{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IMARY3QBJ7XPZ5JUD7S4S5JT7M","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":"61b4d33cf77d42752c90ef64584e42345a7f09bf8b6080fef0ccaad38cd7b5c7","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T18:23:24Z","title_canon_sha256":"13cd5a947e529166e69f7f7d780cfcd39dda5b1565fd3f1a3bfcbb319f0c9607"},"schema_version":"1.0","source":{"id":"1301.5263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5263","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5263v1","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5263","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"IMARY3QBJ7XP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IMARY3QBJ7XPZ5JU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IMARY3QB","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:41898243f48bbef35ed3e16ad1ecdced252adb92f3b4c5784b0aa19a60453a5f","target":"graph","created_at":"2026-05-18T03:35:52Z","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":"We consider the following open question in the spirit of Ramsey theory: Given an aperiodic infinite word $w$, does there exist a finite coloring of its factors such that no factorization of $w$ is monochromatic? We show that such a coloring always exists whenever $w$ is a Sturmian word or a standard episturmian word.","authors_text":"Aldo de Luca, Elena V. Pribavkina, Luca Q. Zamboni","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T18:23:24Z","title":"A Coloring Problem for Sturmian and Episturmian Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5263","kind":"arxiv","version":1},"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:f2396e1b679572500da2d47582dbb8b4d514fd5a295d268044be30255ae32401","target":"record","created_at":"2026-05-18T03:35:52Z","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":"61b4d33cf77d42752c90ef64584e42345a7f09bf8b6080fef0ccaad38cd7b5c7","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T18:23:24Z","title_canon_sha256":"13cd5a947e529166e69f7f7d780cfcd39dda5b1565fd3f1a3bfcbb319f0c9607"},"schema_version":"1.0","source":{"id":"1301.5263","kind":"arxiv","version":1}},"canonical_sha256":"43011c6e014feefcf5341fe5c97533fb1068307e6c9354dd6feb73045bb9eac5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43011c6e014feefcf5341fe5c97533fb1068307e6c9354dd6feb73045bb9eac5","first_computed_at":"2026-05-18T03:35:52.433113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:52.433113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LM1zuZWm/MUeUAWUsE/iN4x0AxkjNFVaP4W+pKjft06V+RkzxSqsToEcP81+csyzpE/bHzr/aJT4dl1OLRcdCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:52.433956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2396e1b679572500da2d47582dbb8b4d514fd5a295d268044be30255ae32401","sha256:41898243f48bbef35ed3e16ad1ecdced252adb92f3b4c5784b0aa19a60453a5f"],"state_sha256":"ab4cd9042ad2e15189ee2c0677e2ca4cbe680a9ce4cb611b15c95223f74db6f5"}