{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:R4ATUCFN7Z7XXHGBOFQBOYU5XA","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":"9d16f749aa5a1ff7895161d25dddd09b0f6d10c3419341da0d14736bcd63490e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-06-03T03:24:36Z","title_canon_sha256":"61459c3006ec2fdd7115c1596cb6b9975376b8a279a4e148934c94cace46c76f"},"schema_version":"1.0","source":{"id":"2106.01567","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.01567","created_at":"2026-07-05T02:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"2106.01567v1","created_at":"2026-07-05T02:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.01567","created_at":"2026-07-05T02:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"R4ATUCFN7Z7X","created_at":"2026-07-05T02:45:53Z"},{"alias_kind":"pith_short_16","alias_value":"R4ATUCFN7Z7XXHGB","created_at":"2026-07-05T02:45:53Z"},{"alias_kind":"pith_short_8","alias_value":"R4ATUCFN","created_at":"2026-07-05T02:45:53Z"}],"graph_snapshots":[{"event_id":"sha256:222e8b7036b2d6d4824bd9644fc2977b48459d601395c2dee337ba01b2a184d0","target":"graph","created_at":"2026-07-05T02:45:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.01567/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we study the expander decomposition problem in a more general setting where the input graph has positively weighted edges and nonnegative demands on its vertices. We show how to extend the techniques of Chuzhoy et al. (FOCS 2020) to this wider setting, obtaining a deterministic algorithm for the problem in almost-linear time.","authors_text":"Jason Li, Thatchaphol Saranurak","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-06-03T03:24:36Z","title":"Deterministic Weighted Expander Decomposition in Almost-linear Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.01567","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":"sha256:1018f595dbab9ad772f916ddf424e8f518554dee15fe05c65ece5e1b06bdbb9d","target":"record","created_at":"2026-07-05T02:45:53Z","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":"9d16f749aa5a1ff7895161d25dddd09b0f6d10c3419341da0d14736bcd63490e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-06-03T03:24:36Z","title_canon_sha256":"61459c3006ec2fdd7115c1596cb6b9975376b8a279a4e148934c94cace46c76f"},"schema_version":"1.0","source":{"id":"2106.01567","kind":"arxiv","version":1}},"canonical_sha256":"8f013a08adfe7f7b9cc1716017629db810d6e0b9a2fa64669c3c5fbc62006486","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f013a08adfe7f7b9cc1716017629db810d6e0b9a2fa64669c3c5fbc62006486","first_computed_at":"2026-07-05T02:45:53.011917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:45:53.011917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WyMrNFdJFi7QadYHvxol4FAyev53/CzYCcvnkZBSPzyEA2WIGOjV9yWcb7rAxNVpT1tu+A+n2gWzlhOdavd+Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:45:53.012327Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.01567","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1018f595dbab9ad772f916ddf424e8f518554dee15fe05c65ece5e1b06bdbb9d","sha256:222e8b7036b2d6d4824bd9644fc2977b48459d601395c2dee337ba01b2a184d0"],"state_sha256":"53a876198404af3db08cf09a5c14aacf062fc2246fbeed2d96212755d5d9ee79"}