{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2YTZDWTS7UFDLFF3HQCC2W4HSY","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":"337927e3aa50bb420c753a4cc5fb45b75a8973b9008db971011548e722c5680c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-19T09:24:47Z","title_canon_sha256":"181ee943714323af6400e1b05937129af5012fb958dd643acef5c721d9c3334a"},"schema_version":"1.0","source":{"id":"1710.07049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07049","created_at":"2026-05-18T00:32:27Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07049v1","created_at":"2026-05-18T00:32:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07049","created_at":"2026-05-18T00:32:27Z"},{"alias_kind":"pith_short_12","alias_value":"2YTZDWTS7UFD","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YTZDWTS7UFDLFF3","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YTZDWTS","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:e8183235cd15c47fd0189f919901ea955b8e09eec05bf34679f9fad143eb5dae","target":"graph","created_at":"2026-05-18T00:32:27Z","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 show that the M\\\"obius disjointess of zero entropy dynamical systems implies the existence of an increasing sequence of positive integers along which the Chowla conjecture on autocorrelations of the M\\\"obius function holds.","authors_text":"Alexander Gomilko, Dominik Kwietniak, Mariusz Lema\\'nczyk","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-19T09:24:47Z","title":"Sarnak's conjecture implies the Chowla conjecture along a subsequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07049","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":"sha256:2e14f5a29b382bcf8130d33b0d06b96bfd00b7c79c4c878b9f5ba9289dfcdd8d","target":"record","created_at":"2026-05-18T00:32:27Z","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":"337927e3aa50bb420c753a4cc5fb45b75a8973b9008db971011548e722c5680c","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-19T09:24:47Z","title_canon_sha256":"181ee943714323af6400e1b05937129af5012fb958dd643acef5c721d9c3334a"},"schema_version":"1.0","source":{"id":"1710.07049","kind":"arxiv","version":1}},"canonical_sha256":"d62791da72fd0a3594bb3c042d5b8796213b4e7978a280c07380691b7ae155f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d62791da72fd0a3594bb3c042d5b8796213b4e7978a280c07380691b7ae155f0","first_computed_at":"2026-05-18T00:32:27.200907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:27.200907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oLmZt5QUygmnYtEY3yfxRoTqrPDYwZPHEAf83Sxr9JefjDPWvV6bZY6FgtPUSZGUNXhBRc/SOMBKWRb1WXjmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:27.201493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.07049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e14f5a29b382bcf8130d33b0d06b96bfd00b7c79c4c878b9f5ba9289dfcdd8d","sha256:e8183235cd15c47fd0189f919901ea955b8e09eec05bf34679f9fad143eb5dae"],"state_sha256":"74a755880118c25b67a5537be04c35b9fcef7f00cdeaeb8e52568fd7eea35441"}