{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CCDDAEJCWSHO5ZX2ZOVKNOCU5N","short_pith_number":"pith:CCDDAEJC","schema_version":"1.0","canonical_sha256":"1086301122b48eeee6facbaaa6b854eb46bee4c23965b5af44e5fa68a09fe7ec","source":{"kind":"arxiv","id":"1205.6025","version":3},"attestation_state":"computed","paper":{"title":"A weak second term identity of the regularized Siegel-Weil formula for unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Wei Xiong","submitted_at":"2012-05-28T03:55:15Z","abstract_excerpt":"Following W.T.Gan and S.Takeda, we obtain a weak second term identity of the regularized Siegel-Weil formula for the unitary dual pair $(U(n,n),U(V))$, where $V$ is a split hermitian space of dimension $2r$ with $r+1 \\leq n \\leq 2r-1$. As an application, we obtain a Rallis inner product formula for theta lifts from $U(W)$ to $U(V)$ for a skew-hermitian space $W$ of dimension $n$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.6025","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-28T03:55:15Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ac777fb6169a9188c2de2790d2305c2f270b030ffe0f0867b1424647ceeac737","abstract_canon_sha256":"011bf1a6e78ca84366091f9a57be8c458a5f86b90605937deff3c50a62133c0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:02.790492Z","signature_b64":"jw8pAiY82jbjbadIPpmjSZ7KVsW7jLVyT/M0HLFpHgExThjYueTxEDq5c4XeCKVCGjTObYvppAU57LBl79P1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1086301122b48eeee6facbaaa6b854eb46bee4c23965b5af44e5fa68a09fe7ec","last_reissued_at":"2026-05-18T03:30:02.789839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:02.789839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A weak second term identity of the regularized Siegel-Weil formula for unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Wei Xiong","submitted_at":"2012-05-28T03:55:15Z","abstract_excerpt":"Following W.T.Gan and S.Takeda, we obtain a weak second term identity of the regularized Siegel-Weil formula for the unitary dual pair $(U(n,n),U(V))$, where $V$ is a split hermitian space of dimension $2r$ with $r+1 \\leq n \\leq 2r-1$. As an application, we obtain a Rallis inner product formula for theta lifts from $U(W)$ to $U(V)$ for a skew-hermitian space $W$ of dimension $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6025","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.6025","created_at":"2026-05-18T03:30:02.789929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.6025v3","created_at":"2026-05-18T03:30:02.789929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6025","created_at":"2026-05-18T03:30:02.789929+00:00"},{"alias_kind":"pith_short_12","alias_value":"CCDDAEJCWSHO","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CCDDAEJCWSHO5ZX2","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CCDDAEJC","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CCDDAEJCWSHO5ZX2ZOVKNOCU5N","json":"https://pith.science/pith/CCDDAEJCWSHO5ZX2ZOVKNOCU5N.json","graph_json":"https://pith.science/api/pith-number/CCDDAEJCWSHO5ZX2ZOVKNOCU5N/graph.json","events_json":"https://pith.science/api/pith-number/CCDDAEJCWSHO5ZX2ZOVKNOCU5N/events.json","paper":"https://pith.science/paper/CCDDAEJC"},"agent_actions":{"view_html":"https://pith.science/pith/CCDDAEJCWSHO5ZX2ZOVKNOCU5N","download_json":"https://pith.science/pith/CCDDAEJCWSHO5ZX2ZOVKNOCU5N.json","view_paper":"https://pith.science/paper/CCDDAEJC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.6025&json=true","fetch_graph":"https://pith.science/api/pith-number/CCDDAEJCWSHO5ZX2ZOVKNOCU5N/graph.json","fetch_events":"https://pith.science/api/pith-number/CCDDAEJCWSHO5ZX2ZOVKNOCU5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CCDDAEJCWSHO5ZX2ZOVKNOCU5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CCDDAEJCWSHO5ZX2ZOVKNOCU5N/action/storage_attestation","attest_author":"https://pith.science/pith/CCDDAEJCWSHO5ZX2ZOVKNOCU5N/action/author_attestation","sign_citation":"https://pith.science/pith/CCDDAEJCWSHO5ZX2ZOVKNOCU5N/action/citation_signature","submit_replication":"https://pith.science/pith/CCDDAEJCWSHO5ZX2ZOVKNOCU5N/action/replication_record"}},"created_at":"2026-05-18T03:30:02.789929+00:00","updated_at":"2026-05-18T03:30:02.789929+00:00"}