{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WTVSJPRILMFBWWGGK4E7DEBF6K","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":"dcb78978c267639ff23bd1f7d63f06e9b75823989c2e6b4df6d70346949b59d0","cross_cats_sorted":["math.CA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-29T14:15:39Z","title_canon_sha256":"5c6aeae94b348b504bb40763f5d084a51c416cc50e8a24b30007e2294c679264"},"schema_version":"1.0","source":{"id":"1311.7572","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7572","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7572v1","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7572","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"WTVSJPRILMFB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WTVSJPRILMFBWWGG","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WTVSJPRI","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:23ddbfd86e13683c4c15af6502c6c462bedf34c4e6bc1ed7d4ba7f2f5a340e43","target":"graph","created_at":"2026-05-18T03:05:55Z","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":"The aim of this paper is to prove Cotlar's ergodic theorem modeled on the set of primes.","authors_text":"Bartosz Trojan, Mariusz Mirek","cross_cats":["math.CA","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-29T14:15:39Z","title":"Cotlar's ergodic theorem along the prime numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7572","kind":"arxiv","version":1},"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":"sha256:2fb45dc752dac6ebf71c90299925b5e5acb694ca66df3abfbd7fb2fdd99f3017","target":"record","created_at":"2026-05-18T03:05:55Z","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":"dcb78978c267639ff23bd1f7d63f06e9b75823989c2e6b4df6d70346949b59d0","cross_cats_sorted":["math.CA","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-29T14:15:39Z","title_canon_sha256":"5c6aeae94b348b504bb40763f5d084a51c416cc50e8a24b30007e2294c679264"},"schema_version":"1.0","source":{"id":"1311.7572","kind":"arxiv","version":1}},"canonical_sha256":"b4eb24be285b0a1b58c65709f19025f2a17c4d0e1200a33c696ff9cde9b9c3fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4eb24be285b0a1b58c65709f19025f2a17c4d0e1200a33c696ff9cde9b9c3fd","first_computed_at":"2026-05-18T03:05:55.870255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:55.870255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8gcqJnau4DxNOuxulVCoTrqvurSHqgRpB/WNTnQqkQq5GZwwsyWyhTZdXNFfTM7BTpwLYyqGzyscZLMnjrL7CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:55.870717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7572","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fb45dc752dac6ebf71c90299925b5e5acb694ca66df3abfbd7fb2fdd99f3017","sha256:23ddbfd86e13683c4c15af6502c6c462bedf34c4e6bc1ed7d4ba7f2f5a340e43"],"state_sha256":"8827f05b4b7fd94321b8055aebf9726d70b5ca282fe7f47c843e171b8062af95"}