{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:22SB5A7Q5ZEJELZEMQWLEVBVD5","short_pith_number":"pith:22SB5A7Q","canonical_record":{"source":{"id":"1904.10701","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-24T08:56:58Z","cross_cats_sorted":[],"title_canon_sha256":"879c9ee04c20ac35b76bef925f42e5961377ba8781be104ec837bd16b88a05e2","abstract_canon_sha256":"114c12928cb04c97ad33f291bd36615673f24cd0e6d517a36b3723b631de6259"},"schema_version":"1.0"},"canonical_sha256":"d6a41e83f0ee48922f24642cb254351f72adfd0fb8c58b0fabf3794628a8e71e","source":{"kind":"arxiv","id":"1904.10701","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10701","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10701v1","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10701","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"pith_short_12","alias_value":"22SB5A7Q5ZEJ","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"22SB5A7Q5ZEJELZE","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"22SB5A7Q","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:22SB5A7Q5ZEJELZEMQWLEVBVD5","target":"record","payload":{"canonical_record":{"source":{"id":"1904.10701","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-24T08:56:58Z","cross_cats_sorted":[],"title_canon_sha256":"879c9ee04c20ac35b76bef925f42e5961377ba8781be104ec837bd16b88a05e2","abstract_canon_sha256":"114c12928cb04c97ad33f291bd36615673f24cd0e6d517a36b3723b631de6259"},"schema_version":"1.0"},"canonical_sha256":"d6a41e83f0ee48922f24642cb254351f72adfd0fb8c58b0fabf3794628a8e71e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:50.276135Z","signature_b64":"IDJN08pd41YwhFKM1pyUJWRj9f1JA0U0iyoqcS2I8n6ArlnQIA0bslNWYFVyISaZgrkn826AiLb5Yhia59XEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6a41e83f0ee48922f24642cb254351f72adfd0fb8c58b0fabf3794628a8e71e","last_reissued_at":"2026-05-17T23:47:50.275690Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:50.275690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.10701","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJlTFcC3rerGvZyVdkEyFHy7dL13v8y06ml+KbWQW6Aw3bV0WdCDbQbnJPcvFlzwlxO1gDHBcWkdAJp8AUPsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:06:35.833236Z"},"content_sha256":"42fb1a68dc836715773bb172192b3b4a12aed113a02e7c899857cefe37ae6b9e","schema_version":"1.0","event_id":"sha256:42fb1a68dc836715773bb172192b3b4a12aed113a02e7c899857cefe37ae6b9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:22SB5A7Q5ZEJELZEMQWLEVBVD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster Algorithms for All Pairs Non-decreasing Paths Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ce Jin, Hongxun Wu, Ran Duan","submitted_at":"2019-04-24T08:56:58Z","abstract_excerpt":"In this paper, we present an improved algorithm for the All Pairs Non-decreasing Paths (APNP) problem on weighted simple digraphs, which has running time $\\tilde{O}(n^{\\frac{3 + \\omega}{2}}) = \\tilde{O}(n^{2.686})$. Here $n$ is the number of vertices, and $\\omega < 2.373$ is the exponent of time complexity of fast matrix multiplication [Williams 2012, Le Gall 2014]. This matches the current best upper bound for $(\\max, \\min)$-matrix product [Duan, Pettie 2009] which is reducible to APNP. Thus, further improvement for APNP will imply a faster algorithm for $(\\max, \\min)$-matrix product. The pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10701","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":""},"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":"2026-05-17T23:47:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XA6kZsHGhHX1g4OQHVXLlu7Kzw5azcxWSh5HZLf/gfJ3yoIVgZnYnovsIloGB6ZdCt14IdkcTkXr6/kfQ+kBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:06:35.833901Z"},"content_sha256":"67dbd51347fb443f845cdd75ebcbc6c2d2bb720db70f2afb4bf6572b4ff9d994","schema_version":"1.0","event_id":"sha256:67dbd51347fb443f845cdd75ebcbc6c2d2bb720db70f2afb4bf6572b4ff9d994"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22SB5A7Q5ZEJELZEMQWLEVBVD5/bundle.json","state_url":"https://pith.science/pith/22SB5A7Q5ZEJELZEMQWLEVBVD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22SB5A7Q5ZEJELZEMQWLEVBVD5/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":"2026-06-04T05:06:35Z","links":{"resolver":"https://pith.science/pith/22SB5A7Q5ZEJELZEMQWLEVBVD5","bundle":"https://pith.science/pith/22SB5A7Q5ZEJELZEMQWLEVBVD5/bundle.json","state":"https://pith.science/pith/22SB5A7Q5ZEJELZEMQWLEVBVD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22SB5A7Q5ZEJELZEMQWLEVBVD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:22SB5A7Q5ZEJELZEMQWLEVBVD5","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":"114c12928cb04c97ad33f291bd36615673f24cd0e6d517a36b3723b631de6259","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-24T08:56:58Z","title_canon_sha256":"879c9ee04c20ac35b76bef925f42e5961377ba8781be104ec837bd16b88a05e2"},"schema_version":"1.0","source":{"id":"1904.10701","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10701","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10701v1","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10701","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"pith_short_12","alias_value":"22SB5A7Q5ZEJ","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"22SB5A7Q5ZEJELZE","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"22SB5A7Q","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:67dbd51347fb443f845cdd75ebcbc6c2d2bb720db70f2afb4bf6572b4ff9d994","target":"graph","created_at":"2026-05-17T23:47:50Z","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":"In this paper, we present an improved algorithm for the All Pairs Non-decreasing Paths (APNP) problem on weighted simple digraphs, which has running time $\\tilde{O}(n^{\\frac{3 + \\omega}{2}}) = \\tilde{O}(n^{2.686})$. Here $n$ is the number of vertices, and $\\omega < 2.373$ is the exponent of time complexity of fast matrix multiplication [Williams 2012, Le Gall 2014]. This matches the current best upper bound for $(\\max, \\min)$-matrix product [Duan, Pettie 2009] which is reducible to APNP. Thus, further improvement for APNP will imply a faster algorithm for $(\\max, \\min)$-matrix product. The pre","authors_text":"Ce Jin, Hongxun Wu, Ran Duan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-24T08:56:58Z","title":"Faster Algorithms for All Pairs Non-decreasing Paths Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10701","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":"sha256:42fb1a68dc836715773bb172192b3b4a12aed113a02e7c899857cefe37ae6b9e","target":"record","created_at":"2026-05-17T23:47:50Z","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":"114c12928cb04c97ad33f291bd36615673f24cd0e6d517a36b3723b631de6259","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-24T08:56:58Z","title_canon_sha256":"879c9ee04c20ac35b76bef925f42e5961377ba8781be104ec837bd16b88a05e2"},"schema_version":"1.0","source":{"id":"1904.10701","kind":"arxiv","version":1}},"canonical_sha256":"d6a41e83f0ee48922f24642cb254351f72adfd0fb8c58b0fabf3794628a8e71e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6a41e83f0ee48922f24642cb254351f72adfd0fb8c58b0fabf3794628a8e71e","first_computed_at":"2026-05-17T23:47:50.275690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:50.275690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IDJN08pd41YwhFKM1pyUJWRj9f1JA0U0iyoqcS2I8n6ArlnQIA0bslNWYFVyISaZgrkn826AiLb5Yhia59XEBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:50.276135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.10701","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42fb1a68dc836715773bb172192b3b4a12aed113a02e7c899857cefe37ae6b9e","sha256:67dbd51347fb443f845cdd75ebcbc6c2d2bb720db70f2afb4bf6572b4ff9d994"],"state_sha256":"98970f15263435dd49d22c77eff3e5d3cbfc99d6f5ab9eb198b93d3c745a956f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Og+FQha5NTVsIzahj9/mymWGpPa9w8tmOvsx9/2nMPPJrV7L1FdO34UoWAvITun00uB6A9y57YfD47NLPgSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:06:35.837517Z","bundle_sha256":"1e53c2b2ceea53f7aca6df081ce73e877434e437e3b4d645ec526dd17e68e425"}}