{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3DZ5ST4TA7CA6M77ISTP5PPGI6","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":"170d333baae8df0eaeb509eca8b3a4eeffcf4a59a73ddcdc28bd388ae0798dd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-07T19:11:55Z","title_canon_sha256":"058a0887bb674f4818bc73d241d69bbcd1c972cf5e67c200b5fb4d8ee9ad8ba6"},"schema_version":"1.0","source":{"id":"1611.02217","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02217","created_at":"2026-05-18T00:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02217v3","created_at":"2026-05-18T00:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02217","created_at":"2026-05-18T00:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"3DZ5ST4TA7CA","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3DZ5ST4TA7CA6M77","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3DZ5ST4T","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:d4359eee288023759eaca155a94ebaf301e6382ffc4b5d8c515cc0bdb4361510","target":"graph","created_at":"2026-05-18T00:06:06Z","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":"In this article, we define functions analogous to Ramanujan's function $f(n)$ defined in his famous paper \"Modular equations and approximations to $\\pi$\". We then use these new functions to study Ramanujan's series for $1/\\pi$ associated with the classical, cubic and quartic bases.","authors_text":"Alex Berkovich, Heng Huat Chan, Michael J. Schlosser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-07T19:11:55Z","title":"Wronskians of theta functions and series for $1/\\pi$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02217","kind":"arxiv","version":3},"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:bdb7eb65413166123fe9d8a5d5086abd79374d4df3117ff271718f47fa57543f","target":"record","created_at":"2026-05-18T00:06:06Z","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":"170d333baae8df0eaeb509eca8b3a4eeffcf4a59a73ddcdc28bd388ae0798dd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-07T19:11:55Z","title_canon_sha256":"058a0887bb674f4818bc73d241d69bbcd1c972cf5e67c200b5fb4d8ee9ad8ba6"},"schema_version":"1.0","source":{"id":"1611.02217","kind":"arxiv","version":3}},"canonical_sha256":"d8f3d94f9307c40f33ff44a6febde647b23ddbc170d1e13e9b902f235ea7aba9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8f3d94f9307c40f33ff44a6febde647b23ddbc170d1e13e9b902f235ea7aba9","first_computed_at":"2026-05-18T00:06:06.476201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:06.476201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xX92GDXXBQiTQr4Q7dxSmKQsC2Su69MkwCqtERM1TlsRD8dRD4/MJ3IwjXzWx7TQnHwpVBoBvNevAYtQDO4wDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:06.476692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02217","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdb7eb65413166123fe9d8a5d5086abd79374d4df3117ff271718f47fa57543f","sha256:d4359eee288023759eaca155a94ebaf301e6382ffc4b5d8c515cc0bdb4361510"],"state_sha256":"8ba88829ae2e26a5b8bba63ee964e86ff312bcdf3639169151123f950a42372c"}