{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:466E537JSHLO6GB422LDBQW2JX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9fadccdddce1844459f0418464dbfe30ec9527ffb0178b4df776b586be1b188d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-17T06:20:15Z","title_canon_sha256":"71612a3cbba65b2262420ea2cbf2a85ee0c04bd1338c2192505a6eba6705de99"},"schema_version":"1.0","source":{"id":"1608.04866","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04866","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04866v4","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04866","created_at":"2026-05-18T00:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"466E537JSHLO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"466E537JSHLO6GB4","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"466E537J","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:8036f5b7fda7e5b4fd3e44991ae5120da0f5e1b2d5d61ab77eecc382921a1ed9","target":"graph","created_at":"2026-05-18T00:03:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Eric Sopena (LaBRI), Kahina Meslem","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-17T06:20:15Z","title":"On the Distinguishing Number of Cyclic Tournaments: Towards the Albertson-Collins Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04866","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7f765d627f61cb49e56b8d95dab6fd11d9b41113c6cca50c16843b49808ddd1e","target":"record","created_at":"2026-05-18T00:03:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9fadccdddce1844459f0418464dbfe30ec9527ffb0178b4df776b586be1b188d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-08-17T06:20:15Z","title_canon_sha256":"71612a3cbba65b2262420ea2cbf2a85ee0c04bd1338c2192505a6eba6705de99"},"schema_version":"1.0","source":{"id":"1608.04866","kind":"arxiv","version":4}},"canonical_sha256":"e7bc4eefe991d6ef183cd69630c2da4df1b2bbf095c9499ba9f495e8bbda7cb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7bc4eefe991d6ef183cd69630c2da4df1b2bbf095c9499ba9f495e8bbda7cb5","first_computed_at":"2026-05-18T00:03:57.311349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:57.311349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mj48uMs/4m5wHCuTZJwKTd02qkqNb4iC4qrwMM+pGxZquCCsMXavHnxMqlpeDTZmqZ9CpFuqodPWKOk+zMohAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:57.311907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04866","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f765d627f61cb49e56b8d95dab6fd11d9b41113c6cca50c16843b49808ddd1e","sha256:8036f5b7fda7e5b4fd3e44991ae5120da0f5e1b2d5d61ab77eecc382921a1ed9"],"state_sha256":"24a3074ca5abfb58e520c4bb843c6cc40fe53839e2d8fbf7af8a125afc9a2a36"}