{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:V52RYXS2YFRNNEXGJOX7XVUE57","short_pith_number":"pith:V52RYXS2","canonical_record":{"source":{"id":"1403.6307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-25T11:25:23Z","cross_cats_sorted":[],"title_canon_sha256":"d31ea2138cbce4fc4ea8ed6b5ecf161e3d1feb58ac282636ccffd36c66204a0f","abstract_canon_sha256":"3c71954dd37e6dec6fe949025f17fb8fddaed487b88d840c7b03d3567c27a494"},"schema_version":"1.0"},"canonical_sha256":"af751c5e5ac162d692e64baffbd684efe60519a199ea7ef1f16a4417c3554c55","source":{"kind":"arxiv","id":"1403.6307","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6307","created_at":"2026-05-18T02:55:37Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6307v1","created_at":"2026-05-18T02:55:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6307","created_at":"2026-05-18T02:55:37Z"},{"alias_kind":"pith_short_12","alias_value":"V52RYXS2YFRN","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V52RYXS2YFRNNEXG","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V52RYXS2","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:V52RYXS2YFRNNEXGJOX7XVUE57","target":"record","payload":{"canonical_record":{"source":{"id":"1403.6307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-25T11:25:23Z","cross_cats_sorted":[],"title_canon_sha256":"d31ea2138cbce4fc4ea8ed6b5ecf161e3d1feb58ac282636ccffd36c66204a0f","abstract_canon_sha256":"3c71954dd37e6dec6fe949025f17fb8fddaed487b88d840c7b03d3567c27a494"},"schema_version":"1.0"},"canonical_sha256":"af751c5e5ac162d692e64baffbd684efe60519a199ea7ef1f16a4417c3554c55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:37.253477Z","signature_b64":"BR73bXk3OvHKth1PfSwG4NvVo8JK3lNfwOqgEzIhgz3sLBOPJNWlih+W9FwVGr0gmhVmRldcQACLXGHoFD34Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af751c5e5ac162d692e64baffbd684efe60519a199ea7ef1f16a4417c3554c55","last_reissued_at":"2026-05-18T02:55:37.252906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:37.252906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.6307","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":"2026-05-18T02:55:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3cx9e/dXITZ2SWoOhnZ1/yfoIkqo/SYYUJQDukKWAwAmzefA7oabOiowbAd/AAqTOWWLPb718dAEylI9KucGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:55:04.510647Z"},"content_sha256":"9e0fbab71356fed7be0102d36648f918c761c360a0e4bb7ae10741bb79c6bd0e","schema_version":"1.0","event_id":"sha256:9e0fbab71356fed7be0102d36648f918c761c360a0e4bb7ae10741bb79c6bd0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:V52RYXS2YFRNNEXGJOX7XVUE57","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Grant Cairns, Stacey Mendan, Yuri Nikolayevsky","submitted_at":"2014-03-25T11:25:23Z","abstract_excerpt":"We give a sharp refinement of a result of Alon, Ben-Shimon and Krivelevich. This gives a sufficient condition for a finite sequence of positive integers to be the vertex degree list of both parts of a bipartite graph. The condition depends only on the length of the sequence and its largest and smallest elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6307","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":"2026-05-18T02:55:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"39ahX6epa4pKQlXzpK1tSuVJMspLhM3PeSzJBqTJbb35lEy8lEmZMflTQniN9CgTjpu2MpHE7cRAtWRWjL1xAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:55:04.511241Z"},"content_sha256":"3b1465c185245ae1b53ec9953f186ec22888b03d3468c3c973e609572ffa9642","schema_version":"1.0","event_id":"sha256:3b1465c185245ae1b53ec9953f186ec22888b03d3468c3c973e609572ffa9642"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V52RYXS2YFRNNEXGJOX7XVUE57/bundle.json","state_url":"https://pith.science/pith/V52RYXS2YFRNNEXGJOX7XVUE57/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V52RYXS2YFRNNEXGJOX7XVUE57/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":"2026-05-27T15:55:04Z","links":{"resolver":"https://pith.science/pith/V52RYXS2YFRNNEXGJOX7XVUE57","bundle":"https://pith.science/pith/V52RYXS2YFRNNEXGJOX7XVUE57/bundle.json","state":"https://pith.science/pith/V52RYXS2YFRNNEXGJOX7XVUE57/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V52RYXS2YFRNNEXGJOX7XVUE57/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:V52RYXS2YFRNNEXGJOX7XVUE57","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":"3c71954dd37e6dec6fe949025f17fb8fddaed487b88d840c7b03d3567c27a494","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-25T11:25:23Z","title_canon_sha256":"d31ea2138cbce4fc4ea8ed6b5ecf161e3d1feb58ac282636ccffd36c66204a0f"},"schema_version":"1.0","source":{"id":"1403.6307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6307","created_at":"2026-05-18T02:55:37Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6307v1","created_at":"2026-05-18T02:55:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6307","created_at":"2026-05-18T02:55:37Z"},{"alias_kind":"pith_short_12","alias_value":"V52RYXS2YFRN","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V52RYXS2YFRNNEXG","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V52RYXS2","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:3b1465c185245ae1b53ec9953f186ec22888b03d3468c3c973e609572ffa9642","target":"graph","created_at":"2026-05-18T02:55:37Z","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 give a sharp refinement of a result of Alon, Ben-Shimon and Krivelevich. This gives a sufficient condition for a finite sequence of positive integers to be the vertex degree list of both parts of a bipartite graph. The condition depends only on the length of the sequence and its largest and smallest elements.","authors_text":"Grant Cairns, Stacey Mendan, Yuri Nikolayevsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-25T11:25:23Z","title":"A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6307","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":"sha256:9e0fbab71356fed7be0102d36648f918c761c360a0e4bb7ae10741bb79c6bd0e","target":"record","created_at":"2026-05-18T02:55:37Z","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":"3c71954dd37e6dec6fe949025f17fb8fddaed487b88d840c7b03d3567c27a494","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-25T11:25:23Z","title_canon_sha256":"d31ea2138cbce4fc4ea8ed6b5ecf161e3d1feb58ac282636ccffd36c66204a0f"},"schema_version":"1.0","source":{"id":"1403.6307","kind":"arxiv","version":1}},"canonical_sha256":"af751c5e5ac162d692e64baffbd684efe60519a199ea7ef1f16a4417c3554c55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af751c5e5ac162d692e64baffbd684efe60519a199ea7ef1f16a4417c3554c55","first_computed_at":"2026-05-18T02:55:37.252906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:37.252906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BR73bXk3OvHKth1PfSwG4NvVo8JK3lNfwOqgEzIhgz3sLBOPJNWlih+W9FwVGr0gmhVmRldcQACLXGHoFD34Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:37.253477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e0fbab71356fed7be0102d36648f918c761c360a0e4bb7ae10741bb79c6bd0e","sha256:3b1465c185245ae1b53ec9953f186ec22888b03d3468c3c973e609572ffa9642"],"state_sha256":"b358a44ae84d4d7075bed8056e7f96816388bd113ec6cd3f21c6a107fde467c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ir1os/HI4JCVzl3X/hWiQ056XpeSqxhP+FHAKgnxoeQs7ZrA0TmKHoiUhe71rHAzRYRTKj8xVVIlUpPBGaUbCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:55:04.513597Z","bundle_sha256":"f312268b4af0096cb5dc2e4f10b5ef0b6691164ff1972e5b9bde347f640042ac"}}