{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DQ5BNYBY3ITIKBRYRYU4TE27L7","short_pith_number":"pith:DQ5BNYBY","schema_version":"1.0","canonical_sha256":"1c3a16e038da268506388e29c9935f5fea4e965372b4cbeb85a0a1a2ebf63aad","source":{"kind":"arxiv","id":"1607.04431","version":1},"attestation_state":"computed","paper":{"title":"Edge-Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Jens M. Schmidt, Lena Schlipf","submitted_at":"2016-07-15T09:33:27Z","abstract_excerpt":"Canonical orderings and their relatives such as st-numberings have been used as a key tool in algorithmic graph theory for the last decades. Recently, a unifying concept behind all these orders has been shown: they can be described by a graph decomposition into parts that have a prescribed vertex-connectivity.\n  Despite extensive interest in canonical orderings, no analogue of this unifying concept is known for edge-connectivity. In this paper, we establish such a concept named edge-orders and show how to compute (1,1)-edge-orders of 2-edge-connected graphs as well as (2,1)-edge-orders of 3-ed"},"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":"1607.04431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-07-15T09:33:27Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"480fef988c9a73aef11b9ff5bd6a310d8e73ec7681cc6f6ab8facbd0011a5adb","abstract_canon_sha256":"71d425d90e9cdb52768c65f16ea27f6874357df057b2eb25b4db61fa25097b3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:01.254886Z","signature_b64":"1CQWY2Dfyjmai2NGclFMGP1KBF3Mr9wvK7ed81VOYK4vsMuayaeecAHx62HCRrNKwpE3Y6DhCQ8o7Fex/ef3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c3a16e038da268506388e29c9935f5fea4e965372b4cbeb85a0a1a2ebf63aad","last_reissued_at":"2026-05-18T01:11:01.254292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:01.254292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge-Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Jens M. Schmidt, Lena Schlipf","submitted_at":"2016-07-15T09:33:27Z","abstract_excerpt":"Canonical orderings and their relatives such as st-numberings have been used as a key tool in algorithmic graph theory for the last decades. Recently, a unifying concept behind all these orders has been shown: they can be described by a graph decomposition into parts that have a prescribed vertex-connectivity.\n  Despite extensive interest in canonical orderings, no analogue of this unifying concept is known for edge-connectivity. In this paper, we establish such a concept named edge-orders and show how to compute (1,1)-edge-orders of 2-edge-connected graphs as well as (2,1)-edge-orders of 3-ed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04431","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.04431","created_at":"2026-05-18T01:11:01.254368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.04431v1","created_at":"2026-05-18T01:11:01.254368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04431","created_at":"2026-05-18T01:11:01.254368+00:00"},{"alias_kind":"pith_short_12","alias_value":"DQ5BNYBY3ITI","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DQ5BNYBY3ITIKBRY","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DQ5BNYBY","created_at":"2026-05-18T12:30:12.583610+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/DQ5BNYBY3ITIKBRYRYU4TE27L7","json":"https://pith.science/pith/DQ5BNYBY3ITIKBRYRYU4TE27L7.json","graph_json":"https://pith.science/api/pith-number/DQ5BNYBY3ITIKBRYRYU4TE27L7/graph.json","events_json":"https://pith.science/api/pith-number/DQ5BNYBY3ITIKBRYRYU4TE27L7/events.json","paper":"https://pith.science/paper/DQ5BNYBY"},"agent_actions":{"view_html":"https://pith.science/pith/DQ5BNYBY3ITIKBRYRYU4TE27L7","download_json":"https://pith.science/pith/DQ5BNYBY3ITIKBRYRYU4TE27L7.json","view_paper":"https://pith.science/paper/DQ5BNYBY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.04431&json=true","fetch_graph":"https://pith.science/api/pith-number/DQ5BNYBY3ITIKBRYRYU4TE27L7/graph.json","fetch_events":"https://pith.science/api/pith-number/DQ5BNYBY3ITIKBRYRYU4TE27L7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DQ5BNYBY3ITIKBRYRYU4TE27L7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DQ5BNYBY3ITIKBRYRYU4TE27L7/action/storage_attestation","attest_author":"https://pith.science/pith/DQ5BNYBY3ITIKBRYRYU4TE27L7/action/author_attestation","sign_citation":"https://pith.science/pith/DQ5BNYBY3ITIKBRYRYU4TE27L7/action/citation_signature","submit_replication":"https://pith.science/pith/DQ5BNYBY3ITIKBRYRYU4TE27L7/action/replication_record"}},"created_at":"2026-05-18T01:11:01.254368+00:00","updated_at":"2026-05-18T01:11:01.254368+00:00"}