{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JBN7QK3BIGSJ4XDLS6PV5RMBSI","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":"3ec9be953ff643182d6e00d8ba22932b85bfcda39dbddb9064001df51ebcb906","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-12-25T07:06:06Z","title_canon_sha256":"904b64cde70ceace0b0e3ced9f11d57937fc4f1a597a64a38288905cf2726a34"},"schema_version":"1.0","source":{"id":"2412.18805","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.18805","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"2412.18805v1","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18805","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"JBN7QK3BIGSJ","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"pith_short_16","alias_value":"JBN7QK3BIGSJ4XDL","created_at":"2026-07-05T09:54:11Z"},{"alias_kind":"pith_short_8","alias_value":"JBN7QK3B","created_at":"2026-07-05T09:54:11Z"}],"graph_snapshots":[{"event_id":"sha256:544e478c2e6babc6f772c4e1de8e6b35f4908944c65bb46e213a5687934a70fe","target":"graph","created_at":"2026-07-05T09:54:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.18805/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We formulate and prove the archimedean period relations for Rankin-Selberg convolutions of $\\text{GL}(n)\\times \\text{GL}(n)$ and $\\text{GL}(n)\\times \\text{GL}(n-1)$, for all generic cohomological representations. As a consequence, we prove the non-vanishing of the archimedean modular symbols. This extends the earlier results in [LLS24] for essentially tempered representations of $\\text{GL}(n)\\times\\text{GL}(n-1)$.","authors_text":"Binyong Sun, Dongwen Liu, Yubo Jin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-12-25T07:06:06Z","title":"Archimedean period relations for Rankin-Selberg convolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18805","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":"sha256:1357e2f533636c840d386f43bf47241b410d19eb2c9e810bed7ce443e9eca1fd","target":"record","created_at":"2026-07-05T09:54:11Z","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":"3ec9be953ff643182d6e00d8ba22932b85bfcda39dbddb9064001df51ebcb906","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-12-25T07:06:06Z","title_canon_sha256":"904b64cde70ceace0b0e3ced9f11d57937fc4f1a597a64a38288905cf2726a34"},"schema_version":"1.0","source":{"id":"2412.18805","kind":"arxiv","version":1}},"canonical_sha256":"485bf82b6141a49e5c6b979f5ec5819220f96c754eb4fb1043442f71aa2485f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"485bf82b6141a49e5c6b979f5ec5819220f96c754eb4fb1043442f71aa2485f7","first_computed_at":"2026-07-05T09:54:11.148257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:11.148257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"arkBzGFH562gipL0gk1Hdnt90xKogkmuHu5D+npo3qwKZqdLxfeyWFG4ePBsc7/eYDmkZJzNHEwXWbGI4GLCCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:11.148658Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.18805","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1357e2f533636c840d386f43bf47241b410d19eb2c9e810bed7ce443e9eca1fd","sha256:544e478c2e6babc6f772c4e1de8e6b35f4908944c65bb46e213a5687934a70fe"],"state_sha256":"5cbf8afe6f71c38ca530d765a2c34bec83d5d81bf184c93d47597259700b58ba"}