{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:CTGVEDXYXVIKR7PZBHJ2X6SMD6","short_pith_number":"pith:CTGVEDXY","canonical_record":{"source":{"id":"0812.1770","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-12-09T18:48:21Z","cross_cats_sorted":[],"title_canon_sha256":"a97824ba83f0e9f730a689e34e61b0ad17405aea24f08fe7f10f8d7f9476e958","abstract_canon_sha256":"09c8e88e5d690b8c653e6d07f4f6a99ef2fdb5f3cd607e3881c3b9ebfd65586f"},"schema_version":"1.0"},"canonical_sha256":"14cd520ef8bd50a8fdf909d3abfa4c1f9f960e4394b923dce7930b896424dfc8","source":{"kind":"arxiv","id":"0812.1770","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.1770","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"0812.1770v3","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.1770","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"CTGVEDXYXVIK","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CTGVEDXYXVIKR7PZ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CTGVEDXY","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:CTGVEDXYXVIKR7PZBHJ2X6SMD6","target":"record","payload":{"canonical_record":{"source":{"id":"0812.1770","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-12-09T18:48:21Z","cross_cats_sorted":[],"title_canon_sha256":"a97824ba83f0e9f730a689e34e61b0ad17405aea24f08fe7f10f8d7f9476e958","abstract_canon_sha256":"09c8e88e5d690b8c653e6d07f4f6a99ef2fdb5f3cd607e3881c3b9ebfd65586f"},"schema_version":"1.0"},"canonical_sha256":"14cd520ef8bd50a8fdf909d3abfa4c1f9f960e4394b923dce7930b896424dfc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:59.328441Z","signature_b64":"zFD0/Ui/Mr25gBSX2a4iWzaLRvXkItKk/6PmKHGV4JdF+rgktTY/n2pCXPZsmuy3uXouK6nq+0SLh8rFICXqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14cd520ef8bd50a8fdf909d3abfa4c1f9f960e4394b923dce7930b896424dfc8","last_reissued_at":"2026-05-18T02:26:59.328079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:59.328079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.1770","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RK7SWxGEvhBQjrDVp+aFNamKNW/VSR8sT0vzrg+FsYaE0aBKPYoszPHq4ocxiQmtHTpCMl3tv8NVfNOiEYKwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:01:03.389075Z"},"content_sha256":"e0c8cefcc40c13ea74d884b8e32670d7621c220f10052b33f8a4fd0a5bc9fa79","schema_version":"1.0","event_id":"sha256:e0c8cefcc40c13ea74d884b8e32670d7621c220f10052b33f8a4fd0a5bc9fa79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:CTGVEDXYXVIKR7PZBHJ2X6SMD6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Laplacian Dynamics and Multiscale Modular Structure in Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"J.-C. Delvenne, M. Barahona, R. Lambiotte","submitted_at":"2008-12-09T18:48:21Z","abstract_excerpt":"Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time-scale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.1770","kind":"arxiv","version":3},"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":"2026-05-18T02:26:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rNL9Ip/abjASZkgrPJhjuL0Ye99J1sRzOEldIFgNFIMLZDkE1f0q9Kdw1bCFVOPp1HnMrfm/rULVO0otQ3IsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:01:03.389436Z"},"content_sha256":"1b9f43102d39a7d8ca8c1e9c647c3a62962ddaa7efdf6663be598487dbf2b56a","schema_version":"1.0","event_id":"sha256:1b9f43102d39a7d8ca8c1e9c647c3a62962ddaa7efdf6663be598487dbf2b56a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CTGVEDXYXVIKR7PZBHJ2X6SMD6/bundle.json","state_url":"https://pith.science/pith/CTGVEDXYXVIKR7PZBHJ2X6SMD6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CTGVEDXYXVIKR7PZBHJ2X6SMD6/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":"2026-06-03T19:01:03Z","links":{"resolver":"https://pith.science/pith/CTGVEDXYXVIKR7PZBHJ2X6SMD6","bundle":"https://pith.science/pith/CTGVEDXYXVIKR7PZBHJ2X6SMD6/bundle.json","state":"https://pith.science/pith/CTGVEDXYXVIKR7PZBHJ2X6SMD6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CTGVEDXYXVIKR7PZBHJ2X6SMD6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:CTGVEDXYXVIKR7PZBHJ2X6SMD6","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":"09c8e88e5d690b8c653e6d07f4f6a99ef2fdb5f3cd607e3881c3b9ebfd65586f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-12-09T18:48:21Z","title_canon_sha256":"a97824ba83f0e9f730a689e34e61b0ad17405aea24f08fe7f10f8d7f9476e958"},"schema_version":"1.0","source":{"id":"0812.1770","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.1770","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"arxiv_version","alias_value":"0812.1770v3","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.1770","created_at":"2026-05-18T02:26:59Z"},{"alias_kind":"pith_short_12","alias_value":"CTGVEDXYXVIK","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CTGVEDXYXVIKR7PZ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CTGVEDXY","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:1b9f43102d39a7d8ca8c1e9c647c3a62962ddaa7efdf6663be598487dbf2b56a","target":"graph","created_at":"2026-05-18T02:26:59Z","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":"Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time-scale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed mu","authors_text":"J.-C. Delvenne, M. Barahona, R. Lambiotte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-12-09T18:48:21Z","title":"Laplacian Dynamics and Multiscale Modular Structure in Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.1770","kind":"arxiv","version":3},"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:e0c8cefcc40c13ea74d884b8e32670d7621c220f10052b33f8a4fd0a5bc9fa79","target":"record","created_at":"2026-05-18T02:26:59Z","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":"09c8e88e5d690b8c653e6d07f4f6a99ef2fdb5f3cd607e3881c3b9ebfd65586f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2008-12-09T18:48:21Z","title_canon_sha256":"a97824ba83f0e9f730a689e34e61b0ad17405aea24f08fe7f10f8d7f9476e958"},"schema_version":"1.0","source":{"id":"0812.1770","kind":"arxiv","version":3}},"canonical_sha256":"14cd520ef8bd50a8fdf909d3abfa4c1f9f960e4394b923dce7930b896424dfc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14cd520ef8bd50a8fdf909d3abfa4c1f9f960e4394b923dce7930b896424dfc8","first_computed_at":"2026-05-18T02:26:59.328079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:59.328079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zFD0/Ui/Mr25gBSX2a4iWzaLRvXkItKk/6PmKHGV4JdF+rgktTY/n2pCXPZsmuy3uXouK6nq+0SLh8rFICXqAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:59.328441Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.1770","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0c8cefcc40c13ea74d884b8e32670d7621c220f10052b33f8a4fd0a5bc9fa79","sha256:1b9f43102d39a7d8ca8c1e9c647c3a62962ddaa7efdf6663be598487dbf2b56a"],"state_sha256":"284bf79dfab2c5a303211e11c766af9f9d7842c3dbd144fc037c515f8cdefce3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RHvfdbOSLe22lVUWQy4JaCNlA1c98PRHs/mTPI4NpG7zKBghHeFGBPWIyjk3ZAZoLq4q+LtnQVuOu1V0vd2HBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:01:03.391434Z","bundle_sha256":"c07c7abbca81e76b037934ae2f8fa4ac13098f5f8b3eaf3f7c3696ab9bb016fa"}}