{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UTNHQQ2ABMFPDSMRM7RW3M5ZCD","short_pith_number":"pith:UTNHQQ2A","canonical_record":{"source":{"id":"1811.03069","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-11-07T18:32:24Z","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"title_canon_sha256":"c5ddcb055a925da398242c69d5fab5eb3156cca8f96bbe59d527ac7cf0123f8c","abstract_canon_sha256":"c920e69d6b857e1a13ec10740b51c8f0cd2449213eba15a7a704d777fb9d1078"},"schema_version":"1.0"},"canonical_sha256":"a4da7843400b0af1c99167e36db3b910e32a86bd2569504ebfbb893cc09ecb14","source":{"kind":"arxiv","id":"1811.03069","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03069","created_at":"2026-05-17T23:53:24Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03069v2","created_at":"2026-05-17T23:53:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03069","created_at":"2026-05-17T23:53:24Z"},{"alias_kind":"pith_short_12","alias_value":"UTNHQQ2ABMFP","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UTNHQQ2ABMFPDSMR","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UTNHQQ2A","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UTNHQQ2ABMFPDSMRM7RW3M5ZCD","target":"record","payload":{"canonical_record":{"source":{"id":"1811.03069","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-11-07T18:32:24Z","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"title_canon_sha256":"c5ddcb055a925da398242c69d5fab5eb3156cca8f96bbe59d527ac7cf0123f8c","abstract_canon_sha256":"c920e69d6b857e1a13ec10740b51c8f0cd2449213eba15a7a704d777fb9d1078"},"schema_version":"1.0"},"canonical_sha256":"a4da7843400b0af1c99167e36db3b910e32a86bd2569504ebfbb893cc09ecb14","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:24.618492Z","signature_b64":"fTqzbLz41nLTw8YYzypC0RM/tqe/NYGht5giBndTESX1zdg3KfmmNIry43VRSuhzLCf9vF2YuspzHEUjvMk9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4da7843400b0af1c99167e36db3b910e32a86bd2569504ebfbb893cc09ecb14","last_reissued_at":"2026-05-17T23:53:24.617966Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:24.617966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.03069","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9dYzoMkJvadedycdlFX9wCbifxKqror/e/R1DSPwXyNI0REMjnWgjyFLCpVwFLC99LiOiXbyCjjPes06eAUMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:17:55.425532Z"},"content_sha256":"a2d4cc5271e3615219d6976633f256105a2378d0a07eb79e5324a3027df740b7","schema_version":"1.0","event_id":"sha256:a2d4cc5271e3615219d6976633f256105a2378d0a07eb79e5324a3027df740b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UTNHQQ2ABMFPDSMRM7RW3M5ZCD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synchronization in Network Geometries with Finite Spectral Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Ana P. Mill\\'an, Ginestra Bianconi, Joaqu\\'in J. Torres","submitted_at":"2018-11-07T18:32:24Z","abstract_excerpt":"Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and its dynamics. Specifically we explore the role of the spectral dimension in determining the synchronization properties of the Kuramoto model. We show that the synchronized phase can only be thermodynamically stable for spectral dimensions above four and that phase entrainment of the oscillators can only be found for spectral dimensions greater than two. We nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03069","kind":"arxiv","version":2},"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":"2026-05-17T23:53:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3tYL3XlckQW0iWhFJgeZMdvaVfF5c3oidc9e4ryRVN5gC3KAfbXWPZxxDjJqJTSHNtXcfoVM58kqyTW0dNS7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:17:55.425893Z"},"content_sha256":"29993214e8768c12f704ff790a6aa3625309a9d335f324beecae86de72c081d5","schema_version":"1.0","event_id":"sha256:29993214e8768c12f704ff790a6aa3625309a9d335f324beecae86de72c081d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UTNHQQ2ABMFPDSMRM7RW3M5ZCD/bundle.json","state_url":"https://pith.science/pith/UTNHQQ2ABMFPDSMRM7RW3M5ZCD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UTNHQQ2ABMFPDSMRM7RW3M5ZCD/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":"2026-06-21T23:17:55Z","links":{"resolver":"https://pith.science/pith/UTNHQQ2ABMFPDSMRM7RW3M5ZCD","bundle":"https://pith.science/pith/UTNHQQ2ABMFPDSMRM7RW3M5ZCD/bundle.json","state":"https://pith.science/pith/UTNHQQ2ABMFPDSMRM7RW3M5ZCD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UTNHQQ2ABMFPDSMRM7RW3M5ZCD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UTNHQQ2ABMFPDSMRM7RW3M5ZCD","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":"c920e69d6b857e1a13ec10740b51c8f0cd2449213eba15a7a704d777fb9d1078","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-11-07T18:32:24Z","title_canon_sha256":"c5ddcb055a925da398242c69d5fab5eb3156cca8f96bbe59d527ac7cf0123f8c"},"schema_version":"1.0","source":{"id":"1811.03069","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03069","created_at":"2026-05-17T23:53:24Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03069v2","created_at":"2026-05-17T23:53:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03069","created_at":"2026-05-17T23:53:24Z"},{"alias_kind":"pith_short_12","alias_value":"UTNHQQ2ABMFP","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UTNHQQ2ABMFPDSMR","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UTNHQQ2A","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:29993214e8768c12f704ff790a6aa3625309a9d335f324beecae86de72c081d5","target":"graph","created_at":"2026-05-17T23:53:24Z","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":"Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and its dynamics. Specifically we explore the role of the spectral dimension in determining the synchronization properties of the Kuramoto model. We show that the synchronized phase can only be thermodynamically stable for spectral dimensions above four and that phase entrainment of the oscillators can only be found for spectral dimensions greater than two. We nu","authors_text":"Ana P. Mill\\'an, Ginestra Bianconi, Joaqu\\'in J. Torres","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-11-07T18:32:24Z","title":"Synchronization in Network Geometries with Finite Spectral Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03069","kind":"arxiv","version":2},"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:a2d4cc5271e3615219d6976633f256105a2378d0a07eb79e5324a3027df740b7","target":"record","created_at":"2026-05-17T23:53:24Z","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":"c920e69d6b857e1a13ec10740b51c8f0cd2449213eba15a7a704d777fb9d1078","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-11-07T18:32:24Z","title_canon_sha256":"c5ddcb055a925da398242c69d5fab5eb3156cca8f96bbe59d527ac7cf0123f8c"},"schema_version":"1.0","source":{"id":"1811.03069","kind":"arxiv","version":2}},"canonical_sha256":"a4da7843400b0af1c99167e36db3b910e32a86bd2569504ebfbb893cc09ecb14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4da7843400b0af1c99167e36db3b910e32a86bd2569504ebfbb893cc09ecb14","first_computed_at":"2026-05-17T23:53:24.617966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:24.617966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fTqzbLz41nLTw8YYzypC0RM/tqe/NYGht5giBndTESX1zdg3KfmmNIry43VRSuhzLCf9vF2YuspzHEUjvMk9Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:24.618492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03069","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2d4cc5271e3615219d6976633f256105a2378d0a07eb79e5324a3027df740b7","sha256:29993214e8768c12f704ff790a6aa3625309a9d335f324beecae86de72c081d5"],"state_sha256":"c11de85232e5d571814765427fe620cc79d1658fc8b8507e2bc57fa9c1f8318b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LT1FZqC48wRY+ZD0u/Vt7id8yyYnjqcBbtYfUxj2oa2MBwb32ngn0tfyu7kgoqekPGhVaBm9ppv6scZkeI7VAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:17:55.427830Z","bundle_sha256":"48d81950fac3282a8f4f0070b44eb6e1da20a45c2b2e1726338b5a3bf14c5d8f"}}