{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JJ2ITHX2ZRFSWPRLC5VDYOXGME","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":"6d3f1b8c95352ca45331d1339a72b5e39f48289c38432e31e608a02c3d864a2f","cross_cats_sorted":["cs.CC","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-03-26T15:39:35Z","title_canon_sha256":"4f2cb153b16beda577f7c2f7137db281e5fbff4fee6fd915bc09f6739a9d3218"},"schema_version":"1.0","source":{"id":"0903.4615","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4615","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4615v2","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4615","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"JJ2ITHX2ZRFS","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JJ2ITHX2ZRFSWPRL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JJ2ITHX2","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:c949b103d9584524eb2c4028b23305f62d30501cd407ab9d14c0eeac648435a3","target":"graph","created_at":"2026-05-18T04:40:08Z","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":"In a recent paper Sutner proved that the first-order theory of the phase-space $\\mathcal{S}_\\mathcal{A}=(Q^\\mathbb{Z}, \\longrightarrow)$ of a one-dimensional cellular automaton $\\mathcal{A}$ whose configurations are elements of $Q^\\mathbb{Z}$, for a finite set of states $Q$, and where $\\longrightarrow$ is the \"next configuration relation\", is decidable. He asked whether this result could be extended to a more expressive logic. We prove in this paper that this is actuallly the case. We first show that, for each one-dimensional cellular automaton $\\mathcal{A}$, the phase-space $\\mathcal{S}_\\math","authors_text":"LIP), Olivier Finkel (ELM","cross_cats":["cs.CC","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-03-26T15:39:35Z","title":"On Decidability Properties of One-Dimensional Cellular Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4615","kind":"arxiv","version":2},"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:e9b6d930f8aa25f8a44ef9969be516a711140daf4b439d90f8feb3faed92066d","target":"record","created_at":"2026-05-18T04:40:08Z","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":"6d3f1b8c95352ca45331d1339a72b5e39f48289c38432e31e608a02c3d864a2f","cross_cats_sorted":["cs.CC","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-03-26T15:39:35Z","title_canon_sha256":"4f2cb153b16beda577f7c2f7137db281e5fbff4fee6fd915bc09f6739a9d3218"},"schema_version":"1.0","source":{"id":"0903.4615","kind":"arxiv","version":2}},"canonical_sha256":"4a74899efacc4b2b3e2b176a3c3ae6611a96edd1176c3342a54457efdf89a03d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a74899efacc4b2b3e2b176a3c3ae6611a96edd1176c3342a54457efdf89a03d","first_computed_at":"2026-05-18T04:40:08.427912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:08.427912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9p0Ff85dzHGe74dJReQx2tm9NXkeK2gMWXaXKNtT4bBLHzK/ig4tLLfP2zJ+pYMDSd6Znc/h8gH2Q+qFxHiLBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:08.428396Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.4615","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9b6d930f8aa25f8a44ef9969be516a711140daf4b439d90f8feb3faed92066d","sha256:c949b103d9584524eb2c4028b23305f62d30501cd407ab9d14c0eeac648435a3"],"state_sha256":"76a5fd3826b3ec26347c8e3fcaa4358207f8a261ed88bb92e833aa9cc3117d21"}