{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:466E537JSHLO6GB422LDBQW2JX","short_pith_number":"pith:466E537J","schema_version":"1.0","canonical_sha256":"e7bc4eefe991d6ef183cd69630c2da4df1b2bbf095c9499ba9f495e8bbda7cb5","source":{"kind":"arxiv","id":"1608.04866","version":4},"attestation_state":"computed","paper":{"title":"On the Distinguishing Number of Cyclic Tournaments: Towards the Albertson-Collins Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Eric Sopena (LaBRI), Kahina Meslem","submitted_at":"2016-08-17T06:20:15Z","abstract_excerpt":"A distinguishing $r$-labeling of a digraph $G$ is a mapping $\\lambda$ from the set of verticesof $G$ to the set of labels $\\{1,\\dots,r\\}$ such that no nontrivial automorphism of $G$ preserves all the labels.The distinguishing number $D(G)$ of $G$ is then the smallest $r$ for which $G$ admits a distinguishing $r$-labeling.From a result of Gluck (David Gluck, Trivial set-stabilizers in finite permutation groups,{\\em Can. J. Math.} 35(1) (1983), 59--67),it follows that $D(T)=2$ for every cyclic tournament~$T$ of (odd) order $2q+1\\ge 3$.Let $V(T)=\\{0,\\dots,2q\\}$ for every such tournament.Albertson"},"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":"1608.04866","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-17T06:20:15Z","cross_cats_sorted":[],"title_canon_sha256":"71612a3cbba65b2262420ea2cbf2a85ee0c04bd1338c2192505a6eba6705de99","abstract_canon_sha256":"9fadccdddce1844459f0418464dbfe30ec9527ffb0178b4df776b586be1b188d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:57.311907Z","signature_b64":"Mj48uMs/4m5wHCuTZJwKTd02qkqNb4iC4qrwMM+pGxZquCCsMXavHnxMqlpeDTZmqZ9CpFuqodPWKOk+zMohAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7bc4eefe991d6ef183cd69630c2da4df1b2bbf095c9499ba9f495e8bbda7cb5","last_reissued_at":"2026-05-18T00:03:57.311349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:57.311349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Distinguishing Number of Cyclic Tournaments: Towards the Albertson-Collins Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Eric Sopena (LaBRI), Kahina Meslem","submitted_at":"2016-08-17T06:20:15Z","abstract_excerpt":"A distinguishing $r$-labeling of a digraph $G$ is a mapping $\\lambda$ from the set of verticesof $G$ to the set of labels $\\{1,\\dots,r\\}$ such that no nontrivial automorphism of $G$ preserves all the labels.The distinguishing number $D(G)$ of $G$ is then the smallest $r$ for which $G$ admits a distinguishing $r$-labeling.From a result of Gluck (David Gluck, Trivial set-stabilizers in finite permutation groups,{\\em Can. J. Math.} 35(1) (1983), 59--67),it follows that $D(T)=2$ for every cyclic tournament~$T$ of (odd) order $2q+1\\ge 3$.Let $V(T)=\\{0,\\dots,2q\\}$ for every such tournament.Albertson"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04866","kind":"arxiv","version":4},"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":"1608.04866","created_at":"2026-05-18T00:03:57.311431+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.04866v4","created_at":"2026-05-18T00:03:57.311431+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04866","created_at":"2026-05-18T00:03:57.311431+00:00"},{"alias_kind":"pith_short_12","alias_value":"466E537JSHLO","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"466E537JSHLO6GB4","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"466E537J","created_at":"2026-05-18T12:29:58.707656+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/466E537JSHLO6GB422LDBQW2JX","json":"https://pith.science/pith/466E537JSHLO6GB422LDBQW2JX.json","graph_json":"https://pith.science/api/pith-number/466E537JSHLO6GB422LDBQW2JX/graph.json","events_json":"https://pith.science/api/pith-number/466E537JSHLO6GB422LDBQW2JX/events.json","paper":"https://pith.science/paper/466E537J"},"agent_actions":{"view_html":"https://pith.science/pith/466E537JSHLO6GB422LDBQW2JX","download_json":"https://pith.science/pith/466E537JSHLO6GB422LDBQW2JX.json","view_paper":"https://pith.science/paper/466E537J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.04866&json=true","fetch_graph":"https://pith.science/api/pith-number/466E537JSHLO6GB422LDBQW2JX/graph.json","fetch_events":"https://pith.science/api/pith-number/466E537JSHLO6GB422LDBQW2JX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/466E537JSHLO6GB422LDBQW2JX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/466E537JSHLO6GB422LDBQW2JX/action/storage_attestation","attest_author":"https://pith.science/pith/466E537JSHLO6GB422LDBQW2JX/action/author_attestation","sign_citation":"https://pith.science/pith/466E537JSHLO6GB422LDBQW2JX/action/citation_signature","submit_replication":"https://pith.science/pith/466E537JSHLO6GB422LDBQW2JX/action/replication_record"}},"created_at":"2026-05-18T00:03:57.311431+00:00","updated_at":"2026-05-18T00:03:57.311431+00:00"}