{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ATFJWT5T3342LBS6YVMQHXOCMH","short_pith_number":"pith:ATFJWT5T","canonical_record":{"source":{"id":"1207.3119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-12T23:21:24Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"eba4fafe068d215c5ca822cf53abbe8a105c53de9f02078aaa12d309b88f5ff5","abstract_canon_sha256":"23c0f8931328ff907e46c2e2229664a42182ddd173ec67482cc24f4c6c4c02bf"},"schema_version":"1.0"},"canonical_sha256":"04ca9b4fb3def9a5865ec55903ddc261ce1587e2965b59c1f62c40bfb4a7ea7b","source":{"kind":"arxiv","id":"1207.3119","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3119","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3119v1","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3119","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"pith_short_12","alias_value":"ATFJWT5T3342","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ATFJWT5T3342LBS6","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ATFJWT5T","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ATFJWT5T3342LBS6YVMQHXOCMH","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-12T23:21:24Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"eba4fafe068d215c5ca822cf53abbe8a105c53de9f02078aaa12d309b88f5ff5","abstract_canon_sha256":"23c0f8931328ff907e46c2e2229664a42182ddd173ec67482cc24f4c6c4c02bf"},"schema_version":"1.0"},"canonical_sha256":"04ca9b4fb3def9a5865ec55903ddc261ce1587e2965b59c1f62c40bfb4a7ea7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:12.428501Z","signature_b64":"61X/kXjrgK2pjA4N48mcwi91jhT6ovDrtPTEIJnbJMOh1AszVvbTzf7hPZzESCExmntZ1wBM6JWpdqhMyMINAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04ca9b4fb3def9a5865ec55903ddc261ce1587e2965b59c1f62c40bfb4a7ea7b","last_reissued_at":"2026-05-18T03:51:12.427813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:12.427813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3119","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":"2026-05-18T03:51:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lmd+fVQRRl3VE46aSC/1PTSrtvnY/ICGJPNS2hNxv8rHMtWNg45nKQ0i/6hufbeskT3c9Nlc7XE4zg5zbrvVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:46:17.427303Z"},"content_sha256":"cdccd98da065295c0269a790f657550aa331761abdb384f088fd41150c4bf15c","schema_version":"1.0","event_id":"sha256:cdccd98da065295c0269a790f657550aa331761abdb384f088fd41150c4bf15c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ATFJWT5T3342LBS6YVMQHXOCMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bessel models for GSp(4): Siegel vectors of square-free level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Ameya Pitale, Ralf Schmidt","submitted_at":"2012-07-12T23:21:24Z","abstract_excerpt":"We determine test vectors and explicit formulas for all Bessel models for those Iwahori-spherical representations of GSp(4) over a p-adic field that have non-zero vectors fixed under the Siegel congruence subgroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3119","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":"2026-05-18T03:51:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6JUY3KX1mongscYv+SN9+V55bXOh/naY+NWHUnlUJ3Uj+TVZbu9Y+4x4Bee6R5TzDEJLkjKF1ybcXfG3PK8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:46:17.427971Z"},"content_sha256":"a7d593922b23bb7c2dfdf893c1e47f58d397d8d40e089b158bf22faf1da861f9","schema_version":"1.0","event_id":"sha256:a7d593922b23bb7c2dfdf893c1e47f58d397d8d40e089b158bf22faf1da861f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ATFJWT5T3342LBS6YVMQHXOCMH/bundle.json","state_url":"https://pith.science/pith/ATFJWT5T3342LBS6YVMQHXOCMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ATFJWT5T3342LBS6YVMQHXOCMH/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":"2026-05-28T15:46:17Z","links":{"resolver":"https://pith.science/pith/ATFJWT5T3342LBS6YVMQHXOCMH","bundle":"https://pith.science/pith/ATFJWT5T3342LBS6YVMQHXOCMH/bundle.json","state":"https://pith.science/pith/ATFJWT5T3342LBS6YVMQHXOCMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ATFJWT5T3342LBS6YVMQHXOCMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ATFJWT5T3342LBS6YVMQHXOCMH","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":"23c0f8931328ff907e46c2e2229664a42182ddd173ec67482cc24f4c6c4c02bf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-12T23:21:24Z","title_canon_sha256":"eba4fafe068d215c5ca822cf53abbe8a105c53de9f02078aaa12d309b88f5ff5"},"schema_version":"1.0","source":{"id":"1207.3119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3119","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3119v1","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3119","created_at":"2026-05-18T03:51:12Z"},{"alias_kind":"pith_short_12","alias_value":"ATFJWT5T3342","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ATFJWT5T3342LBS6","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ATFJWT5T","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:a7d593922b23bb7c2dfdf893c1e47f58d397d8d40e089b158bf22faf1da861f9","target":"graph","created_at":"2026-05-18T03:51:12Z","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 determine test vectors and explicit formulas for all Bessel models for those Iwahori-spherical representations of GSp(4) over a p-adic field that have non-zero vectors fixed under the Siegel congruence subgroup.","authors_text":"Ameya Pitale, Ralf Schmidt","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-12T23:21:24Z","title":"Bessel models for GSp(4): Siegel vectors of square-free level"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3119","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:cdccd98da065295c0269a790f657550aa331761abdb384f088fd41150c4bf15c","target":"record","created_at":"2026-05-18T03:51:12Z","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":"23c0f8931328ff907e46c2e2229664a42182ddd173ec67482cc24f4c6c4c02bf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-12T23:21:24Z","title_canon_sha256":"eba4fafe068d215c5ca822cf53abbe8a105c53de9f02078aaa12d309b88f5ff5"},"schema_version":"1.0","source":{"id":"1207.3119","kind":"arxiv","version":1}},"canonical_sha256":"04ca9b4fb3def9a5865ec55903ddc261ce1587e2965b59c1f62c40bfb4a7ea7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04ca9b4fb3def9a5865ec55903ddc261ce1587e2965b59c1f62c40bfb4a7ea7b","first_computed_at":"2026-05-18T03:51:12.427813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:12.427813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"61X/kXjrgK2pjA4N48mcwi91jhT6ovDrtPTEIJnbJMOh1AszVvbTzf7hPZzESCExmntZ1wBM6JWpdqhMyMINAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:12.428501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdccd98da065295c0269a790f657550aa331761abdb384f088fd41150c4bf15c","sha256:a7d593922b23bb7c2dfdf893c1e47f58d397d8d40e089b158bf22faf1da861f9"],"state_sha256":"8921077c999f5f9c8158c6d27b9a11487ff76e46165af7b215a6086ef36b9b5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x09QGI1VnwHr+VoXg3+j6KaG0nN6LtmOEs/itbbV5Z0K95RqiAg8cFGkxrbUHSxI3ufGL8J33cRzX9e/WBEPDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:46:17.431558Z","bundle_sha256":"da412802c89271e24861d094e31299eb0c6d1fb35e4ef23b2e62e61b509e582c"}}