{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4II56TG76P2S47QDYV5QSGSWI2","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":"4199dc389b5f5bf60bc7602ccb3acca1b350c01ee9f667326a6b8f0e07b0263c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-20T17:40:29Z","title_canon_sha256":"bdb39bbb12b3be76dd2f241df8fea025b8661be9bb8d0325cf1fe4e06d73cf3c"},"schema_version":"1.0","source":{"id":"1509.06030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06030","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06030v1","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06030","created_at":"2026-05-18T01:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"4II56TG76P2S","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4II56TG76P2S47QD","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4II56TG7","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:893c6b85d86bc2e266203033857596a9b1926784af527f4069d439f5a3062632","target":"graph","created_at":"2026-05-18T01:32:36Z","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":"We discuss a consequence of Green and Tao's factorisation theorem for polynomial orbits on nilmanifolds, adjusted to the requirements of certain arithmetic applications. More precisely, we prove a generalisation of Theorem 16.4, Acta Arith. 154 (2012), 235-306, by slightly rearranging its proof. The thus achieved strengthening of the result removes an oversight in the above-cited paper which resulted from the previously too weak conclusion. Since this type of result proved essential for further applications, we take the opportunity to discuss it in more detail.","authors_text":"Lilian Matthiesen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-20T17:40:29Z","title":"A consequence of the factorisation theorem for polynomial orbits on nilmanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06030","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":"sha256:6e70221013facb3df304f57d4ec5df752480c64d83be8d8d5911895ea2ab67af","target":"record","created_at":"2026-05-18T01:32:36Z","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":"4199dc389b5f5bf60bc7602ccb3acca1b350c01ee9f667326a6b8f0e07b0263c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-20T17:40:29Z","title_canon_sha256":"bdb39bbb12b3be76dd2f241df8fea025b8661be9bb8d0325cf1fe4e06d73cf3c"},"schema_version":"1.0","source":{"id":"1509.06030","kind":"arxiv","version":1}},"canonical_sha256":"e211df4cdff3f52e7e03c57b091a564697af7815ccdef44280d06f0142e9bb77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e211df4cdff3f52e7e03c57b091a564697af7815ccdef44280d06f0142e9bb77","first_computed_at":"2026-05-18T01:32:36.053099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:36.053099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v3yk3wrChYpapu7lH13ynMiGS4qQhctYzmymO+YE54N693G3cfYmPGZFx0ua1ajkXVP7X6uZc3fZPg6teKmgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:36.053727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e70221013facb3df304f57d4ec5df752480c64d83be8d8d5911895ea2ab67af","sha256:893c6b85d86bc2e266203033857596a9b1926784af527f4069d439f5a3062632"],"state_sha256":"eb46fd062ffe2c7816d1447c6a4fb32d9931c7cc01b078bd794861399c203285"}