{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RZRG723LKIKGBXDR5PKLKWZMD6","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":"61fbe64f0f524f251e5b2c5388688ec8d049d9b18c0b3b74c583a562464511c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-09T01:32:09Z","title_canon_sha256":"ddd0c08d921b90fb3f80f4ab7ce87fd6e242bef443dc1b44823d16af7b8fb0d9"},"schema_version":"1.0","source":{"id":"1602.02835","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02835","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02835v4","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02835","created_at":"2026-05-18T01:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"RZRG723LKIKG","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RZRG723LKIKGBXDR","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RZRG723L","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:2254d6b1cf56c0b7bb04066158aadc28e81b926163dd7c1899c948ade8b83ed0","target":"graph","created_at":"2026-05-18T01:11:21Z","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 give a short proof of Zagier's conjecture / Mersmann's theorem which states that each holomorphic eta quotient of weight 1/2 is an integral rescaling of some eta quotient from Zagier's list of fourteen primitive holomorphic eta quotients. In particular, given any holomorphic eta quotient $f$ of weight 1/2, this result enables us to provide a closed-form expression for the coefficient of qn in the $q$-series expansion of $f$, for all $n$. We also demonstrate another application of the above theorem in extending the levels of the simple (resp. irreducible) holomorphic eta quotients.","authors_text":"Soumya Bhattacharya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-09T01:32:09Z","title":"Holomorphic eta quotients of weight 1/2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02835","kind":"arxiv","version":4},"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":"sha256:373c19a3c446d39d0b92db8eae4d5d6f83f2d0ecaf5e3e3738d6307b643a7e74","target":"record","created_at":"2026-05-18T01:11:21Z","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":"61fbe64f0f524f251e5b2c5388688ec8d049d9b18c0b3b74c583a562464511c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-09T01:32:09Z","title_canon_sha256":"ddd0c08d921b90fb3f80f4ab7ce87fd6e242bef443dc1b44823d16af7b8fb0d9"},"schema_version":"1.0","source":{"id":"1602.02835","kind":"arxiv","version":4}},"canonical_sha256":"8e626feb6b521460dc71ebd4b55b2c1f87d58581d33ce90be857fdb3673d0365","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e626feb6b521460dc71ebd4b55b2c1f87d58581d33ce90be857fdb3673d0365","first_computed_at":"2026-05-18T01:11:21.508325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:21.508325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FammtiYhmzqYyVkC4tth3CADEm36YCrm58kKL7AsPKF0JvkhWw7LGhdSMITO1Q9d4zDwfeSeUrYfxYqkmTgoBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:21.508766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02835","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:373c19a3c446d39d0b92db8eae4d5d6f83f2d0ecaf5e3e3738d6307b643a7e74","sha256:2254d6b1cf56c0b7bb04066158aadc28e81b926163dd7c1899c948ade8b83ed0"],"state_sha256":"771ac0144f3704d5dea9a7fdf9b07bc183156d4542270b57a1b738ee7d5a851c"}