{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QDXPWYEUA5N6U3DBEOJ45YBIOH","short_pith_number":"pith:QDXPWYEU","schema_version":"1.0","canonical_sha256":"80eefb6094075bea6c612393cee02871ed57284670b22434687874cd802abf23","source":{"kind":"arxiv","id":"1803.09100","version":1},"attestation_state":"computed","paper":{"title":"On limit theorems for fields of martingale differences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dalibor Volny","submitted_at":"2018-03-24T12:43:09Z","abstract_excerpt":"We prove a central limit theorem for stationary multiple (random) fields of martingale differences $f\\circ T_{\\underline{i}}$, $\\underline{i}\\in \\Bbb Z^d$, where $T_{\\underline{i}}$ is a $\\Bbb Z^d$ action. In most cases the multiple (random) fields of martingale differences is given by a completely commuting filtration. A central limit theorem proving convergence to a normal law has been known for Bernoulli random fields and in [V15] this result was extended to random fields where one of generating transformations is ergodic. In the present paper it is proved that a convergence takes place alw"},"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":"1803.09100","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-24T12:43:09Z","cross_cats_sorted":[],"title_canon_sha256":"5b1fd5bb975a0e91b7dafc5df06a8f5f3cc4692a1337b1f0e83fd546d3e4a9c5","abstract_canon_sha256":"b13a4b2218236c5f5e88eed61ce1ff8fe10903d74d04bc53a8467fa2f781778d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:12.606723Z","signature_b64":"bn+kQuqdTxW9ExI5kbdHVLTiM+gzjBcSJgaiN806nRgHyTr6fwdYRIC0gQNUpF9BEqS4zOmEjSdGuMYQbesFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80eefb6094075bea6c612393cee02871ed57284670b22434687874cd802abf23","last_reissued_at":"2026-05-18T00:20:12.606241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:12.606241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On limit theorems for fields of martingale differences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dalibor Volny","submitted_at":"2018-03-24T12:43:09Z","abstract_excerpt":"We prove a central limit theorem for stationary multiple (random) fields of martingale differences $f\\circ T_{\\underline{i}}$, $\\underline{i}\\in \\Bbb Z^d$, where $T_{\\underline{i}}$ is a $\\Bbb Z^d$ action. In most cases the multiple (random) fields of martingale differences is given by a completely commuting filtration. A central limit theorem proving convergence to a normal law has been known for Bernoulli random fields and in [V15] this result was extended to random fields where one of generating transformations is ergodic. In the present paper it is proved that a convergence takes place alw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09100","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":"1803.09100","created_at":"2026-05-18T00:20:12.606329+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.09100v1","created_at":"2026-05-18T00:20:12.606329+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09100","created_at":"2026-05-18T00:20:12.606329+00:00"},{"alias_kind":"pith_short_12","alias_value":"QDXPWYEUA5N6","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QDXPWYEUA5N6U3DB","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QDXPWYEU","created_at":"2026-05-18T12:32:46.962924+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/QDXPWYEUA5N6U3DBEOJ45YBIOH","json":"https://pith.science/pith/QDXPWYEUA5N6U3DBEOJ45YBIOH.json","graph_json":"https://pith.science/api/pith-number/QDXPWYEUA5N6U3DBEOJ45YBIOH/graph.json","events_json":"https://pith.science/api/pith-number/QDXPWYEUA5N6U3DBEOJ45YBIOH/events.json","paper":"https://pith.science/paper/QDXPWYEU"},"agent_actions":{"view_html":"https://pith.science/pith/QDXPWYEUA5N6U3DBEOJ45YBIOH","download_json":"https://pith.science/pith/QDXPWYEUA5N6U3DBEOJ45YBIOH.json","view_paper":"https://pith.science/paper/QDXPWYEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.09100&json=true","fetch_graph":"https://pith.science/api/pith-number/QDXPWYEUA5N6U3DBEOJ45YBIOH/graph.json","fetch_events":"https://pith.science/api/pith-number/QDXPWYEUA5N6U3DBEOJ45YBIOH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QDXPWYEUA5N6U3DBEOJ45YBIOH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QDXPWYEUA5N6U3DBEOJ45YBIOH/action/storage_attestation","attest_author":"https://pith.science/pith/QDXPWYEUA5N6U3DBEOJ45YBIOH/action/author_attestation","sign_citation":"https://pith.science/pith/QDXPWYEUA5N6U3DBEOJ45YBIOH/action/citation_signature","submit_replication":"https://pith.science/pith/QDXPWYEUA5N6U3DBEOJ45YBIOH/action/replication_record"}},"created_at":"2026-05-18T00:20:12.606329+00:00","updated_at":"2026-05-18T00:20:12.606329+00:00"}