{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RECZ76ANDHSDRNNSLZFJT2B5JP","short_pith_number":"pith:RECZ76AN","canonical_record":{"source":{"id":"1104.4728","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-04-25T14:44:26Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"0909a84c027d9f08f1199cca9ac7fe4941438f448e4977713c7c945121f4982f","abstract_canon_sha256":"a1651bd4e76adab1cd3fb501020576275b3f89ebfd8d171b2497821f21b6e719"},"schema_version":"1.0"},"canonical_sha256":"89059ff80d19e438b5b25e4a99e83d4bfd3c93b963c1f12fb4f1b810a7b2100d","source":{"kind":"arxiv","id":"1104.4728","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4728","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4728v2","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4728","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"RECZ76ANDHSD","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RECZ76ANDHSDRNNS","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RECZ76AN","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RECZ76ANDHSDRNNSLZFJT2B5JP","target":"record","payload":{"canonical_record":{"source":{"id":"1104.4728","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-04-25T14:44:26Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"0909a84c027d9f08f1199cca9ac7fe4941438f448e4977713c7c945121f4982f","abstract_canon_sha256":"a1651bd4e76adab1cd3fb501020576275b3f89ebfd8d171b2497821f21b6e719"},"schema_version":"1.0"},"canonical_sha256":"89059ff80d19e438b5b25e4a99e83d4bfd3c93b963c1f12fb4f1b810a7b2100d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:31.657853Z","signature_b64":"K7VnDfXZOrD9Syc9TMCdZuksxRWykxcaiYHnOmPtJwGlw0mJIzrN1xZDwTLEjJ1V/O4EzB2HFBDPGU6AvZV1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89059ff80d19e438b5b25e4a99e83d4bfd3c93b963c1f12fb4f1b810a7b2100d","last_reissued_at":"2026-05-18T04:22:31.657438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:31.657438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.4728","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TmXalIP1PZA0EMaafoSUQFqSGGQ0U4UPu+cgtR4uXxv+zdqR7sjcoPyY2gFcNlW0GDfGUJIGrHAVNPKYG4n7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:53:09.817853Z"},"content_sha256":"28cdb5622878710d4017ed9a895e0f8b57048c9b982fcea4257c23eaafc8d093","schema_version":"1.0","event_id":"sha256:28cdb5622878710d4017ed9a895e0f8b57048c9b982fcea4257c23eaafc8d093"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RECZ76ANDHSDRNNSLZFJT2B5JP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiple-Source Single-Sink Maximum Flow in Directed Planar Graphs in O(diameter*n*log(n)) Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Philip N. Klein, Shay Mozes","submitted_at":"2011-04-25T14:44:26Z","abstract_excerpt":"We develop a new technique for computing maximum flow in directed planar graphs with multiple sources and a single sink that significantly deviates from previously known techniques for flow problems. This gives rise to an O(diameter*n*log(n)) algorithm for the problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4728","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":""},"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":"2026-05-18T04:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GMIhkaZfHn772kEjrreiS3UStzEBHVpSYiVgsw5uLm2wHjN9l51UdTrkHp8qO3xpejuliusAc9RWxDEQGJf9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:53:09.818198Z"},"content_sha256":"3b0f33361a61d16a675d0517abc6f32a563e4faae4d0754e3a36999d223331ae","schema_version":"1.0","event_id":"sha256:3b0f33361a61d16a675d0517abc6f32a563e4faae4d0754e3a36999d223331ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RECZ76ANDHSDRNNSLZFJT2B5JP/bundle.json","state_url":"https://pith.science/pith/RECZ76ANDHSDRNNSLZFJT2B5JP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RECZ76ANDHSDRNNSLZFJT2B5JP/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":"2026-06-20T02:53:09Z","links":{"resolver":"https://pith.science/pith/RECZ76ANDHSDRNNSLZFJT2B5JP","bundle":"https://pith.science/pith/RECZ76ANDHSDRNNSLZFJT2B5JP/bundle.json","state":"https://pith.science/pith/RECZ76ANDHSDRNNSLZFJT2B5JP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RECZ76ANDHSDRNNSLZFJT2B5JP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RECZ76ANDHSDRNNSLZFJT2B5JP","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":"a1651bd4e76adab1cd3fb501020576275b3f89ebfd8d171b2497821f21b6e719","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-04-25T14:44:26Z","title_canon_sha256":"0909a84c027d9f08f1199cca9ac7fe4941438f448e4977713c7c945121f4982f"},"schema_version":"1.0","source":{"id":"1104.4728","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4728","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4728v2","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4728","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"RECZ76ANDHSD","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RECZ76ANDHSDRNNS","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RECZ76AN","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:3b0f33361a61d16a675d0517abc6f32a563e4faae4d0754e3a36999d223331ae","target":"graph","created_at":"2026-05-18T04:22:31Z","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":"We develop a new technique for computing maximum flow in directed planar graphs with multiple sources and a single sink that significantly deviates from previously known techniques for flow problems. This gives rise to an O(diameter*n*log(n)) algorithm for the problem.","authors_text":"Philip N. Klein, Shay Mozes","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-04-25T14:44:26Z","title":"Multiple-Source Single-Sink Maximum Flow in Directed Planar Graphs in O(diameter*n*log(n)) Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4728","kind":"arxiv","version":2},"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":"sha256:28cdb5622878710d4017ed9a895e0f8b57048c9b982fcea4257c23eaafc8d093","target":"record","created_at":"2026-05-18T04:22:31Z","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":"a1651bd4e76adab1cd3fb501020576275b3f89ebfd8d171b2497821f21b6e719","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-04-25T14:44:26Z","title_canon_sha256":"0909a84c027d9f08f1199cca9ac7fe4941438f448e4977713c7c945121f4982f"},"schema_version":"1.0","source":{"id":"1104.4728","kind":"arxiv","version":2}},"canonical_sha256":"89059ff80d19e438b5b25e4a99e83d4bfd3c93b963c1f12fb4f1b810a7b2100d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89059ff80d19e438b5b25e4a99e83d4bfd3c93b963c1f12fb4f1b810a7b2100d","first_computed_at":"2026-05-18T04:22:31.657438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:31.657438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K7VnDfXZOrD9Syc9TMCdZuksxRWykxcaiYHnOmPtJwGlw0mJIzrN1xZDwTLEjJ1V/O4EzB2HFBDPGU6AvZV1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:31.657853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4728","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28cdb5622878710d4017ed9a895e0f8b57048c9b982fcea4257c23eaafc8d093","sha256:3b0f33361a61d16a675d0517abc6f32a563e4faae4d0754e3a36999d223331ae"],"state_sha256":"2172414e564e3d474636c3d86b68282637f55bd42820aff85d4a7ae84c00505b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jon2BtA159b49QIzzTaXqHPVS/7Umf1GyxNGnloGxJpVg+Lx/mQAoEfEKuviERYSm0Dl6Rcws7EP5M0p9xfLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T02:53:09.820217Z","bundle_sha256":"a47a83e70abbbc09db8e8114012b4cf9125eddcbac38a5dce5ba679a84565eda"}}