{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UBYIR5R4WK6BYNQXJ64UHOWV4Y","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":"881097e59a1128fb3d22295c2fa35bda3df7a2b3514ebf0284f6abe08eca3fbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-25T03:02:46Z","title_canon_sha256":"5825b186568122781e202b07b76337b1efcde73268fb8d176826c7fbbb6dd474"},"schema_version":"1.0","source":{"id":"2606.26554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26554","created_at":"2026-06-26T01:15:34Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26554v1","created_at":"2026-06-26T01:15:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26554","created_at":"2026-06-26T01:15:34Z"},{"alias_kind":"pith_short_12","alias_value":"UBYIR5R4WK6B","created_at":"2026-06-26T01:15:34Z"},{"alias_kind":"pith_short_16","alias_value":"UBYIR5R4WK6BYNQX","created_at":"2026-06-26T01:15:34Z"},{"alias_kind":"pith_short_8","alias_value":"UBYIR5R4","created_at":"2026-06-26T01:15:34Z"}],"graph_snapshots":[{"event_id":"sha256:1fb0a6a9f9499f7b359e909be744139d140f84174448ec2a71c007c09e7109a1","target":"graph","created_at":"2026-06-26T01:15:34Z","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/2606.26554/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a graph, computing distances and reachabilities from a small set of vertices to the whole graph is an important primitive both in theory and in practice.\n  In undirected unweighted graphs, while computing single-source shortest path (SSSP) requires $O(n^2)$ time in dense graphs, all-pairs shortest paths (APSP) can be computed in $\\hat{O}(n^\\omega) = O(n^{2.372})$ time [Seidel '95] providing significant savings over running $n$ SSSP instances separately. However, if one needs to compute multiple-source shortest paths (MSSP) from a set of $n^\\sigma$ vertices, the previously best known runn","authors_text":"Barna Saha, Christopher Ye, Yinzhan Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-25T03:02:46Z","title":"Almost Optimal Multiple Source Shortest Paths and Reachability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26554","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:b62116b5705e10af393125f3078f14fdcb16e1e8bfe15d3283493252bd27208a","target":"record","created_at":"2026-06-26T01:15:34Z","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":"881097e59a1128fb3d22295c2fa35bda3df7a2b3514ebf0284f6abe08eca3fbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-25T03:02:46Z","title_canon_sha256":"5825b186568122781e202b07b76337b1efcde73268fb8d176826c7fbbb6dd474"},"schema_version":"1.0","source":{"id":"2606.26554","kind":"arxiv","version":1}},"canonical_sha256":"a07088f63cb2bc1c36174fb943bad5e610aaefb89c79dfdef60543fd6d00b109","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a07088f63cb2bc1c36174fb943bad5e610aaefb89c79dfdef60543fd6d00b109","first_computed_at":"2026-06-26T01:15:34.466507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:15:34.466507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qhFsFDKZ+L+EoVPSHYyhMuok4WFQjOqfreBXaVepw1TZhOxJaGoJhwx9P+P1lL917DEeB1Qil13MPWCs9oPQCQ==","signature_status":"signed_v1","signed_at":"2026-06-26T01:15:34.466917Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.26554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b62116b5705e10af393125f3078f14fdcb16e1e8bfe15d3283493252bd27208a","sha256:1fb0a6a9f9499f7b359e909be744139d140f84174448ec2a71c007c09e7109a1"],"state_sha256":"3f80718d81ddd7a816c59ad6264040f31ec8b4b04d97e8047c0b887f1fa92a98"}