{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YMZA6XAB3GPYL2ERJY77FXB5EO","short_pith_number":"pith:YMZA6XAB","schema_version":"1.0","canonical_sha256":"c3320f5c01d99f85e8914e3ff2dc3d23a4f7b96d8987509c4afc5950de9f8f89","source":{"kind":"arxiv","id":"1110.2776","version":2},"attestation_state":"computed","paper":{"title":"Graph Reachability and Pebble Automata over Infinite Alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.FL","authors_text":"Tony Tan","submitted_at":"2011-10-12T18:23:36Z","abstract_excerpt":"Let D denote an infinite alphabet -- a set that consists of infinitely many symbols. A word w = a_0 b_0 a_1 b_1 ... a_n b_n of even length over D can be viewed as a directed graph G_w whose vertices are the symbols that appear in w, and the edges are (a_0,b_0),(a_1,b_1),...,(a_n,b_n). For a positive integer m, define a language R_m such that a word w = a_0 b_0 ... a_n b_n is in R_m if and only if there is a path in the graph G_w of length <= m from the vertex a_0 to the vertex b_n.\n  We establish the following hierarchy theorem for pebble automata over infinite alphabet. For every positive int"},"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":"1110.2776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2011-10-12T18:23:36Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"62a141154c3f86ab682d1b159eff53c3bc702fa92631cc0b004d8a90580cf97c","abstract_canon_sha256":"68e7ca6ad271c804c61a248979c76e895223eff99edceac55378aa0c7c5cb1f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:13.963525Z","signature_b64":"Cr/rkSKYp4sJpQ2Ye+QU+2fiOtPux55IwrExLvPMLi+X5vJTqCKdk+qvPvP4cSrT8gykHZe59nhc6xhm+tNPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3320f5c01d99f85e8914e3ff2dc3d23a4f7b96d8987509c4afc5950de9f8f89","last_reissued_at":"2026-05-18T03:58:13.962999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:13.962999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graph Reachability and Pebble Automata over Infinite Alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.FL","authors_text":"Tony Tan","submitted_at":"2011-10-12T18:23:36Z","abstract_excerpt":"Let D denote an infinite alphabet -- a set that consists of infinitely many symbols. A word w = a_0 b_0 a_1 b_1 ... a_n b_n of even length over D can be viewed as a directed graph G_w whose vertices are the symbols that appear in w, and the edges are (a_0,b_0),(a_1,b_1),...,(a_n,b_n). For a positive integer m, define a language R_m such that a word w = a_0 b_0 ... a_n b_n is in R_m if and only if there is a path in the graph G_w of length <= m from the vertex a_0 to the vertex b_n.\n  We establish the following hierarchy theorem for pebble automata over infinite alphabet. For every positive int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2776","kind":"arxiv","version":2},"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":"1110.2776","created_at":"2026-05-18T03:58:13.963081+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.2776v2","created_at":"2026-05-18T03:58:13.963081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2776","created_at":"2026-05-18T03:58:13.963081+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMZA6XAB3GPY","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMZA6XAB3GPYL2ER","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMZA6XAB","created_at":"2026-05-18T12:26:47.523578+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/YMZA6XAB3GPYL2ERJY77FXB5EO","json":"https://pith.science/pith/YMZA6XAB3GPYL2ERJY77FXB5EO.json","graph_json":"https://pith.science/api/pith-number/YMZA6XAB3GPYL2ERJY77FXB5EO/graph.json","events_json":"https://pith.science/api/pith-number/YMZA6XAB3GPYL2ERJY77FXB5EO/events.json","paper":"https://pith.science/paper/YMZA6XAB"},"agent_actions":{"view_html":"https://pith.science/pith/YMZA6XAB3GPYL2ERJY77FXB5EO","download_json":"https://pith.science/pith/YMZA6XAB3GPYL2ERJY77FXB5EO.json","view_paper":"https://pith.science/paper/YMZA6XAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.2776&json=true","fetch_graph":"https://pith.science/api/pith-number/YMZA6XAB3GPYL2ERJY77FXB5EO/graph.json","fetch_events":"https://pith.science/api/pith-number/YMZA6XAB3GPYL2ERJY77FXB5EO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMZA6XAB3GPYL2ERJY77FXB5EO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMZA6XAB3GPYL2ERJY77FXB5EO/action/storage_attestation","attest_author":"https://pith.science/pith/YMZA6XAB3GPYL2ERJY77FXB5EO/action/author_attestation","sign_citation":"https://pith.science/pith/YMZA6XAB3GPYL2ERJY77FXB5EO/action/citation_signature","submit_replication":"https://pith.science/pith/YMZA6XAB3GPYL2ERJY77FXB5EO/action/replication_record"}},"created_at":"2026-05-18T03:58:13.963081+00:00","updated_at":"2026-05-18T03:58:13.963081+00:00"}