{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VDWCLGGIMOHGFOMGJ6MLUUKY7S","short_pith_number":"pith:VDWCLGGI","schema_version":"1.0","canonical_sha256":"a8ec2598c8638e62b9864f98ba5158fcbad7b3dd75f5f0dd7d88252a2df9d001","source":{"kind":"arxiv","id":"1512.08448","version":2},"attestation_state":"computed","paper":{"title":"On degree sequences of undirected, directed, and bidirected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Laura Gellert, Raman Sanyal","submitted_at":"2015-12-28T16:32:25Z","abstract_excerpt":"Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we extend the following four topics from (un)directed graphs to bidirected graphs:\n  - Erd\\H{o}s-Gallai-type results: characterization of net-degree sequences,\n  - Havel-Hakimi-type results: complete sets of degree-preserving operations,\n  - Extremal degree sequences: characterization of uniquely realizable sequences, and\n  - Enumerative aspects: counting formul"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.08448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-28T16:32:25Z","cross_cats_sorted":[],"title_canon_sha256":"99b3ccce69f6019bff9dc56b7ea0606687345d000d3c2616217a720c73281537","abstract_canon_sha256":"21f33fcbf6f207e31a90358c3027e42bb8159510bb6615b4f4e5921b2a07d12f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:49.599544Z","signature_b64":"n0zVSTzKCip8asbdUe17u75NZl9g+yMdRdByCVSNkbiMY3FER3w/ZfuPKtbv6i+taeGB2W/V/4ZuuobHSit+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8ec2598c8638e62b9864f98ba5158fcbad7b3dd75f5f0dd7d88252a2df9d001","last_reissued_at":"2026-05-18T00:46:49.598849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:49.598849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On degree sequences of undirected, directed, and bidirected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Laura Gellert, Raman Sanyal","submitted_at":"2015-12-28T16:32:25Z","abstract_excerpt":"Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we extend the following four topics from (un)directed graphs to bidirected graphs:\n  - Erd\\H{o}s-Gallai-type results: characterization of net-degree sequences,\n  - Havel-Hakimi-type results: complete sets of degree-preserving operations,\n  - Extremal degree sequences: characterization of uniquely realizable sequences, and\n  - Enumerative aspects: counting formul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08448","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.08448","created_at":"2026-05-18T00:46:49.598954+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.08448v2","created_at":"2026-05-18T00:46:49.598954+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08448","created_at":"2026-05-18T00:46:49.598954+00:00"},{"alias_kind":"pith_short_12","alias_value":"VDWCLGGIMOHG","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"VDWCLGGIMOHGFOMG","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"VDWCLGGI","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VDWCLGGIMOHGFOMGJ6MLUUKY7S","json":"https://pith.science/pith/VDWCLGGIMOHGFOMGJ6MLUUKY7S.json","graph_json":"https://pith.science/api/pith-number/VDWCLGGIMOHGFOMGJ6MLUUKY7S/graph.json","events_json":"https://pith.science/api/pith-number/VDWCLGGIMOHGFOMGJ6MLUUKY7S/events.json","paper":"https://pith.science/paper/VDWCLGGI"},"agent_actions":{"view_html":"https://pith.science/pith/VDWCLGGIMOHGFOMGJ6MLUUKY7S","download_json":"https://pith.science/pith/VDWCLGGIMOHGFOMGJ6MLUUKY7S.json","view_paper":"https://pith.science/paper/VDWCLGGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.08448&json=true","fetch_graph":"https://pith.science/api/pith-number/VDWCLGGIMOHGFOMGJ6MLUUKY7S/graph.json","fetch_events":"https://pith.science/api/pith-number/VDWCLGGIMOHGFOMGJ6MLUUKY7S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VDWCLGGIMOHGFOMGJ6MLUUKY7S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VDWCLGGIMOHGFOMGJ6MLUUKY7S/action/storage_attestation","attest_author":"https://pith.science/pith/VDWCLGGIMOHGFOMGJ6MLUUKY7S/action/author_attestation","sign_citation":"https://pith.science/pith/VDWCLGGIMOHGFOMGJ6MLUUKY7S/action/citation_signature","submit_replication":"https://pith.science/pith/VDWCLGGIMOHGFOMGJ6MLUUKY7S/action/replication_record"}},"created_at":"2026-05-18T00:46:49.598954+00:00","updated_at":"2026-05-18T00:46:49.598954+00:00"}