{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HZIG5NHUBYUPNKTUBCF5IHI55H","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":"261f3b36fc688ea8353e10ce9b41432891afa57e7ea8840afa9be6c47ea8559a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-08T21:11:59Z","title_canon_sha256":"0baf931174ea61f5f65bac227856092884852965f1dccf6dae159f515ebaa442"},"schema_version":"1.0","source":{"id":"1609.05778","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05778","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05778v2","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05778","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"HZIG5NHUBYUP","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HZIG5NHUBYUPNKTU","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HZIG5NHU","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:869203935abfe6f2d7e2b205a0ba491739c0b86efdaf410073b54b396b14303c","target":"graph","created_at":"2026-05-18T00:41:08Z","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 a well-known 1914 paper, Ramanujan gave a number of rapidly converging series for $1/\\pi$ which are derived using modular functions of higher level. D. V. and G. V. Chudnovsky in their 1988 paper derived an analogous series representing $1/\\pi$ using the modular function $J$ of level 1, which results in highly convergent series for $1/\\pi$, often used in practice. In this paper, we explain the Chudnovsky method in the context of elliptic curves, modular curves, and the Picard-Fuchs differential equation. In doing so, we also generalize their method to produce formulae which are valid around","authors_text":"Gleb Glebov, Imin Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-08T21:11:59Z","title":"On Chudnovsky-Ramanujan Type Formulae"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05778","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":"sha256:65c7c62b19e2252a7c859be2114adcca3a6f5fbbcd23c8ed7ca06d333266d502","target":"record","created_at":"2026-05-18T00:41:08Z","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":"261f3b36fc688ea8353e10ce9b41432891afa57e7ea8840afa9be6c47ea8559a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-08T21:11:59Z","title_canon_sha256":"0baf931174ea61f5f65bac227856092884852965f1dccf6dae159f515ebaa442"},"schema_version":"1.0","source":{"id":"1609.05778","kind":"arxiv","version":2}},"canonical_sha256":"3e506eb4f40e28f6aa74088bd41d1de9deba6999250d75dcbc25150f776f70ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e506eb4f40e28f6aa74088bd41d1de9deba6999250d75dcbc25150f776f70ba","first_computed_at":"2026-05-18T00:41:08.899832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:08.899832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EBBzozSFmw/tBBAJ4at0OEhd0+K5VRxGCnwZRceG/zXFw+jdtQSIs5gD0Uly7Uy5vdzz0OpBzQUj2+nfWZ03CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:08.900489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05778","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65c7c62b19e2252a7c859be2114adcca3a6f5fbbcd23c8ed7ca06d333266d502","sha256:869203935abfe6f2d7e2b205a0ba491739c0b86efdaf410073b54b396b14303c"],"state_sha256":"2500137d0825f0587dea549656b1d37736d6bbad3e0a82235b97a5f4a7fdefe7"}