{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XSFBTC54TXE2QE765I7IFOK4SE","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":"885c1abd699618d2851ffcdbd11e0efbea067ab081d2a5c557aab23675ddd427","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-11T20:51:47Z","title_canon_sha256":"b7f86582b7f523edfdbe378e4c05607c9ce3bb7695d70ae2352ba59a173be876"},"schema_version":"1.0","source":{"id":"1602.03881","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03881","created_at":"2026-05-18T01:19:10Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03881v2","created_at":"2026-05-18T01:19:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03881","created_at":"2026-05-18T01:19:10Z"},{"alias_kind":"pith_short_12","alias_value":"XSFBTC54TXE2","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XSFBTC54TXE2QE76","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XSFBTC54","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:e5c58e0c3aa2e2184510a6d3151fec32228a552849e8af5d774784eb21ad3757","target":"graph","created_at":"2026-05-18T01:19:10Z","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":"The single-source shortest path problem (SSSP) with nonnegative edge weights is a notoriously difficult problem to solve efficiently in parallel---it is one of the graph problems said to suffer from the transitive-closure bottleneck. In practice, the $\\Delta$-stepping algorithm of Meyer and Sanders (J. Algorithms, 2003) often works efficiently but has no known theoretical bounds on general graphs. The algorithm takes a sequence of steps, each increasing the radius by a user-specified value $\\Delta$. Each step settles the vertices in its annulus but can take $\\Theta(n)$ substeps, each requiring","authors_text":"Guy E. Blelloch, Kanat Tangwongsan, Yan Gu, Yihan Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-11T20:51:47Z","title":"Parallel Shortest-Paths Using Radius Stepping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03881","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:ae3cbc4e38c3fd612a7b38410fad6bc5290b0e3b2680f23dabfac546e35bc7ca","target":"record","created_at":"2026-05-18T01:19:10Z","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":"885c1abd699618d2851ffcdbd11e0efbea067ab081d2a5c557aab23675ddd427","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-11T20:51:47Z","title_canon_sha256":"b7f86582b7f523edfdbe378e4c05607c9ce3bb7695d70ae2352ba59a173be876"},"schema_version":"1.0","source":{"id":"1602.03881","kind":"arxiv","version":2}},"canonical_sha256":"bc8a198bbc9dc9a813feea3e82b95c911a36c9ea826a0fa79fcc737757a85a32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc8a198bbc9dc9a813feea3e82b95c911a36c9ea826a0fa79fcc737757a85a32","first_computed_at":"2026-05-18T01:19:10.906413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:10.906413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ENRY8aLzdDAjL3hK72hwNss/DsvDECJ48Nk9h7xAKRwdVeBmij05Srr4PJKaIkxChRC/XFz7qVhOnCxSEIjmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:10.907139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03881","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae3cbc4e38c3fd612a7b38410fad6bc5290b0e3b2680f23dabfac546e35bc7ca","sha256:e5c58e0c3aa2e2184510a6d3151fec32228a552849e8af5d774784eb21ad3757"],"state_sha256":"ffc0c003d0a0ab83d6639bedec0b2d6e327785fb199dd0fc91426b56c9a310fc"}