{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3NXE3NRAJAQD5ORFPZC44VEL24","short_pith_number":"pith:3NXE3NRA","canonical_record":{"source":{"id":"1410.7081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T20:53:20Z","cross_cats_sorted":[],"title_canon_sha256":"0297fde3b047041a858685ee318d1c6a2517fd8030e78a8c626dc8fc7436aa09","abstract_canon_sha256":"7fa89a6dffc604ac38e2eb8b3a8c9498ef1a84a8e48e4f0371b316c0c7172a01"},"schema_version":"1.0"},"canonical_sha256":"db6e4db62048203eba257e45ce548bd70659ff5b98f53ad987a663ab8d7d4169","source":{"kind":"arxiv","id":"1410.7081","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7081","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7081v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7081","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"3NXE3NRAJAQD","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3NXE3NRAJAQD5ORF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3NXE3NRA","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3NXE3NRAJAQD5ORFPZC44VEL24","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T20:53:20Z","cross_cats_sorted":[],"title_canon_sha256":"0297fde3b047041a858685ee318d1c6a2517fd8030e78a8c626dc8fc7436aa09","abstract_canon_sha256":"7fa89a6dffc604ac38e2eb8b3a8c9498ef1a84a8e48e4f0371b316c0c7172a01"},"schema_version":"1.0"},"canonical_sha256":"db6e4db62048203eba257e45ce548bd70659ff5b98f53ad987a663ab8d7d4169","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:18.037108Z","signature_b64":"AHInQ/2Qx1xKU/IifH4XQ2KdTwhaWfg58ED1JNfmuk3id1bF6VeOp6YKCG9vhL3fe7CbYc1avvQBHocs9Kw5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db6e4db62048203eba257e45ce548bd70659ff5b98f53ad987a663ab8d7d4169","last_reissued_at":"2026-05-18T02:39:18.036545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:18.036545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7081","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MYFxHDRO6NiWQQoz1yENiie4PgAqEA/V3qjAnOi7cR/uwIofgjm6ZDruTCtExlta6mv4g/bajsEB1g2Lb2vAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:27:05.904453Z"},"content_sha256":"f91e2938cc7c73b33326cf8163dde745043871606670c91458b3770ef05f6ad5","schema_version":"1.0","event_id":"sha256:f91e2938cc7c73b33326cf8163dde745043871606670c91458b3770ef05f6ad5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3NXE3NRAJAQD5ORFPZC44VEL24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integrals of $K$ and $E$ from Lattice Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"I. J. Zucker, J. G. Wan","submitted_at":"2014-10-26T20:53:20Z","abstract_excerpt":"We give closed form evaluations for many families of integrals, whose integrands contain algebraic functions of the complete elliptic integrals $K$ and $E$. Our methods exploit the rich structures connecting complete elliptic integrals, Jacobi theta functions, lattice sums, and Eisenstein series. Various examples are given, and along the way new (including 10-dimensional) lattice sum evaluations are produced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7081","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNR9WRpeIraUgHxXCiz6yyTljChi4UbMBriV0mAaK3miBJmKLMobquQpmH3I7ISSCtezfB1ZEHWe3cbEypVYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:27:05.905110Z"},"content_sha256":"c0a7ebfb293744be3756fb03d59738f423eb4d8c6ab980981fb5e310c2899d20","schema_version":"1.0","event_id":"sha256:c0a7ebfb293744be3756fb03d59738f423eb4d8c6ab980981fb5e310c2899d20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3NXE3NRAJAQD5ORFPZC44VEL24/bundle.json","state_url":"https://pith.science/pith/3NXE3NRAJAQD5ORFPZC44VEL24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3NXE3NRAJAQD5ORFPZC44VEL24/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T04:27:05Z","links":{"resolver":"https://pith.science/pith/3NXE3NRAJAQD5ORFPZC44VEL24","bundle":"https://pith.science/pith/3NXE3NRAJAQD5ORFPZC44VEL24/bundle.json","state":"https://pith.science/pith/3NXE3NRAJAQD5ORFPZC44VEL24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3NXE3NRAJAQD5ORFPZC44VEL24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3NXE3NRAJAQD5ORFPZC44VEL24","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":"7fa89a6dffc604ac38e2eb8b3a8c9498ef1a84a8e48e4f0371b316c0c7172a01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T20:53:20Z","title_canon_sha256":"0297fde3b047041a858685ee318d1c6a2517fd8030e78a8c626dc8fc7436aa09"},"schema_version":"1.0","source":{"id":"1410.7081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7081","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7081v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7081","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"3NXE3NRAJAQD","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3NXE3NRAJAQD5ORF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3NXE3NRA","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:c0a7ebfb293744be3756fb03d59738f423eb4d8c6ab980981fb5e310c2899d20","target":"graph","created_at":"2026-05-18T02:39:18Z","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 closed form evaluations for many families of integrals, whose integrands contain algebraic functions of the complete elliptic integrals $K$ and $E$. Our methods exploit the rich structures connecting complete elliptic integrals, Jacobi theta functions, lattice sums, and Eisenstein series. Various examples are given, and along the way new (including 10-dimensional) lattice sum evaluations are produced.","authors_text":"I. J. Zucker, J. G. Wan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T20:53:20Z","title":"Integrals of $K$ and $E$ from Lattice Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7081","kind":"arxiv","version":1},"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:f91e2938cc7c73b33326cf8163dde745043871606670c91458b3770ef05f6ad5","target":"record","created_at":"2026-05-18T02:39:18Z","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":"7fa89a6dffc604ac38e2eb8b3a8c9498ef1a84a8e48e4f0371b316c0c7172a01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T20:53:20Z","title_canon_sha256":"0297fde3b047041a858685ee318d1c6a2517fd8030e78a8c626dc8fc7436aa09"},"schema_version":"1.0","source":{"id":"1410.7081","kind":"arxiv","version":1}},"canonical_sha256":"db6e4db62048203eba257e45ce548bd70659ff5b98f53ad987a663ab8d7d4169","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db6e4db62048203eba257e45ce548bd70659ff5b98f53ad987a663ab8d7d4169","first_computed_at":"2026-05-18T02:39:18.036545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:18.036545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AHInQ/2Qx1xKU/IifH4XQ2KdTwhaWfg58ED1JNfmuk3id1bF6VeOp6YKCG9vhL3fe7CbYc1avvQBHocs9Kw5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:18.037108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f91e2938cc7c73b33326cf8163dde745043871606670c91458b3770ef05f6ad5","sha256:c0a7ebfb293744be3756fb03d59738f423eb4d8c6ab980981fb5e310c2899d20"],"state_sha256":"154e07c51942e3a799ae8012f67908f19a05c5a86e332b20b48a654e76b80b37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K+7RnO0uuTMMmQixvvgat7FO3zO7Z2a9nHl2ildeFRq2dlqLvgF9+A4ucZHPMPBBI3wFcg/Gk7plgIv0lyWCAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:27:05.909801Z","bundle_sha256":"07d7386ebcb27cf2abaff66c6eca6694984b51eafea6ec9d374fb06ea65f17e7"}}