{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ANCJPBU7PHB7XBT3MFD6O6VWOO","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":"b236fd1ba36bd72c353fac56d90c3179cb134e0d52ca57ab500669f841b50372","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-05T19:41:00Z","title_canon_sha256":"607f8812e5904c9eb3c7ee8ae114daac72aa5aa018eb8f30adde1b1fe72577d5"},"schema_version":"1.0","source":{"id":"1612.01492","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01492","created_at":"2026-05-18T00:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01492v2","created_at":"2026-05-18T00:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01492","created_at":"2026-05-18T00:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"ANCJPBU7PHB7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ANCJPBU7PHB7XBT3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ANCJPBU7","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:74baab04087095d7f5e3760ea02733d729b32befadad5098735c76c3a541dee0","target":"graph","created_at":"2026-05-18T00:40:17Z","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":"We study the design of schedules for multi-commodity multicast; we are given an undirected graph $G$ and a collection of source destination pairs, and the goal is to schedule a minimum-length sequence of matchings that connects every source with its respective destination. Multi-commodity multicast models a classic information dissemination problem in networks where the primary communication constraint is the number of connections that a node can make, not link bandwidth.\n  Multi-commodity multicast is closely related to the problem of finding a subgraph, $H$, of optimal poise, where the poise","authors_text":"Jennifer Iglesias, Rajmohan Rajaraman, Ravi Sundaram, R Ravi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-05T19:41:00Z","title":"Plane Gossip: Approximating rumor spread in planar graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01492","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:ac48711708efa925b7d72f66a2b879f30989f7ffaaacb2edded41d95bd2012db","target":"record","created_at":"2026-05-18T00:40:17Z","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":"b236fd1ba36bd72c353fac56d90c3179cb134e0d52ca57ab500669f841b50372","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-05T19:41:00Z","title_canon_sha256":"607f8812e5904c9eb3c7ee8ae114daac72aa5aa018eb8f30adde1b1fe72577d5"},"schema_version":"1.0","source":{"id":"1612.01492","kind":"arxiv","version":2}},"canonical_sha256":"034497869f79c3fb867b6147e77ab673a99668011b8b6636acf5f871b7157018","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"034497869f79c3fb867b6147e77ab673a99668011b8b6636acf5f871b7157018","first_computed_at":"2026-05-18T00:40:17.398303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:17.398303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z67MTp6vTgzj5dfTdqvoYYUIMCAPQpvklNZaOlZ2VlwSLk2tOUS/svo8gDpq/208o3h+Facyqq9HLt2DGZr5Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:17.399139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01492","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac48711708efa925b7d72f66a2b879f30989f7ffaaacb2edded41d95bd2012db","sha256:74baab04087095d7f5e3760ea02733d729b32befadad5098735c76c3a541dee0"],"state_sha256":"0d2b4f5fa80f0c5adaac4c7b94c9de74cbc495aa9be10b4a2da5aeaf34acaed1"}