{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2HF5Q76JMAWSD3FNL6PK4AKPNG","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":"def77f6a04f48362a2e225823243e59d7d046f46abae990265aa620ba98ab978","cross_cats_sorted":["cs.DM","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-12-04T11:52:17Z","title_canon_sha256":"73ad3e97a353dcca2db1d8118ee5a6f760a899ae35bda4c9da452d199b099838"},"schema_version":"1.0","source":{"id":"1212.0689","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0689","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0689v2","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0689","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"pith_short_12","alias_value":"2HF5Q76JMAWS","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2HF5Q76JMAWSD3FN","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2HF5Q76J","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:f3ee9d69319522362fb2978e51f8a9c91900b6b68bb145416d848324eef2aeb1","target":"graph","created_at":"2026-05-18T03:07:42Z","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":"For data represented by networks, the community structure of the underlying graph is of great interest. A classical clustering problem is to uncover the overall ``best'' partition of nodes in communities. Here, a more elaborate description is proposed in which community structures are identified at different scales. To this end, we take advantage of the local and scale-dependent information encoded in graph wavelets. After new developments for the practical use of graph wavelets, studying proper scale boundaries and parameters and introducing scaling functions, we propose a method to mine for ","authors_text":"Nicolas Tremblay, Pierre Borgnat","cross_cats":["cs.DM","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-12-04T11:52:17Z","title":"Multiscale Community Mining in Networks Using Spectral Graph Wavelets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0689","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":"sha256:0bdb99204282b70b8312aab980ace929e5fea5a7b2a67cba07475d5201320730","target":"record","created_at":"2026-05-18T03:07:42Z","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":"def77f6a04f48362a2e225823243e59d7d046f46abae990265aa620ba98ab978","cross_cats_sorted":["cs.DM","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-12-04T11:52:17Z","title_canon_sha256":"73ad3e97a353dcca2db1d8118ee5a6f760a899ae35bda4c9da452d199b099838"},"schema_version":"1.0","source":{"id":"1212.0689","kind":"arxiv","version":2}},"canonical_sha256":"d1cbd87fc9602d21ecad5f9eae014f69bc03662289c4b6de835f33ee30cf27f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1cbd87fc9602d21ecad5f9eae014f69bc03662289c4b6de835f33ee30cf27f7","first_computed_at":"2026-05-18T03:07:42.426164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:42.426164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AS12dAUMrQlgFhO8W5iBJM+7e80oyjmfNPRkCthYeXLaXXGc3Cud9tVrnOlFUmC0PU0hDWEwmw1/O5ZMMkeXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:42.426705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0689","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bdb99204282b70b8312aab980ace929e5fea5a7b2a67cba07475d5201320730","sha256:f3ee9d69319522362fb2978e51f8a9c91900b6b68bb145416d848324eef2aeb1"],"state_sha256":"b6e60614bc442a509e7db5d0afa36ce0ea8efa6dd2fa1008a4ede69b4b60649b"}