{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Q5HOM2I4RWB5ZNUWNZUPBPTATI","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":"a2efc9207f20fab6a8deef36ac96c9eb479666ca17e40b5eaa41cd7c57646676","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-19T06:37:54Z","title_canon_sha256":"7b41d818c91237a636db67c6cfce104aebd1b7d7477ad13c7639454ee7cb5581"},"schema_version":"1.0","source":{"id":"2501.10962","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.10962","created_at":"2026-07-05T10:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"2501.10962v2","created_at":"2026-07-05T10:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.10962","created_at":"2026-07-05T10:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"Q5HOM2I4RWB5","created_at":"2026-07-05T10:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"Q5HOM2I4RWB5ZNUW","created_at":"2026-07-05T10:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"Q5HOM2I4","created_at":"2026-07-05T10:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:1dd72956f440a98074c5da0525a3b0df076517f04e962b5200572fd23dc19e00","target":"graph","created_at":"2026-07-05T10:27:23Z","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/2501.10962/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the shifted convolution sums associated to completely multiplicative functions taking values in $\\{\\pm 1\\}$ and give combinatorical proofs of two recent results in the direction of Chowla's conjecture. We also determine the corresponding \"spectrum\".","authors_text":"Krishnarjun Krishnamoorthy","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-19T06:37:54Z","title":"On variants of Chowla's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.10962","kind":"arxiv","version":2},"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:f4dfec6b56188a74db5652b790f2f7bcd214213944a4803663adb689dff241bf","target":"record","created_at":"2026-07-05T10:27:23Z","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":"a2efc9207f20fab6a8deef36ac96c9eb479666ca17e40b5eaa41cd7c57646676","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-19T06:37:54Z","title_canon_sha256":"7b41d818c91237a636db67c6cfce104aebd1b7d7477ad13c7639454ee7cb5581"},"schema_version":"1.0","source":{"id":"2501.10962","kind":"arxiv","version":2}},"canonical_sha256":"874ee6691c8d83dcb6966e68f0be609a01bd0a3601072d120506e0d183ed97c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"874ee6691c8d83dcb6966e68f0be609a01bd0a3601072d120506e0d183ed97c0","first_computed_at":"2026-07-05T10:27:23.564016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:27:23.564016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QTWSNnP7TpX6/VYKmtTiWBHxv1x7kHpQV241jsMufJvsA+ZE8MnwXnkFuplSGGO5ktFAifmrJtlrrILrV8PqAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:27:23.564913Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.10962","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4dfec6b56188a74db5652b790f2f7bcd214213944a4803663adb689dff241bf","sha256:1dd72956f440a98074c5da0525a3b0df076517f04e962b5200572fd23dc19e00"],"state_sha256":"b4e2ed4ee65e5f9bf49f20a43fb49e90c40700acdcba3cf853ec65a0d5b2b1c4"}