{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NCWLR6JPMJITWJI6K33GZSBS2L","short_pith_number":"pith:NCWLR6JP","canonical_record":{"source":{"id":"2203.03456","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-07T15:15:09Z","cross_cats_sorted":[],"title_canon_sha256":"1b2ea687aebaa87f5ca54e5a7b49e417eb58654b9aeefc6ff1b66f517b9944ae","abstract_canon_sha256":"170903bca1c7c15fa595d862af879159d65a5b3b8410c97677c71a73b9517898"},"schema_version":"1.0"},"canonical_sha256":"68acb8f92f62513b251e56f66cc832d2f70cc8ad42144b54daf1a69199fad752","source":{"kind":"arxiv","id":"2203.03456","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.03456","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"2203.03456v6","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.03456","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"NCWLR6JPMJIT","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"pith_short_16","alias_value":"NCWLR6JPMJITWJI6","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"pith_short_8","alias_value":"NCWLR6JP","created_at":"2026-07-05T11:05:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NCWLR6JPMJITWJI6K33GZSBS2L","target":"record","payload":{"canonical_record":{"source":{"id":"2203.03456","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-07T15:15:09Z","cross_cats_sorted":[],"title_canon_sha256":"1b2ea687aebaa87f5ca54e5a7b49e417eb58654b9aeefc6ff1b66f517b9944ae","abstract_canon_sha256":"170903bca1c7c15fa595d862af879159d65a5b3b8410c97677c71a73b9517898"},"schema_version":"1.0"},"canonical_sha256":"68acb8f92f62513b251e56f66cc832d2f70cc8ad42144b54daf1a69199fad752","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:30.695144Z","signature_b64":"TkoVylp7DvA/ogYQPp6nC3u4pQ/WXmmTEpaJU22OuIxVHX5j8CCvCXeniKZhfylcfyKtWXnIzkE/mLRjwz9dDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68acb8f92f62513b251e56f66cc832d2f70cc8ad42144b54daf1a69199fad752","last_reissued_at":"2026-07-05T11:05:30.694690Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:30.694690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.03456","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:05:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7WF+NHFb05gUG0DFRi5+/geKzDrIqU9mtWHBQXyGhILJO0kuExQiRecIGiLRA7RmVA4VmBXegp8q3ugxwUXzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:06:20.606522Z"},"content_sha256":"dd60fee16839fe54c8e69fd056403d232efa4fe2b96c261339016ffdc09a7d56","schema_version":"1.0","event_id":"sha256:dd60fee16839fe54c8e69fd056403d232efa4fe2b96c261339016ffdc09a7d56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NCWLR6JPMJITWJI6K33GZSBS2L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Negative-Weight Single-Source Shortest Paths in Near-linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aaron Bernstein, Christian Wulff-Nilsen, Danupon Nanongkai","submitted_at":"2022-03-07T15:15:09Z","abstract_excerpt":"We present a randomized algorithm that computes single-source shortest paths (SSSP) in $O(m\\log^8(n)\\log W)$ time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight SSSP problem. The previous bounds are $\\tilde O((m+n^{1.5})\\log W)$ [BLNPSSSW FOCS'20] and $m^{4/3+o(1)}\\log W$ [AMV FOCS'20]. Near-linear time algorithms were known previously only for the special case of planar directed graphs [Fakcharoenphol and Rao FOCS'01].\n  In contrast to all recent developments that rely on sophisticated continuous optimization methods and dynamic algor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03456","kind":"arxiv","version":6},"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/2203.03456/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:05:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dobNTxonk3gJyoya6VlYM0L1CJPq0+SomEZs7zPgew1ZFXSiuyvOYxUqDoWq4F/7qsuZ/x1YKljrqmYNARG0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:06:20.607132Z"},"content_sha256":"62a38a60a518e861691fafa1c54873ff18404b58fac3bafbb77ffdc2265c307f","schema_version":"1.0","event_id":"sha256:62a38a60a518e861691fafa1c54873ff18404b58fac3bafbb77ffdc2265c307f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NCWLR6JPMJITWJI6K33GZSBS2L/bundle.json","state_url":"https://pith.science/pith/NCWLR6JPMJITWJI6K33GZSBS2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NCWLR6JPMJITWJI6K33GZSBS2L/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T12:06:20Z","links":{"resolver":"https://pith.science/pith/NCWLR6JPMJITWJI6K33GZSBS2L","bundle":"https://pith.science/pith/NCWLR6JPMJITWJI6K33GZSBS2L/bundle.json","state":"https://pith.science/pith/NCWLR6JPMJITWJI6K33GZSBS2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NCWLR6JPMJITWJI6K33GZSBS2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NCWLR6JPMJITWJI6K33GZSBS2L","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":"170903bca1c7c15fa595d862af879159d65a5b3b8410c97677c71a73b9517898","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-07T15:15:09Z","title_canon_sha256":"1b2ea687aebaa87f5ca54e5a7b49e417eb58654b9aeefc6ff1b66f517b9944ae"},"schema_version":"1.0","source":{"id":"2203.03456","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.03456","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"2203.03456v6","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.03456","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"NCWLR6JPMJIT","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"pith_short_16","alias_value":"NCWLR6JPMJITWJI6","created_at":"2026-07-05T11:05:30Z"},{"alias_kind":"pith_short_8","alias_value":"NCWLR6JP","created_at":"2026-07-05T11:05:30Z"}],"graph_snapshots":[{"event_id":"sha256:62a38a60a518e861691fafa1c54873ff18404b58fac3bafbb77ffdc2265c307f","target":"graph","created_at":"2026-07-05T11:05:30Z","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/2203.03456/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a randomized algorithm that computes single-source shortest paths (SSSP) in $O(m\\log^8(n)\\log W)$ time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight SSSP problem. The previous bounds are $\\tilde O((m+n^{1.5})\\log W)$ [BLNPSSSW FOCS'20] and $m^{4/3+o(1)}\\log W$ [AMV FOCS'20]. Near-linear time algorithms were known previously only for the special case of planar directed graphs [Fakcharoenphol and Rao FOCS'01].\n  In contrast to all recent developments that rely on sophisticated continuous optimization methods and dynamic algor","authors_text":"Aaron Bernstein, Christian Wulff-Nilsen, Danupon Nanongkai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-07T15:15:09Z","title":"Negative-Weight Single-Source Shortest Paths in Near-linear Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03456","kind":"arxiv","version":6},"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:dd60fee16839fe54c8e69fd056403d232efa4fe2b96c261339016ffdc09a7d56","target":"record","created_at":"2026-07-05T11:05:30Z","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":"170903bca1c7c15fa595d862af879159d65a5b3b8410c97677c71a73b9517898","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-07T15:15:09Z","title_canon_sha256":"1b2ea687aebaa87f5ca54e5a7b49e417eb58654b9aeefc6ff1b66f517b9944ae"},"schema_version":"1.0","source":{"id":"2203.03456","kind":"arxiv","version":6}},"canonical_sha256":"68acb8f92f62513b251e56f66cc832d2f70cc8ad42144b54daf1a69199fad752","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68acb8f92f62513b251e56f66cc832d2f70cc8ad42144b54daf1a69199fad752","first_computed_at":"2026-07-05T11:05:30.694690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:30.694690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TkoVylp7DvA/ogYQPp6nC3u4pQ/WXmmTEpaJU22OuIxVHX5j8CCvCXeniKZhfylcfyKtWXnIzkE/mLRjwz9dDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:30.695144Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.03456","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd60fee16839fe54c8e69fd056403d232efa4fe2b96c261339016ffdc09a7d56","sha256:62a38a60a518e861691fafa1c54873ff18404b58fac3bafbb77ffdc2265c307f"],"state_sha256":"3761e94032222f4231d3bd0bb0d20cd264243e3e4c8d3b5e5fa0cdc1313b0ab2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8VVbAgjQzb7HzN/ee8+cZR9+H/qvBFs1N0Q3FyazX52mwf8whn/aIctSn/gC973DcIxF/bChVKof8xysGjRBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T12:06:20.610971Z","bundle_sha256":"cb5a32cd477024e2a0b0e21da476d4e2cbacca4a9a43d86d996425dba8db1510"}}