{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PY2YDUJCOHXIIWA2UFFVVGA45C","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":"89d054bb0573d2f96cb612f5c880f0e9cedfa7a16a542c70ece3740cda923465","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-08-21T11:40:07Z","title_canon_sha256":"ea0c18189ba4e02b25489f1a462672e883258391c80111b090533489a4b5f862"},"schema_version":"1.0","source":{"id":"2508.15466","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.15466","created_at":"2026-07-05T11:57:12Z"},{"alias_kind":"arxiv_version","alias_value":"2508.15466v1","created_at":"2026-07-05T11:57:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.15466","created_at":"2026-07-05T11:57:12Z"},{"alias_kind":"pith_short_12","alias_value":"PY2YDUJCOHXI","created_at":"2026-07-05T11:57:12Z"},{"alias_kind":"pith_short_16","alias_value":"PY2YDUJCOHXIIWA2","created_at":"2026-07-05T11:57:12Z"},{"alias_kind":"pith_short_8","alias_value":"PY2YDUJC","created_at":"2026-07-05T11:57:12Z"}],"graph_snapshots":[{"event_id":"sha256:a9090d0e6257201eca7aa5f2025db6f50520d334e0f2b46779b301b13175945a","target":"graph","created_at":"2026-07-05T11:57:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.15466/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper resolves the question of pointwise convergence for ergodic averages of a single function along the set of polynomial values of primes of the form $x^2 + ny^2$. Following the influential paper of Bourgain \\cite{bourgain1989pointwise}, we employ the Hardy-Littlewood circle method where major arc and minor arc estimates for the set of prime ideals constitute the main novelty of the paper. We also prove that our convergence results cannot be extended to class of $L^1$ functions.","authors_text":"Jan Fornal","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-08-21T11:40:07Z","title":"Pointwise ergodic theorem along primes of the form $x^2 + ny^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.15466","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:a391b4a864df6a610f0506ef48e34735f4c58ddd7f0d7a3cc87120d763909f55","target":"record","created_at":"2026-07-05T11:57:12Z","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":"89d054bb0573d2f96cb612f5c880f0e9cedfa7a16a542c70ece3740cda923465","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-08-21T11:40:07Z","title_canon_sha256":"ea0c18189ba4e02b25489f1a462672e883258391c80111b090533489a4b5f862"},"schema_version":"1.0","source":{"id":"2508.15466","kind":"arxiv","version":1}},"canonical_sha256":"7e3581d12271ee84581aa14b5a981ce8ba10f2dc346f12165e99a3cc041cc726","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e3581d12271ee84581aa14b5a981ce8ba10f2dc346f12165e99a3cc041cc726","first_computed_at":"2026-07-05T11:57:12.745561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:57:12.745561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"da6ueCd3JOsUG50veblUN2f9gFSfCr7Nosc5v1XNR6DmGvbUKAeDsJTPYi2vqV+NKS9rzUphvdj2v0zIa/XHAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:57:12.745957Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.15466","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a391b4a864df6a610f0506ef48e34735f4c58ddd7f0d7a3cc87120d763909f55","sha256:a9090d0e6257201eca7aa5f2025db6f50520d334e0f2b46779b301b13175945a"],"state_sha256":"f01f9f073df917afb094b517758cd165c02839a38b7294e4209ade6bc912139d"}