{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:VREBRIV76HZEKXFKQ22JKJEKHF","short_pith_number":"pith:VREBRIV7","canonical_record":{"source":{"id":"2302.04050","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-02-08T13:44:14Z","cross_cats_sorted":[],"title_canon_sha256":"ae9a486a0393a8523e211ee811de08a7441b1d54eefc47cfddbf9a82594f9d18","abstract_canon_sha256":"f6477314b659b1ae88774c7ab6fca956328a44be893035e3a796f3a77e2c4111"},"schema_version":"1.0"},"canonical_sha256":"ac4818a2bff1f2455caa86b495248a3941a9f83bec76b1de0bdf65ca19fff4ae","source":{"kind":"arxiv","id":"2302.04050","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.04050","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"2302.04050v1","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.04050","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"VREBRIV76HZE","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"pith_short_16","alias_value":"VREBRIV76HZEKXFK","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"pith_short_8","alias_value":"VREBRIV7","created_at":"2026-07-05T05:40:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:VREBRIV76HZEKXFKQ22JKJEKHF","target":"record","payload":{"canonical_record":{"source":{"id":"2302.04050","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-02-08T13:44:14Z","cross_cats_sorted":[],"title_canon_sha256":"ae9a486a0393a8523e211ee811de08a7441b1d54eefc47cfddbf9a82594f9d18","abstract_canon_sha256":"f6477314b659b1ae88774c7ab6fca956328a44be893035e3a796f3a77e2c4111"},"schema_version":"1.0"},"canonical_sha256":"ac4818a2bff1f2455caa86b495248a3941a9f83bec76b1de0bdf65ca19fff4ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:40:00.519327Z","signature_b64":"uRlA5RuaP2p6xVPSNqFX/zI639T7IN+2Au0OAqd6OMOnzORypu34t72nSyU89o9Vu529neYmPmjH6NBvzcS/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac4818a2bff1f2455caa86b495248a3941a9f83bec76b1de0bdf65ca19fff4ae","last_reissued_at":"2026-07-05T05:40:00.518985Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:40:00.518985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.04050","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":"2026-07-05T05:40:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2onnPEhcS0qEjesP+vYaHe7Egu+sWRMJjii/GhlAtOnJcT+YyQBColL+QN3ZwzMN8n4jGy+vi7DDExBCDWPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T21:20:47.081252Z"},"content_sha256":"25607daf9ec98d01c7c4a2a9011974ee4e53059cfd03c2b4bf562579538f6b62","schema_version":"1.0","event_id":"sha256:25607daf9ec98d01c7c4a2a9011974ee4e53059cfd03c2b4bf562579538f6b62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:VREBRIV76HZEKXFKQ22JKJEKHF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal bisections of directed graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chunlei Zu, Guanwu Liu, Jie Ma","submitted_at":"2023-02-08T13:44:14Z","abstract_excerpt":"In this paper, motivated by a problem of Scott and a conjecture of Lee, Loh and Sudakov we consider bisections of directed graphs. We prove that every directed graph with $m$ arcs and minimum semidegree at least $d$ admits a bisection in which at least $\\left(\\frac{d}{2(2d+1)}+o(1)\\right)m$ arcs cross in each direction. This provides an optimal bound as well as a positive answer to a question of Hou and Wu in a stronger form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.04050","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/2302.04050/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":"2026-07-05T05:40:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h432xWyrYdUqVK4ZZ5QX0Hks89Qzwk1Z/K65q3DZl5JdgZyBpJm7JL67e7qGTxizbyh7VVF7UpvOmMxsmKd9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T21:20:47.081961Z"},"content_sha256":"0fd61b6c19a89a36d25f31d1bf26cf9fbdd9845e21cca4f5b6fb3f632f236951","schema_version":"1.0","event_id":"sha256:0fd61b6c19a89a36d25f31d1bf26cf9fbdd9845e21cca4f5b6fb3f632f236951"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VREBRIV76HZEKXFKQ22JKJEKHF/bundle.json","state_url":"https://pith.science/pith/VREBRIV76HZEKXFKQ22JKJEKHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VREBRIV76HZEKXFKQ22JKJEKHF/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":"2026-08-18T21:20:47Z","links":{"resolver":"https://pith.science/pith/VREBRIV76HZEKXFKQ22JKJEKHF","bundle":"https://pith.science/pith/VREBRIV76HZEKXFKQ22JKJEKHF/bundle.json","state":"https://pith.science/pith/VREBRIV76HZEKXFKQ22JKJEKHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VREBRIV76HZEKXFKQ22JKJEKHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VREBRIV76HZEKXFKQ22JKJEKHF","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":"f6477314b659b1ae88774c7ab6fca956328a44be893035e3a796f3a77e2c4111","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-02-08T13:44:14Z","title_canon_sha256":"ae9a486a0393a8523e211ee811de08a7441b1d54eefc47cfddbf9a82594f9d18"},"schema_version":"1.0","source":{"id":"2302.04050","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.04050","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"2302.04050v1","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.04050","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"VREBRIV76HZE","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"pith_short_16","alias_value":"VREBRIV76HZEKXFK","created_at":"2026-07-05T05:40:00Z"},{"alias_kind":"pith_short_8","alias_value":"VREBRIV7","created_at":"2026-07-05T05:40:00Z"}],"graph_snapshots":[{"event_id":"sha256:0fd61b6c19a89a36d25f31d1bf26cf9fbdd9845e21cca4f5b6fb3f632f236951","target":"graph","created_at":"2026-07-05T05:40:00Z","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/2302.04050/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, motivated by a problem of Scott and a conjecture of Lee, Loh and Sudakov we consider bisections of directed graphs. We prove that every directed graph with $m$ arcs and minimum semidegree at least $d$ admits a bisection in which at least $\\left(\\frac{d}{2(2d+1)}+o(1)\\right)m$ arcs cross in each direction. This provides an optimal bound as well as a positive answer to a question of Hou and Wu in a stronger form.","authors_text":"Chunlei Zu, Guanwu Liu, Jie Ma","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-02-08T13:44:14Z","title":"Optimal bisections of directed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.04050","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":"sha256:25607daf9ec98d01c7c4a2a9011974ee4e53059cfd03c2b4bf562579538f6b62","target":"record","created_at":"2026-07-05T05:40:00Z","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":"f6477314b659b1ae88774c7ab6fca956328a44be893035e3a796f3a77e2c4111","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-02-08T13:44:14Z","title_canon_sha256":"ae9a486a0393a8523e211ee811de08a7441b1d54eefc47cfddbf9a82594f9d18"},"schema_version":"1.0","source":{"id":"2302.04050","kind":"arxiv","version":1}},"canonical_sha256":"ac4818a2bff1f2455caa86b495248a3941a9f83bec76b1de0bdf65ca19fff4ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac4818a2bff1f2455caa86b495248a3941a9f83bec76b1de0bdf65ca19fff4ae","first_computed_at":"2026-07-05T05:40:00.518985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:40:00.518985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uRlA5RuaP2p6xVPSNqFX/zI639T7IN+2Au0OAqd6OMOnzORypu34t72nSyU89o9Vu529neYmPmjH6NBvzcS/CA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:40:00.519327Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.04050","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25607daf9ec98d01c7c4a2a9011974ee4e53059cfd03c2b4bf562579538f6b62","sha256:0fd61b6c19a89a36d25f31d1bf26cf9fbdd9845e21cca4f5b6fb3f632f236951"],"state_sha256":"ff629670d227a9bf39ea3b9c7a7c043c64bb4e3aaad5f03e519d15822ba7be5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eSMEJXnJsboKjLNFFrVsAOCT/i71LURiKZ2icdeOdykaqKm7+63U+aYhUCq8JnVCiVUkVJHSHpVqjbeaplUJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T21:20:47.087903Z","bundle_sha256":"c42371c20354f85a0da09345461c403b300bc7da57e3d2c8b08814e84aa97922"}}