{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:EPUGT7IWT2IQLTYOW7ER4KH6F5","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":"6c1bb62b4d41f2d2cc05edc999928008e01f6b3ec84d2f55a48e2fc884efa902","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"1995-07-11T00:00:00Z","title_canon_sha256":"875ae699f22a8b3be8be4251c25bdbfc82405b9803ec8f0c7c605148ba365d35"},"schema_version":"1.0","source":{"id":"math/9507218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9507218","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/9507218v1","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9507218","created_at":"2026-05-18T01:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"EPUGT7IWT2IQ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"EPUGT7IWT2IQLTYO","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"EPUGT7IW","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:5c197dfccf466893b8dbe597b539cf877ee7107704ab987af782951f1886eabc","target":"graph","created_at":"2026-05-18T01:05:48Z","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 compute the central critical value of the triple product $L$-function associated to three cusp forms $f_1,f_2,f_3$ with trivial character for groups $\\Gamma_0(N_i)$ with square free levels $N_i$ not all of which are $1$ and weights $k_i$ satisfying $k_1\\ge k_2\\ge k_3$ and $k_1<k_2+k_3$. This generalizes work of Gross and Kudla and gives an alternative classical proof of their results in the case $N_1=N_2=N_3$ with $k_1=k_2=k_3=2$.","authors_text":"Rainer Schulze-Pillot, Siegfried B\\\"ocherer","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"1995-07-11T00:00:00Z","title":"On the central critical value of the triple product L-function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9507218","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":"sha256:0de6998ad32fe030f8124dc1eedbd04e4fb444c424492f69db4fdddd3dc0b6a2","target":"record","created_at":"2026-05-18T01:05:48Z","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":"6c1bb62b4d41f2d2cc05edc999928008e01f6b3ec84d2f55a48e2fc884efa902","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"1995-07-11T00:00:00Z","title_canon_sha256":"875ae699f22a8b3be8be4251c25bdbfc82405b9803ec8f0c7c605148ba365d35"},"schema_version":"1.0","source":{"id":"math/9507218","kind":"arxiv","version":1}},"canonical_sha256":"23e869fd169e9105cf0eb7c91e28fe2f5fcba668e1463162410b7a3364fea806","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23e869fd169e9105cf0eb7c91e28fe2f5fcba668e1463162410b7a3364fea806","first_computed_at":"2026-05-18T01:05:48.481758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:48.481758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5+s86yVF7PQaqd8eNczGBOhAg/3AA1acdDtVgUVMy818DOYU2XO2aV8FvxxETEMDnVvK3qwotdidx0B7383mAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:48.482207Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9507218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0de6998ad32fe030f8124dc1eedbd04e4fb444c424492f69db4fdddd3dc0b6a2","sha256:5c197dfccf466893b8dbe597b539cf877ee7107704ab987af782951f1886eabc"],"state_sha256":"b1e9f9f06afd3cc296c1c1986a44d8b830ab584fb361897e88079919b294f724"}