{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ARSQ6EETW3KCUSWQWN46N7K6ZN","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":"275e52a2df14be5068f52147f0ff75b407e2728f2c0bb7494fa52d72254fe3ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-21T09:07:33Z","title_canon_sha256":"05e8a1b3783bbca5d4162b09f195d3f33d74d7aa725f69a7abb6d99c88175d63"},"schema_version":"1.0","source":{"id":"1603.06357","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06357","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06357v2","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06357","created_at":"2026-05-18T00:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"ARSQ6EETW3KC","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ARSQ6EETW3KCUSWQ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ARSQ6EET","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:91501b89903990cda93f8b3346e3ff0e26e5fd846e73a321cd75066ba81b6a81","target":"graph","created_at":"2026-05-18T00:31:45Z","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 compute the Fourier coefficients of the weight one modular form $\\eta(z)\\eta(2z)\\eta(3z)/\\eta(6z)$ in terms of the number of representations of an integer as a sum of two squares. We deduce a relation between this modular form and translates of the modular form $\\eta(z)^4/\\eta(2z)^2$. In the last section we use our main result to give an elementary proof of an identity by Victor Kac.","authors_text":"Christian Kassel, Christophe Reutenauer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-21T09:07:33Z","title":"The Fourier expansion of \\eta(z)\\eta(2z)\\eta(3z)/\\eta(6z)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06357","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":"sha256:8481152b403a7a225978375fd1d818c782b4ab9e353661c87c88dafca30747c2","target":"record","created_at":"2026-05-18T00:31:45Z","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":"275e52a2df14be5068f52147f0ff75b407e2728f2c0bb7494fa52d72254fe3ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-21T09:07:33Z","title_canon_sha256":"05e8a1b3783bbca5d4162b09f195d3f33d74d7aa725f69a7abb6d99c88175d63"},"schema_version":"1.0","source":{"id":"1603.06357","kind":"arxiv","version":2}},"canonical_sha256":"04650f1093b6d42a4ad0b379e6fd5ecb73a7b1d239e4c352aa0ce46e5787f038","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04650f1093b6d42a4ad0b379e6fd5ecb73a7b1d239e4c352aa0ce46e5787f038","first_computed_at":"2026-05-18T00:31:45.448403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:45.448403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NJtQsCUDNp2K/BjgjuNA5g03DBrPnP8k3+ULd/9ggcci0s857OwKUtjOIXlRoChEwFuRLzDa4b/e2fk5xa7NAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:45.448879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06357","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8481152b403a7a225978375fd1d818c782b4ab9e353661c87c88dafca30747c2","sha256:91501b89903990cda93f8b3346e3ff0e26e5fd846e73a321cd75066ba81b6a81"],"state_sha256":"e1be0b226ecd86317fdb3033653ef4699523a8ccfc1a9aeb422f8824559b5c7c"}