{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UX55SVHARRBMRBJ6HMAEJBGHWQ","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":"2a9cf9a44baba91735b2b2fb474dc8cf93c9fcf7d4029f8dbea37140a8d870cb","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2017-08-10T11:23:54Z","title_canon_sha256":"9d1b4e895e8491479d0c9199343b342b4712551f60082db279af534945977387"},"schema_version":"1.0","source":{"id":"1708.03167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03167","created_at":"2026-05-18T00:20:16Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03167v1","created_at":"2026-05-18T00:20:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03167","created_at":"2026-05-18T00:20:16Z"},{"alias_kind":"pith_short_12","alias_value":"UX55SVHARRBM","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UX55SVHARRBMRBJ6","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UX55SVHA","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:81ac072249db80f9b53196e892eb1e1f9f9c9eae3b04a2b7f8a3fb3c19192826","target":"graph","created_at":"2026-05-18T00:20:16Z","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":"Multiscale community detection can be viewed from a dynamical perspective within the Markov Stability framework, which uses the diffusion of a Markov process on the graph to uncover intrinsic network substructures across all scales. Here we reformulate multiscale community detection as a max-sum length vector partitioning problem with respect to the set of time-dependent node vectors expressed in terms of eigenvectors of the transition matrix. This formulation provides a geometric interpretation of Markov Stability in terms of a time-dependent spectral embedding, where the Markov time acts as ","authors_text":"Mauricio Barahona, Zijing Liu","cross_cats":["cond-mat.stat-mech","physics.soc-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2017-08-10T11:23:54Z","title":"Geometric Multiscale Community Detection: Markov Stability and Vector Partitioning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03167","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":"sha256:9d41f70748683af76c0b17b6c65af15f58bc0378c3bff8ffa9fb1239562c361b","target":"record","created_at":"2026-05-18T00:20:16Z","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":"2a9cf9a44baba91735b2b2fb474dc8cf93c9fcf7d4029f8dbea37140a8d870cb","cross_cats_sorted":["cond-mat.stat-mech","physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SI","submitted_at":"2017-08-10T11:23:54Z","title_canon_sha256":"9d1b4e895e8491479d0c9199343b342b4712551f60082db279af534945977387"},"schema_version":"1.0","source":{"id":"1708.03167","kind":"arxiv","version":1}},"canonical_sha256":"a5fbd954e08c42c8853e3b004484c7b43e059993ee004127de8b4cb8654c2295","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5fbd954e08c42c8853e3b004484c7b43e059993ee004127de8b4cb8654c2295","first_computed_at":"2026-05-18T00:20:16.888632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:16.888632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9KK4kOkclBUnmIgb9fzU+7OSWzJ75nx+Dj12joQmuSkQdyJV8g6MDf73abw7f5UL5EHFLGlEEFFw09IaSDUMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:16.889148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d41f70748683af76c0b17b6c65af15f58bc0378c3bff8ffa9fb1239562c361b","sha256:81ac072249db80f9b53196e892eb1e1f9f9c9eae3b04a2b7f8a3fb3c19192826"],"state_sha256":"c6d615b1012dd741fdabe361689a0c4916dd1721d0adc719e4eeda588da6bc33"}