{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JYGD4N54N4NNQJQHQXQVT6VER7","short_pith_number":"pith:JYGD4N54","schema_version":"1.0","canonical_sha256":"4e0c3e37bc6f1ad8260785e159faa48ff14584da2934f2b7ee407b42fd4ccc6c","source":{"kind":"arxiv","id":"1203.1449","version":1},"attestation_state":"computed","paper":{"title":"Skolem-Mahler-Lech type theorems and Picard-Vessiot theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.AC","authors_text":"Michael Wibmer","submitted_at":"2012-03-07T12:07:23Z","abstract_excerpt":"We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem-Mahler-Lech theorem to rational function coefficients. The second problem is the question whether or not for a given linear difference equation there exists a Picard-Vessiot extension inside the ring of sequences. The third problem is a certain special case of the dynamical Mordell-Lang conjecture. This allows us to deduce solutions to the first two problems in a particular but fairly general special ca"},"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":"1203.1449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-03-07T12:07:23Z","cross_cats_sorted":["math.AG","math.DS"],"title_canon_sha256":"61da3d9ff50fca2491e3d2b9ad6b5a174d055278a42223756ac28ff8752252ad","abstract_canon_sha256":"6004805dc1f4223d47a6e61374ece9d6342a86b37fc1ed0d37016dda659e0e49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:38.694864Z","signature_b64":"ept7VDSUNZJ/ogbfeNSLtWbQn5Jt9/aIUYYlRtrIMdyKzFup3DcAonA1EL7hqFxcJnZgr42vy3U4rbYvzJgaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e0c3e37bc6f1ad8260785e159faa48ff14584da2934f2b7ee407b42fd4ccc6c","last_reissued_at":"2026-05-18T04:00:38.694207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:38.694207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skolem-Mahler-Lech type theorems and Picard-Vessiot theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.AC","authors_text":"Michael Wibmer","submitted_at":"2012-03-07T12:07:23Z","abstract_excerpt":"We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem-Mahler-Lech theorem to rational function coefficients. The second problem is the question whether or not for a given linear difference equation there exists a Picard-Vessiot extension inside the ring of sequences. The third problem is a certain special case of the dynamical Mordell-Lang conjecture. This allows us to deduce solutions to the first two problems in a particular but fairly general special ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1449","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":"1203.1449","created_at":"2026-05-18T04:00:38.694335+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.1449v1","created_at":"2026-05-18T04:00:38.694335+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1449","created_at":"2026-05-18T04:00:38.694335+00:00"},{"alias_kind":"pith_short_12","alias_value":"JYGD4N54N4NN","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JYGD4N54N4NNQJQH","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JYGD4N54","created_at":"2026-05-18T12:27:11.947152+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/JYGD4N54N4NNQJQHQXQVT6VER7","json":"https://pith.science/pith/JYGD4N54N4NNQJQHQXQVT6VER7.json","graph_json":"https://pith.science/api/pith-number/JYGD4N54N4NNQJQHQXQVT6VER7/graph.json","events_json":"https://pith.science/api/pith-number/JYGD4N54N4NNQJQHQXQVT6VER7/events.json","paper":"https://pith.science/paper/JYGD4N54"},"agent_actions":{"view_html":"https://pith.science/pith/JYGD4N54N4NNQJQHQXQVT6VER7","download_json":"https://pith.science/pith/JYGD4N54N4NNQJQHQXQVT6VER7.json","view_paper":"https://pith.science/paper/JYGD4N54","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.1449&json=true","fetch_graph":"https://pith.science/api/pith-number/JYGD4N54N4NNQJQHQXQVT6VER7/graph.json","fetch_events":"https://pith.science/api/pith-number/JYGD4N54N4NNQJQHQXQVT6VER7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JYGD4N54N4NNQJQHQXQVT6VER7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JYGD4N54N4NNQJQHQXQVT6VER7/action/storage_attestation","attest_author":"https://pith.science/pith/JYGD4N54N4NNQJQHQXQVT6VER7/action/author_attestation","sign_citation":"https://pith.science/pith/JYGD4N54N4NNQJQHQXQVT6VER7/action/citation_signature","submit_replication":"https://pith.science/pith/JYGD4N54N4NNQJQHQXQVT6VER7/action/replication_record"}},"created_at":"2026-05-18T04:00:38.694335+00:00","updated_at":"2026-05-18T04:00:38.694335+00:00"}