{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZDXEUDSNLZU26NFDWKWVQKMGGB","short_pith_number":"pith:ZDXEUDSN","canonical_record":{"source":{"id":"1408.1840","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-08T13:00:41Z","cross_cats_sorted":[],"title_canon_sha256":"572ada3653573f95adf46a0b6caf90b8528e58b53c609eabe5a223bdbbfb536c","abstract_canon_sha256":"050fd5759b678aaa2839dee1462ee373a1943fcb5a14e7b07d370fe277a80476"},"schema_version":"1.0"},"canonical_sha256":"c8ee4a0e4d5e69af34a3b2ad5829863074fbfd4f3889c1d365c100d2911a47de","source":{"kind":"arxiv","id":"1408.1840","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1840","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1840v2","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1840","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZDXEUDSNLZU2","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZDXEUDSNLZU26NFD","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZDXEUDSN","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZDXEUDSNLZU26NFDWKWVQKMGGB","target":"record","payload":{"canonical_record":{"source":{"id":"1408.1840","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-08T13:00:41Z","cross_cats_sorted":[],"title_canon_sha256":"572ada3653573f95adf46a0b6caf90b8528e58b53c609eabe5a223bdbbfb536c","abstract_canon_sha256":"050fd5759b678aaa2839dee1462ee373a1943fcb5a14e7b07d370fe277a80476"},"schema_version":"1.0"},"canonical_sha256":"c8ee4a0e4d5e69af34a3b2ad5829863074fbfd4f3889c1d365c100d2911a47de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:03.064491Z","signature_b64":"NH5YM2/NdofZNgdHl0i0q+IQwyD25HwoSVlYHQR9EHKmsoNNfYq/fz/FpGytl0z6wNIY4/1xT/JPJq+qBq1MDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8ee4a0e4d5e69af34a3b2ad5829863074fbfd4f3889c1d365c100d2911a47de","last_reissued_at":"2026-05-18T00:53:03.063994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:03.063994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.1840","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e0ku0Xptp7nZjLlfVlNqfkrD/zETEXUxmvq3n2nGFo+LQnKnzFJVklzuJVzAKWc1wCnnyV5P/XOwGNKLWFb7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:38:05.791137Z"},"content_sha256":"19b64b0929456859d5cd0275ab2223fa3221b294906e571ad97e00cc78b8b79b","schema_version":"1.0","event_id":"sha256:19b64b0929456859d5cd0275ab2223fa3221b294906e571ad97e00cc78b8b79b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZDXEUDSNLZU26NFDWKWVQKMGGB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Whittaker rational structures and special values of the Asai $L$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Erez Lapid, Harald Grobner, Michael Harris","submitted_at":"2014-08-08T13:00:41Z","abstract_excerpt":"Let $F$ be a totally real number field and $E/F$ a totally imaginary quadratic extension of $F$. Let $\\Pi$ be a cohomological, conjugate self-dual cuspidal automorphic representation of $GL_n(\\mathbb A_E)$. Under a certain non-vanishing condition we relate the residue and the value of the Asai $L$-functions at $s=1$ with rational structures obtained from the cohomologies in top and bottom degrees via the Whittaker coefficient map. This generalizes a result in Eric Urban's thesis when $n = 2$, as well as a result of the first two named authors, both in the case $F = \\mathbb Q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1840","kind":"arxiv","version":2},"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":"2026-05-18T00:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79Hx1zJc1hslkubtbGclSNZyO92szTsuqe7/fIjkPlX1N+ZrrLdQXPXImJVLTDeuMU3PzLEBiaHp/FPkT+RECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:38:05.791497Z"},"content_sha256":"7fda16c549b9a40cb373e459a9a377208f519ce67f6fb46673925002bfd8aae2","schema_version":"1.0","event_id":"sha256:7fda16c549b9a40cb373e459a9a377208f519ce67f6fb46673925002bfd8aae2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZDXEUDSNLZU26NFDWKWVQKMGGB/bundle.json","state_url":"https://pith.science/pith/ZDXEUDSNLZU26NFDWKWVQKMGGB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZDXEUDSNLZU26NFDWKWVQKMGGB/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":"2026-05-28T16:38:05Z","links":{"resolver":"https://pith.science/pith/ZDXEUDSNLZU26NFDWKWVQKMGGB","bundle":"https://pith.science/pith/ZDXEUDSNLZU26NFDWKWVQKMGGB/bundle.json","state":"https://pith.science/pith/ZDXEUDSNLZU26NFDWKWVQKMGGB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZDXEUDSNLZU26NFDWKWVQKMGGB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZDXEUDSNLZU26NFDWKWVQKMGGB","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":"050fd5759b678aaa2839dee1462ee373a1943fcb5a14e7b07d370fe277a80476","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-08T13:00:41Z","title_canon_sha256":"572ada3653573f95adf46a0b6caf90b8528e58b53c609eabe5a223bdbbfb536c"},"schema_version":"1.0","source":{"id":"1408.1840","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1840","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1840v2","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1840","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZDXEUDSNLZU2","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZDXEUDSNLZU26NFD","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZDXEUDSN","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:7fda16c549b9a40cb373e459a9a377208f519ce67f6fb46673925002bfd8aae2","target":"graph","created_at":"2026-05-18T00:53:03Z","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":"Let $F$ be a totally real number field and $E/F$ a totally imaginary quadratic extension of $F$. Let $\\Pi$ be a cohomological, conjugate self-dual cuspidal automorphic representation of $GL_n(\\mathbb A_E)$. Under a certain non-vanishing condition we relate the residue and the value of the Asai $L$-functions at $s=1$ with rational structures obtained from the cohomologies in top and bottom degrees via the Whittaker coefficient map. This generalizes a result in Eric Urban's thesis when $n = 2$, as well as a result of the first two named authors, both in the case $F = \\mathbb Q$.","authors_text":"Erez Lapid, Harald Grobner, Michael Harris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-08T13:00:41Z","title":"Whittaker rational structures and special values of the Asai $L$-function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1840","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":"sha256:19b64b0929456859d5cd0275ab2223fa3221b294906e571ad97e00cc78b8b79b","target":"record","created_at":"2026-05-18T00:53:03Z","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":"050fd5759b678aaa2839dee1462ee373a1943fcb5a14e7b07d370fe277a80476","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-08T13:00:41Z","title_canon_sha256":"572ada3653573f95adf46a0b6caf90b8528e58b53c609eabe5a223bdbbfb536c"},"schema_version":"1.0","source":{"id":"1408.1840","kind":"arxiv","version":2}},"canonical_sha256":"c8ee4a0e4d5e69af34a3b2ad5829863074fbfd4f3889c1d365c100d2911a47de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8ee4a0e4d5e69af34a3b2ad5829863074fbfd4f3889c1d365c100d2911a47de","first_computed_at":"2026-05-18T00:53:03.063994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:03.063994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NH5YM2/NdofZNgdHl0i0q+IQwyD25HwoSVlYHQR9EHKmsoNNfYq/fz/FpGytl0z6wNIY4/1xT/JPJq+qBq1MDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:03.064491Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1840","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19b64b0929456859d5cd0275ab2223fa3221b294906e571ad97e00cc78b8b79b","sha256:7fda16c549b9a40cb373e459a9a377208f519ce67f6fb46673925002bfd8aae2"],"state_sha256":"142145f7322295467c73b7db99cfab866e1e896c1321fcd836c98c87ab0b42e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9oTJ1ahoaaGJBb32m9P1IIU/bqho//rdi5db+uZSAENkynj9nFVNdD368zh087hxXdJvwwYOk//KJkYyK/7QAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:38:05.793391Z","bundle_sha256":"1f4826da44f34a8593d181b60e4b63e6d5950ba4c0990b49038beede46a9312d"}}