{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:Z4GTYOW74BZN22RG4UTMRR5MWP","short_pith_number":"pith:Z4GTYOW7","schema_version":"1.0","canonical_sha256":"cf0d3c3adfe072dd6a26e526c8c7acb3d342d150b52d7a9a4c2df5eb860bf3b9","source":{"kind":"arxiv","id":"1807.03331","version":1},"attestation_state":"computed","paper":{"title":"An Interesting Structural Property Related to the Problem of Computing All the Best Swap Edges of a Tree Spanner in Unweighted Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Davide Bil\\`o, Kleitos Papadopoulos","submitted_at":"2018-07-09T18:34:50Z","abstract_excerpt":"In this draft we prove an interesting structural property related to the problem of computing {\\em all the best swap edges} of a {\\em tree spanner} in unweighted graphs. Previous papers show that the maximum stretch factor of the tree where a failing edge is temporarily swapped with any other available edge that reconnects the tree depends only on the {\\em critical edge}. However, in principle, each of the $O(n^2)$ swap edges, where $n$ is the number of vertices of the tree, may have its own critical edge. In this draft we show that there are at most 6 critical edges, i.e., each tree edge $e$ "},"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":"1807.03331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-07-09T18:34:50Z","cross_cats_sorted":[],"title_canon_sha256":"444793a7cefebfde42900ce68164fb814ae9be4a88efed4e4ad64fe1792c8221","abstract_canon_sha256":"77cee623531ea05f397366a0cced7e63b764f1aec8b42cb3605d3c3643a4c9c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:10.803983Z","signature_b64":"fi0Of/FQ+E6wJ3PgDXlfZl6MPF/KctBkrJJ1ep2NHpYnISfAgw/N6q9bH3D8b/bBaCYGk1lcJ7QVI9Y2j2oMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf0d3c3adfe072dd6a26e526c8c7acb3d342d150b52d7a9a4c2df5eb860bf3b9","last_reissued_at":"2026-05-18T00:11:10.803247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:10.803247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Interesting Structural Property Related to the Problem of Computing All the Best Swap Edges of a Tree Spanner in Unweighted Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Davide Bil\\`o, Kleitos Papadopoulos","submitted_at":"2018-07-09T18:34:50Z","abstract_excerpt":"In this draft we prove an interesting structural property related to the problem of computing {\\em all the best swap edges} of a {\\em tree spanner} in unweighted graphs. Previous papers show that the maximum stretch factor of the tree where a failing edge is temporarily swapped with any other available edge that reconnects the tree depends only on the {\\em critical edge}. However, in principle, each of the $O(n^2)$ swap edges, where $n$ is the number of vertices of the tree, may have its own critical edge. In this draft we show that there are at most 6 critical edges, i.e., each tree edge $e$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03331","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":"1807.03331","created_at":"2026-05-18T00:11:10.803368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.03331v1","created_at":"2026-05-18T00:11:10.803368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03331","created_at":"2026-05-18T00:11:10.803368+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4GTYOW74BZN","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4GTYOW74BZN22RG","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4GTYOW7","created_at":"2026-05-18T12:33:04.347982+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/Z4GTYOW74BZN22RG4UTMRR5MWP","json":"https://pith.science/pith/Z4GTYOW74BZN22RG4UTMRR5MWP.json","graph_json":"https://pith.science/api/pith-number/Z4GTYOW74BZN22RG4UTMRR5MWP/graph.json","events_json":"https://pith.science/api/pith-number/Z4GTYOW74BZN22RG4UTMRR5MWP/events.json","paper":"https://pith.science/paper/Z4GTYOW7"},"agent_actions":{"view_html":"https://pith.science/pith/Z4GTYOW74BZN22RG4UTMRR5MWP","download_json":"https://pith.science/pith/Z4GTYOW74BZN22RG4UTMRR5MWP.json","view_paper":"https://pith.science/paper/Z4GTYOW7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.03331&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4GTYOW74BZN22RG4UTMRR5MWP/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4GTYOW74BZN22RG4UTMRR5MWP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4GTYOW74BZN22RG4UTMRR5MWP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4GTYOW74BZN22RG4UTMRR5MWP/action/storage_attestation","attest_author":"https://pith.science/pith/Z4GTYOW74BZN22RG4UTMRR5MWP/action/author_attestation","sign_citation":"https://pith.science/pith/Z4GTYOW74BZN22RG4UTMRR5MWP/action/citation_signature","submit_replication":"https://pith.science/pith/Z4GTYOW74BZN22RG4UTMRR5MWP/action/replication_record"}},"created_at":"2026-05-18T00:11:10.803368+00:00","updated_at":"2026-05-18T00:11:10.803368+00:00"}