{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CEXPY4HB2Q4C4F2LGS7NHQTSQ2","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":"862320194dad75a28f37c4439b3ea6a11cf15f53722e6539679959bba23a83cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-17T16:50:03Z","title_canon_sha256":"abac0854aec0bd927e2cebb0b746fdd627eb5b3ae258ddd8da0ea6d3f01c0892"},"schema_version":"1.0","source":{"id":"1309.4384","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4384","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4384v3","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4384","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"CEXPY4HB2Q4C","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CEXPY4HB2Q4C4F2L","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CEXPY4HB","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:cae9fa9dc34a19da3d9a236845d3cebb8e0a0131021285a47d550ffa76fe4ec0","target":"graph","created_at":"2026-05-18T02:40:54Z","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 paper, using p-adic integration with values in spaces of modular forms, we construct the p-adic analogue of Weil's elliptic functions according to Eisenstein in the book \"Elliptic functions according to Eisenstein and and Kronecker\". This construction extends Serre's p-adic family of Eisenstein series in \"Formes modulaires et fonctions z\\^eta p-adiques\". We show that the power series expansion of Weil's elliptic functions also exists in the p-adic case.","authors_text":"Min-Soo Kim, Su Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-17T16:50:03Z","title":"On p-adic analogue of Weil's elliptic functions according to Eisenstein"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4384","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:bbebb2414de317251569f4e059b0f438449124cd072f61fa6cf7e760c12c1d0a","target":"record","created_at":"2026-05-18T02:40:54Z","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":"862320194dad75a28f37c4439b3ea6a11cf15f53722e6539679959bba23a83cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-17T16:50:03Z","title_canon_sha256":"abac0854aec0bd927e2cebb0b746fdd627eb5b3ae258ddd8da0ea6d3f01c0892"},"schema_version":"1.0","source":{"id":"1309.4384","kind":"arxiv","version":3}},"canonical_sha256":"112efc70e1d4382e174b34bed3c272868491dbaa3818c0f37fe294fbef7caec9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"112efc70e1d4382e174b34bed3c272868491dbaa3818c0f37fe294fbef7caec9","first_computed_at":"2026-05-18T02:40:54.238032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:54.238032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"65tD9GoEHjXYtZepFfMpVpKvMyixpbPXodI1fkKLLjK7dmgEPwxQMn6c7LbGxmV9ZIww5U8tBtnwJp3FNzlcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:54.238547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4384","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbebb2414de317251569f4e059b0f438449124cd072f61fa6cf7e760c12c1d0a","sha256:cae9fa9dc34a19da3d9a236845d3cebb8e0a0131021285a47d550ffa76fe4ec0"],"state_sha256":"77dd7ea5ec8b8925af54aa5cedb146af61130c6e945601e166dd5b094c5ddb63"}