{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MYJUAP4WIALHEMJKCWZ224BXVV","short_pith_number":"pith:MYJUAP4W","schema_version":"1.0","canonical_sha256":"6613403f96401672312a15b3ad7037ad65ca36177f7d95576fe819dc08788361","source":{"kind":"arxiv","id":"1707.05549","version":1},"attestation_state":"computed","paper":{"title":"Distinguishing Tournaments with Small Label Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Antoni Lozano","submitted_at":"2017-07-18T10:14:53Z","abstract_excerpt":"A $d$-distinguishing vertex (arc) labeling of a digraph is a vertex (arc) labeling using $d$ labels that is not preserved by any nontrivial automorphism. Let $\\rho(T)$ ($\\rho'(T)$) be the minimum size of a label class in a 2-distinguishing vertex (arc) labeling of a tournament $T$. Gluck's Theorem implies that $\\rho(T) \\le \\lfloor n/2 \\rfloor$ for any tournament $T$ of order $n$. In this paper we construct a family of tournaments $\\cal H$ such that $\\rho(T) \\ge \\lfloor n/2 \\rfloor$ for any order $n$ tournament in $\\cal H$. Additionally, we prove that $\\rho'(T) \\le \\lfloor 7n/36 \\rfloor + 3$ fo"},"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":"1707.05549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-18T10:14:53Z","cross_cats_sorted":[],"title_canon_sha256":"553778cdadc16b3610c9e36b3677d922c4b186f6482bf089750bf7500a6e46af","abstract_canon_sha256":"ad5c19b99751a61d129fdf58a966cae127ad20a172bbcbfd185a13d77697c6bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:02.060998Z","signature_b64":"t3X7X+ItqA/ivRdqq71kf4GezAVxOi+I3sUREjpI7DLvft1VMBzawSlOlOAaBWiNpC/MND2mbRW7RJd0X8nuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6613403f96401672312a15b3ad7037ad65ca36177f7d95576fe819dc08788361","last_reissued_at":"2026-05-18T00:40:02.060526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:02.060526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distinguishing Tournaments with Small Label Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Antoni Lozano","submitted_at":"2017-07-18T10:14:53Z","abstract_excerpt":"A $d$-distinguishing vertex (arc) labeling of a digraph is a vertex (arc) labeling using $d$ labels that is not preserved by any nontrivial automorphism. Let $\\rho(T)$ ($\\rho'(T)$) be the minimum size of a label class in a 2-distinguishing vertex (arc) labeling of a tournament $T$. Gluck's Theorem implies that $\\rho(T) \\le \\lfloor n/2 \\rfloor$ for any tournament $T$ of order $n$. In this paper we construct a family of tournaments $\\cal H$ such that $\\rho(T) \\ge \\lfloor n/2 \\rfloor$ for any order $n$ tournament in $\\cal H$. Additionally, we prove that $\\rho'(T) \\le \\lfloor 7n/36 \\rfloor + 3$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05549","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":"1707.05549","created_at":"2026-05-18T00:40:02.060591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.05549v1","created_at":"2026-05-18T00:40:02.060591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05549","created_at":"2026-05-18T00:40:02.060591+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYJUAP4WIALH","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYJUAP4WIALHEMJK","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYJUAP4W","created_at":"2026-05-18T12:31:31.346846+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/MYJUAP4WIALHEMJKCWZ224BXVV","json":"https://pith.science/pith/MYJUAP4WIALHEMJKCWZ224BXVV.json","graph_json":"https://pith.science/api/pith-number/MYJUAP4WIALHEMJKCWZ224BXVV/graph.json","events_json":"https://pith.science/api/pith-number/MYJUAP4WIALHEMJKCWZ224BXVV/events.json","paper":"https://pith.science/paper/MYJUAP4W"},"agent_actions":{"view_html":"https://pith.science/pith/MYJUAP4WIALHEMJKCWZ224BXVV","download_json":"https://pith.science/pith/MYJUAP4WIALHEMJKCWZ224BXVV.json","view_paper":"https://pith.science/paper/MYJUAP4W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.05549&json=true","fetch_graph":"https://pith.science/api/pith-number/MYJUAP4WIALHEMJKCWZ224BXVV/graph.json","fetch_events":"https://pith.science/api/pith-number/MYJUAP4WIALHEMJKCWZ224BXVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYJUAP4WIALHEMJKCWZ224BXVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYJUAP4WIALHEMJKCWZ224BXVV/action/storage_attestation","attest_author":"https://pith.science/pith/MYJUAP4WIALHEMJKCWZ224BXVV/action/author_attestation","sign_citation":"https://pith.science/pith/MYJUAP4WIALHEMJKCWZ224BXVV/action/citation_signature","submit_replication":"https://pith.science/pith/MYJUAP4WIALHEMJKCWZ224BXVV/action/replication_record"}},"created_at":"2026-05-18T00:40:02.060591+00:00","updated_at":"2026-05-18T00:40:02.060591+00:00"}