{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:KESXRJ45SPQ5JDOMGAGKWNU4PH","short_pith_number":"pith:KESXRJ45","schema_version":"1.0","canonical_sha256":"512578a79d93e1d48dcc300cab369c79e3ad6ae6e45f2af2485eedff5ec52d15","source":{"kind":"arxiv","id":"1107.5896","version":1},"attestation_state":"computed","paper":{"title":"Decision Problems for Recognizable Languages of Infinite Pictures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Olivier Finkel (ELM)","submitted_at":"2011-07-29T08:48:07Z","abstract_excerpt":"Altenbernd, Thomas and W\\\"ohrle have considered in [ATW02] acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\\\"uchi and Muller ones, firstly used for infinite words. Many classical decision problems are studied in formal language theory and in automata theory and arise now naturally about recognizable languages of infinite pictures. We first review in this paper some recent results of [Fin09b] where we gave the exact degree of numerous undecidable problems for B\\\"uchi-recognizable languages"},"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":"1107.5896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-07-29T08:48:07Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"3645eeff65fdd5371d78b0489aa709ab7464c2530dc86be7857e89175c7152aa","abstract_canon_sha256":"cc16004cb32d2d9a4a22e892c4f2adae97432801f04b2198da7f530abc1d7423"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:30.475991Z","signature_b64":"qii+4PwTYSvCUg/ZnvbwqbLxeIfsHGPIFpyHxmAySs3Kj0iUtnKbSejvyQb9kIKPT1C+8aH7yhp8RmpRE5nYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"512578a79d93e1d48dcc300cab369c79e3ad6ae6e45f2af2485eedff5ec52d15","last_reissued_at":"2026-05-18T04:16:30.475337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:30.475337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decision Problems for Recognizable Languages of Infinite Pictures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Olivier Finkel (ELM)","submitted_at":"2011-07-29T08:48:07Z","abstract_excerpt":"Altenbernd, Thomas and W\\\"ohrle have considered in [ATW02] acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\\\"uchi and Muller ones, firstly used for infinite words. Many classical decision problems are studied in formal language theory and in automata theory and arise now naturally about recognizable languages of infinite pictures. We first review in this paper some recent results of [Fin09b] where we gave the exact degree of numerous undecidable problems for B\\\"uchi-recognizable languages"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5896","kind":"arxiv","version":1},"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":"1107.5896","created_at":"2026-05-18T04:16:30.475438+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.5896v1","created_at":"2026-05-18T04:16:30.475438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5896","created_at":"2026-05-18T04:16:30.475438+00:00"},{"alias_kind":"pith_short_12","alias_value":"KESXRJ45SPQ5","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"KESXRJ45SPQ5JDOM","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"KESXRJ45","created_at":"2026-05-18T12:26:32.869790+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/KESXRJ45SPQ5JDOMGAGKWNU4PH","json":"https://pith.science/pith/KESXRJ45SPQ5JDOMGAGKWNU4PH.json","graph_json":"https://pith.science/api/pith-number/KESXRJ45SPQ5JDOMGAGKWNU4PH/graph.json","events_json":"https://pith.science/api/pith-number/KESXRJ45SPQ5JDOMGAGKWNU4PH/events.json","paper":"https://pith.science/paper/KESXRJ45"},"agent_actions":{"view_html":"https://pith.science/pith/KESXRJ45SPQ5JDOMGAGKWNU4PH","download_json":"https://pith.science/pith/KESXRJ45SPQ5JDOMGAGKWNU4PH.json","view_paper":"https://pith.science/paper/KESXRJ45","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.5896&json=true","fetch_graph":"https://pith.science/api/pith-number/KESXRJ45SPQ5JDOMGAGKWNU4PH/graph.json","fetch_events":"https://pith.science/api/pith-number/KESXRJ45SPQ5JDOMGAGKWNU4PH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KESXRJ45SPQ5JDOMGAGKWNU4PH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KESXRJ45SPQ5JDOMGAGKWNU4PH/action/storage_attestation","attest_author":"https://pith.science/pith/KESXRJ45SPQ5JDOMGAGKWNU4PH/action/author_attestation","sign_citation":"https://pith.science/pith/KESXRJ45SPQ5JDOMGAGKWNU4PH/action/citation_signature","submit_replication":"https://pith.science/pith/KESXRJ45SPQ5JDOMGAGKWNU4PH/action/replication_record"}},"created_at":"2026-05-18T04:16:30.475438+00:00","updated_at":"2026-05-18T04:16:30.475438+00:00"}