{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AJWYH4E5PYGW6HEELRRGA4GOGD","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":"e28285c7a3f29a795575f13498faa09e94affc7a6e523c15b47d2cf20d10822c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-11-26T17:55:57Z","title_canon_sha256":"fe0c5fcbae00c4ad13d2fb7e0c37f404f26a580eb43cd57b7dc3a0ea4f91d3c2"},"schema_version":"1.0","source":{"id":"2411.17638","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.17638","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"arxiv_version","alias_value":"2411.17638v1","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17638","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"pith_short_12","alias_value":"AJWYH4E5PYGW","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"pith_short_16","alias_value":"AJWYH4E5PYGW6HEE","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"pith_short_8","alias_value":"AJWYH4E5","created_at":"2026-07-05T09:40:49Z"}],"graph_snapshots":[{"event_id":"sha256:671c662bcee81b1860725fb0fcc3ab15c87bd815353674fde1d9f5451704ced3","target":"graph","created_at":"2026-07-05T09:40:49Z","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/2411.17638/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a special subsequence of the Fourier coefficients of powers of the Dedekind $\\eta$-function, analogous to the sequence $\\delta_\\ell := 24^{-1} \\pmod{\\ell}$ on which exceptional congruences of the partition function are supported. Therefrom we define a notion of density $D(r)$ for a normalized eta-power $\\eta^r$ measuring the proportion of primes $\\ell$ for which the order at infinity of $U_\\ell (\\eta^r)$ modulo 2 is maximal. We relate $D(r)$ to a notion of density measuring nonzero prime Fourier coefficients introduced by Bella\\\"iche, and use this to completely classify the vanishi","authors_text":"Anna Medvedovsky, Lukas Mauth, Steven Charlton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-11-26T17:55:57Z","title":"On the parity of coefficients of eta powers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17638","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":"sha256:102cffbb0130d06e1ecfac41f0f57470ba719b79ac1c9a99857fd0f7c58713c5","target":"record","created_at":"2026-07-05T09:40:49Z","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":"e28285c7a3f29a795575f13498faa09e94affc7a6e523c15b47d2cf20d10822c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-11-26T17:55:57Z","title_canon_sha256":"fe0c5fcbae00c4ad13d2fb7e0c37f404f26a580eb43cd57b7dc3a0ea4f91d3c2"},"schema_version":"1.0","source":{"id":"2411.17638","kind":"arxiv","version":1}},"canonical_sha256":"026d83f09d7e0d6f1c845c626070ce30eef480115b7f45d89d032d762af91354","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"026d83f09d7e0d6f1c845c626070ce30eef480115b7f45d89d032d762af91354","first_computed_at":"2026-07-05T09:40:49.911360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:49.911360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MGgnnMiTYZ7H6L2E7p0510YMuhaFASaBSAcXsybtESanHWtnqY3xDHc38n4aRTWdtI65f8ER1LQr2EsPhhbSBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:49.911822Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.17638","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:102cffbb0130d06e1ecfac41f0f57470ba719b79ac1c9a99857fd0f7c58713c5","sha256:671c662bcee81b1860725fb0fcc3ab15c87bd815353674fde1d9f5451704ced3"],"state_sha256":"ceb58ba904178ea8d528e514f6015523244c92ffbd7cb2e7896ac089414e3144"}