{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:RIHUNSW2XTLHQA4CPK7RCBNUZT","short_pith_number":"pith:RIHUNSW2","schema_version":"1.0","canonical_sha256":"8a0f46cadabcd67803827abf1105b4ccfc03ea9ad84c825faf34090b551338a9","source":{"kind":"arxiv","id":"2606.25612","version":1},"attestation_state":"computed","paper":{"title":"Multi-Source Reachability in Near-Optimal Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Merav Parter, Shimon Kogan","submitted_at":"2026-06-24T09:21:25Z","abstract_excerpt":"The multi-source reachability problem asks to compute the reachable sets from a given subset of source vertices. For $n$-vertex digraphs $G=(V,E)$ and a subset of sources $S \\subseteq V$ with $|S|=n^{\\sigma}$ for some $\\sigma \\in [0,1]$, we present a near-optimal deterministic algorithm that solves this problem in $\\tilde{O}(n^{\\omega(\\sigma)})$ time, where $\\omega(\\sigma)$ is the rectangular matrix multiplication exponent for multiplying an $n^{\\sigma}\\times n$ matrix by an $n \\times n$ matrix. For dense graphs, this yields reachability from up to $n^{0.32}$ sources in near-linear time, break"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.25612","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-06-24T09:21:25Z","cross_cats_sorted":[],"title_canon_sha256":"0c9f341f535063de900ac2e06f90f74dc31476c9aa7f81b0b0fdc147b3238c28","abstract_canon_sha256":"897ca4f09707abe1aaaae31661d9a8ac65412809b99ecb5f700cf6acd3dd8e3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:10.418102Z","signature_b64":"bNUR8JI2FHtpz51MM5Yol3wFGjoXvib7zOXqgOw0dhfeNMzV/wHOgqc8Dcxmzf4TeW8BsHYJl4Uk4I6OftZzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a0f46cadabcd67803827abf1105b4ccfc03ea9ad84c825faf34090b551338a9","last_reissued_at":"2026-06-25T01:18:10.417705Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:10.417705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multi-Source Reachability in Near-Optimal Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Merav Parter, Shimon Kogan","submitted_at":"2026-06-24T09:21:25Z","abstract_excerpt":"The multi-source reachability problem asks to compute the reachable sets from a given subset of source vertices. For $n$-vertex digraphs $G=(V,E)$ and a subset of sources $S \\subseteq V$ with $|S|=n^{\\sigma}$ for some $\\sigma \\in [0,1]$, we present a near-optimal deterministic algorithm that solves this problem in $\\tilde{O}(n^{\\omega(\\sigma)})$ time, where $\\omega(\\sigma)$ is the rectangular matrix multiplication exponent for multiplying an $n^{\\sigma}\\times n$ matrix by an $n \\times n$ matrix. For dense graphs, this yields reachability from up to $n^{0.32}$ sources in near-linear time, break"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25612","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25612/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.25612","created_at":"2026-06-25T01:18:10.417769+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.25612v1","created_at":"2026-06-25T01:18:10.417769+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25612","created_at":"2026-06-25T01:18:10.417769+00:00"},{"alias_kind":"pith_short_12","alias_value":"RIHUNSW2XTLH","created_at":"2026-06-25T01:18:10.417769+00:00"},{"alias_kind":"pith_short_16","alias_value":"RIHUNSW2XTLHQA4C","created_at":"2026-06-25T01:18:10.417769+00:00"},{"alias_kind":"pith_short_8","alias_value":"RIHUNSW2","created_at":"2026-06-25T01:18:10.417769+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RIHUNSW2XTLHQA4CPK7RCBNUZT","json":"https://pith.science/pith/RIHUNSW2XTLHQA4CPK7RCBNUZT.json","graph_json":"https://pith.science/api/pith-number/RIHUNSW2XTLHQA4CPK7RCBNUZT/graph.json","events_json":"https://pith.science/api/pith-number/RIHUNSW2XTLHQA4CPK7RCBNUZT/events.json","paper":"https://pith.science/paper/RIHUNSW2"},"agent_actions":{"view_html":"https://pith.science/pith/RIHUNSW2XTLHQA4CPK7RCBNUZT","download_json":"https://pith.science/pith/RIHUNSW2XTLHQA4CPK7RCBNUZT.json","view_paper":"https://pith.science/paper/RIHUNSW2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.25612&json=true","fetch_graph":"https://pith.science/api/pith-number/RIHUNSW2XTLHQA4CPK7RCBNUZT/graph.json","fetch_events":"https://pith.science/api/pith-number/RIHUNSW2XTLHQA4CPK7RCBNUZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RIHUNSW2XTLHQA4CPK7RCBNUZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RIHUNSW2XTLHQA4CPK7RCBNUZT/action/storage_attestation","attest_author":"https://pith.science/pith/RIHUNSW2XTLHQA4CPK7RCBNUZT/action/author_attestation","sign_citation":"https://pith.science/pith/RIHUNSW2XTLHQA4CPK7RCBNUZT/action/citation_signature","submit_replication":"https://pith.science/pith/RIHUNSW2XTLHQA4CPK7RCBNUZT/action/replication_record"}},"created_at":"2026-06-25T01:18:10.417769+00:00","updated_at":"2026-06-25T01:18:10.417769+00:00"}