77GMBABMMTWO","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"77GMBABMMTWOHATV","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"77GMBABM","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:77GMBABMMTWOHATVCVIWJL3HNF","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-01-27T17:34:57Z","cross_cats_sorted":["cs.SI","physics.data-an","stat.AP"],"title_canon_sha256":"b789838804b38d04c845487fc7db81d344a88fa74b51b85a01ef476cd7c9d44a","abstract_canon_sha256":"c2ad3111ae9501dbdf4ebcda6f81f38703da18dcddbbd13449a6443ef068520d"},"schema_version":"1.0"},"canonical_sha256":"ffccc0802c64ece38275155164af67697d7bdc21e981268d8c1abdfab2abaf78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:24.100005Z","signature_b64":"xxFFSaIsA4X+RUnni4MdHt2KY5uyLtdYqXndelG7PDPFxe945LIb8SuAr9scEArOwj3gaWMbbiHTiT0XLGvQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffccc0802c64ece38275155164af67697d7bdc21e981268d8c1abdfab2abaf78","last_reissued_at":"2026-05-18T02:17:24.099201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:24.099201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06835","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zuhJYJp39d/rvgED9PffJ8grTqrANiNMzDuQyQ/+VacUnJTFkaS+V/ZjyvVi4ozgjvDGBtKdAIDkFY1Ki/0QDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:17:19.841555Z"},"content_sha256":"dd65aef7bc59f64b0449ef5d6b151ff7b9aecc28f64d61c4ad86e0ef20af5ac9","schema_version":"1.0","event_id":"sha256:dd65aef7bc59f64b0449ef5d6b151ff7b9aecc28f64d61c4ad86e0ef20af5ac9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:77GMBABMMTWOHATVCVIWJL3HNF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Emergence of Soft Communities from Geometric Preferential Attachment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.data-an","stat.AP"],"primary_cat":"physics.soc-ph","authors_text":"Dmitri Krioukov, Ginestra Bianconi, Konstantin Zuev, Marian Boguna","submitted_at":"2015-01-27T17:34:57Z","abstract_excerpt":"All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06835","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:17:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5KIAiyAwnl9TyyQz1lDb12dLvk+XYLzTZOSVogDPNfxSY5oeJNFdZ4hj6tPcp95WOY6ku1m5Y/ppsNS0NnW8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:17:19.841901Z"},"content_sha256":"38c3b5775232510efa032be875737f4036fcdd548fa3350d390222ead5f2b68e","schema_version":"1.0","event_id":"sha256:38c3b5775232510efa032be875737f4036fcdd548fa3350d390222ead5f2b68e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/77GMBABMMTWOHATVCVIWJL3HNF/bundle.json","state_url":"https://pith.science/pith/77GMBABMMTWOHATVCVIWJL3HNF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/77GMBABMMTWOHATVCVIWJL3HNF/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":"2026-06-03T21:17:19Z","links":{"resolver":"https://pith.science/pith/77GMBABMMTWOHATVCVIWJL3HNF","bundle":"https://pith.science/pith/77GMBABMMTWOHATVCVIWJL3HNF/bundle.json","state":"https://pith.science/pith/77GMBABMMTWOHATVCVIWJL3HNF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/77GMBABMMTWOHATVCVIWJL3HNF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:77GMBABMMTWOHATVCVIWJL3HNF","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":"c2ad3111ae9501dbdf4ebcda6f81f38703da18dcddbbd13449a6443ef068520d","cross_cats_sorted":["cs.SI","physics.data-an","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-01-27T17:34:57Z","title_canon_sha256":"b789838804b38d04c845487fc7db81d344a88fa74b51b85a01ef476cd7c9d44a"},"schema_version":"1.0","source":{"id":"1501.06835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06835","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06835v1","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06835","created_at":"2026-05-18T02:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"77GMBABMMTWO","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"77GMBABMMTWOHATV","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"77GMBABM","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:38c3b5775232510efa032be875737f4036fcdd548fa3350d390222ead5f2b68e","target":"graph","created_at":"2026-05-18T02:17:24Z","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"},"paper":{"abstract_excerpt":"All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate i","authors_text":"Dmitri Krioukov, Ginestra Bianconi, Konstantin Zuev, Marian Boguna","cross_cats":["cs.SI","physics.data-an","stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-01-27T17:34:57Z","title":"Emergence of Soft Communities from Geometric Preferential Attachment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06835","kind":"arxiv","version":1},"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:dd65aef7bc59f64b0449ef5d6b151ff7b9aecc28f64d61c4ad86e0ef20af5ac9","target":"record","created_at":"2026-05-18T02:17:24Z","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":"c2ad3111ae9501dbdf4ebcda6f81f38703da18dcddbbd13449a6443ef068520d","cross_cats_sorted":["cs.SI","physics.data-an","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-01-27T17:34:57Z","title_canon_sha256":"b789838804b38d04c845487fc7db81d344a88fa74b51b85a01ef476cd7c9d44a"},"schema_version":"1.0","source":{"id":"1501.06835","kind":"arxiv","version":1}},"canonical_sha256":"ffccc0802c64ece38275155164af67697d7bdc21e981268d8c1abdfab2abaf78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffccc0802c64ece38275155164af67697d7bdc21e981268d8c1abdfab2abaf78","first_computed_at":"2026-05-18T02:17:24.099201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:24.099201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xxFFSaIsA4X+RUnni4MdHt2KY5uyLtdYqXndelG7PDPFxe945LIb8SuAr9scEArOwj3gaWMbbiHTiT0XLGvQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:24.100005Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd65aef7bc59f64b0449ef5d6b151ff7b9aecc28f64d61c4ad86e0ef20af5ac9","sha256:38c3b5775232510efa032be875737f4036fcdd548fa3350d390222ead5f2b68e"],"state_sha256":"4b6ceb0fbe52976ac977a86e758cbdbb4f361aafe284cda800785a866fcd4911"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dNtvlHPyKTx5aNZmTKbblLHeAQDrWlc+4HBIW2aQQhbIkLYLXHB1U+xtbPgkE6gWHRdUBqNt58SXriMQnKRtDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:17:19.843798Z","bundle_sha256":"1c4b2c701f11cb10bff5aff682f92ca92175d61bf2e23b884a70aa69669f8c15"}}