{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VXCYBE3A36FNPVY7HSLINUGOF5","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":"a1f5c23883d8b1d35348e3bd47c7a9214da73b9b279c7ce91551898384a062a1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-02T17:10:59Z","title_canon_sha256":"7479d4a5dbe3013ff5ac383db7c46dd2aea86fe69d37a16e6d6b836bddd430f6"},"schema_version":"1.0","source":{"id":"2607.02443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02443","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02443v1","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02443","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"pith_short_12","alias_value":"VXCYBE3A36FN","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"pith_short_16","alias_value":"VXCYBE3A36FNPVY7","created_at":"2026-07-03T01:17:59Z"},{"alias_kind":"pith_short_8","alias_value":"VXCYBE3A","created_at":"2026-07-03T01:17:59Z"}],"graph_snapshots":[{"event_id":"sha256:cb8cc801b0a0e6505043b966b6f247b77a184ade41baf84183feedf64bf8ee34","target":"graph","created_at":"2026-07-03T01:17:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.02443/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G = (V, E)$ be a graph with $n = |V|$ nodes and $m = |E|$ edges. The $t$-Pairs Shortest Paths problem, introduced by Cohen [FOCS'93; SICOMP'99], asks to approximate the distances between $t$ prespecified pairs of vertices. Recently, this problem has received renewed attention, particularly in the case where $t = \\Theta(n)$: the $n$-Pairs Shortest Paths problem. In this setting, new algorithms and conditional lower bounds have been developed by Dalirrooyfard, Jin, Vassilevska Williams, and Wein [FOCS'22], and Chechik, Hoch, and Lifshitz [SODA'25].\n  In this paper, we present the first algo","authors_text":"Avi Kadria, Liam Roditty, Virginia Vassilevska Williams","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-02T17:10:59Z","title":"Improved Approximation Algorithms for n-Pairs Shortest Paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02443","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":"sha256:88dbb8ad58dc5e61014b52e7b21e3b4231eb7b757d74c0973248758bf3d414df","target":"record","created_at":"2026-07-03T01:17:59Z","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":"a1f5c23883d8b1d35348e3bd47c7a9214da73b9b279c7ce91551898384a062a1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-02T17:10:59Z","title_canon_sha256":"7479d4a5dbe3013ff5ac383db7c46dd2aea86fe69d37a16e6d6b836bddd430f6"},"schema_version":"1.0","source":{"id":"2607.02443","kind":"arxiv","version":1}},"canonical_sha256":"adc5809360df8ad7d71f3c9686d0ce2f4f44ec6d7940fc990329cdf7eee22f2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adc5809360df8ad7d71f3c9686d0ce2f4f44ec6d7940fc990329cdf7eee22f2c","first_computed_at":"2026-07-03T01:17:59.375872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:59.375872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1YMFNg5K1lQSdb+8e6YfMFQMwXoBaw5jG9uspYofXqKuEQhISMiX23P4QoDVSkrNBDJ/5vtnmLiYXNJGWJQ8BQ==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:59.376266Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88dbb8ad58dc5e61014b52e7b21e3b4231eb7b757d74c0973248758bf3d414df","sha256:cb8cc801b0a0e6505043b966b6f247b77a184ade41baf84183feedf64bf8ee34"],"state_sha256":"1d4c10b2f93fcb5447f22981be077d4c6ce68fba622729092d85e9e243d985bc"}