{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:LTNI6UBBBAPSBE6PGEHFDO5LDS","short_pith_number":"pith:LTNI6UBB","schema_version":"1.0","canonical_sha256":"5cda8f5021081f2093cf310e51bbab1c98f3bb57cd6b88e17709e412e087420f","source":{"kind":"arxiv","id":"2101.07149","version":2},"attestation_state":"computed","paper":{"title":"Deterministic Decremental SSSP and Approximate Min-Cost Flow in Almost-Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aaron Bernstein, Maximilian Probst Gutenberg, Thatchaphol Saranurak","submitted_at":"2021-01-18T16:29:31Z","abstract_excerpt":"In the decremental single-source shortest paths problem, the goal is to maintain distances from a fixed source $s$ to every vertex $v$ in an $m$-edge graph undergoing edge deletions. In this paper, we conclude a long line of research on this problem by showing a near-optimal deterministic data structure that maintains $(1+\\epsilon)$-approximate distance estimates and runs in $m^{1+o(1)}$ total update time.\n  Our result, in particular, removes the oblivious adversary assumption required by the previous breakthrough result by Henzinger et al. [FOCS'14], which leads to our second result: the firs"},"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":"2101.07149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-01-18T16:29:31Z","cross_cats_sorted":[],"title_canon_sha256":"b8c97a736fe72b62ca9f799c3c3bf044ea28509ac6fc098b3e2ed4a12a1f0dd0","abstract_canon_sha256":"0fb1ef3d0ed8bd9caffb377b0d135c7ebf222ff4fb954cf3875ce237dcc0c93d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:07:56.126439Z","signature_b64":"Fh2ijylVtzDZphVHSjiVxRzBCJrEfb4Rueq/FS7RPQ7e/MHZxZOnmsZa1tU/aeeSO4PmtVuYtoZYZlnEXqmsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cda8f5021081f2093cf310e51bbab1c98f3bb57cd6b88e17709e412e087420f","last_reissued_at":"2026-07-05T02:07:56.126026Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:07:56.126026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deterministic Decremental SSSP and Approximate Min-Cost Flow in Almost-Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aaron Bernstein, Maximilian Probst Gutenberg, Thatchaphol Saranurak","submitted_at":"2021-01-18T16:29:31Z","abstract_excerpt":"In the decremental single-source shortest paths problem, the goal is to maintain distances from a fixed source $s$ to every vertex $v$ in an $m$-edge graph undergoing edge deletions. In this paper, we conclude a long line of research on this problem by showing a near-optimal deterministic data structure that maintains $(1+\\epsilon)$-approximate distance estimates and runs in $m^{1+o(1)}$ total update time.\n  Our result, in particular, removes the oblivious adversary assumption required by the previous breakthrough result by Henzinger et al. [FOCS'14], which leads to our second result: the firs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.07149","kind":"arxiv","version":2},"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/2101.07149/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":"2101.07149","created_at":"2026-07-05T02:07:56.126085+00:00"},{"alias_kind":"arxiv_version","alias_value":"2101.07149v2","created_at":"2026-07-05T02:07:56.126085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.07149","created_at":"2026-07-05T02:07:56.126085+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTNI6UBBBAPS","created_at":"2026-07-05T02:07:56.126085+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTNI6UBBBAPSBE6P","created_at":"2026-07-05T02:07:56.126085+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTNI6UBB","created_at":"2026-07-05T02:07:56.126085+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.05063","citing_title":"Computing and Learning on Combinatorial Data","ref_index":140,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LTNI6UBBBAPSBE6PGEHFDO5LDS","json":"https://pith.science/pith/LTNI6UBBBAPSBE6PGEHFDO5LDS.json","graph_json":"https://pith.science/api/pith-number/LTNI6UBBBAPSBE6PGEHFDO5LDS/graph.json","events_json":"https://pith.science/api/pith-number/LTNI6UBBBAPSBE6PGEHFDO5LDS/events.json","paper":"https://pith.science/paper/LTNI6UBB"},"agent_actions":{"view_html":"https://pith.science/pith/LTNI6UBBBAPSBE6PGEHFDO5LDS","download_json":"https://pith.science/pith/LTNI6UBBBAPSBE6PGEHFDO5LDS.json","view_paper":"https://pith.science/paper/LTNI6UBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2101.07149&json=true","fetch_graph":"https://pith.science/api/pith-number/LTNI6UBBBAPSBE6PGEHFDO5LDS/graph.json","fetch_events":"https://pith.science/api/pith-number/LTNI6UBBBAPSBE6PGEHFDO5LDS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTNI6UBBBAPSBE6PGEHFDO5LDS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTNI6UBBBAPSBE6PGEHFDO5LDS/action/storage_attestation","attest_author":"https://pith.science/pith/LTNI6UBBBAPSBE6PGEHFDO5LDS/action/author_attestation","sign_citation":"https://pith.science/pith/LTNI6UBBBAPSBE6PGEHFDO5LDS/action/citation_signature","submit_replication":"https://pith.science/pith/LTNI6UBBBAPSBE6PGEHFDO5LDS/action/replication_record"}},"created_at":"2026-07-05T02:07:56.126085+00:00","updated_at":"2026-07-05T02:07:56.126085+00:00"}