{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5O6ZRE3K6NADGEMQNH5SNUEF2M","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":"5854477afadadc22cb2af2b2917966ae354dd08845b4958f1d594d35f6c14fd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-02T11:42:15Z","title_canon_sha256":"b496163eb9c5be1f439204fa2970b74dfb9266541e79b42de3f6335e6c5535bf"},"schema_version":"1.0","source":{"id":"1011.0580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0580","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0580v1","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0580","created_at":"2026-05-18T04:37:21Z"},{"alias_kind":"pith_short_12","alias_value":"5O6ZRE3K6NAD","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5O6ZRE3K6NADGEMQ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5O6ZRE3K","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:000413d2a2cc9bb00fd99b0673ef84792420dc64af1fcd3759bda7626b3b96ef","target":"graph","created_at":"2026-05-18T04:37:21Z","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":"Ramsey theory for words over a finite alphabet was unified in the work of Carlson and Furstenberg-Katznelson. Carlson, in the same work, outlined a method to extend the theory for words over an infinite alphabet, but subject to a fixed dominating principle, proving in particular an Ellentuck version, and a corresponding Ramsey theorem for k=1. In the present work we develop in a systematic way a Ramsey theory for words (in fact for {\\omega}-Z*-located words) over a doubly infinite alphabet extending Carlson's approach (to countable ordinals and Schreier-type families), and we apply this theory","authors_text":"Andreas Koutsogiannis, Vassiliki Farmaki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-02T11:42:15Z","title":"Ramsey Theory for Words Representing Rationals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0580","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:e0349f588ddef497227b2b61663135fef8ee1204e9a63ad22c90fd07245bf88b","target":"record","created_at":"2026-05-18T04:37:21Z","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":"5854477afadadc22cb2af2b2917966ae354dd08845b4958f1d594d35f6c14fd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-02T11:42:15Z","title_canon_sha256":"b496163eb9c5be1f439204fa2970b74dfb9266541e79b42de3f6335e6c5535bf"},"schema_version":"1.0","source":{"id":"1011.0580","kind":"arxiv","version":1}},"canonical_sha256":"ebbd98936af34033119069fb26d085d30cc2d4b779035d28508d7b3e141d9379","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebbd98936af34033119069fb26d085d30cc2d4b779035d28508d7b3e141d9379","first_computed_at":"2026-05-18T04:37:21.308977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:21.308977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o6DWB8z5QSJS4i4Rqztl+hwMDym4avippk5GORsdfateiP77HotMo3mfXh3+4CvG6ND9lM0NHbsKFi865O5ABw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:21.309473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0349f588ddef497227b2b61663135fef8ee1204e9a63ad22c90fd07245bf88b","sha256:000413d2a2cc9bb00fd99b0673ef84792420dc64af1fcd3759bda7626b3b96ef"],"state_sha256":"a65a85654b4135db444dc2ae986b811d8027a46eb5faf132181bd943fd1a23a3"}