{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KGCXWVOKVK4RNSECYFI7XRHCYI","short_pith_number":"pith:KGCXWVOK","canonical_record":{"source":{"id":"1712.06370","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-18T12:37:46Z","cross_cats_sorted":[],"title_canon_sha256":"7b31ebcd028d887637c68beb0288a3b57621f978bae21a5f8ffa15b7d769e552","abstract_canon_sha256":"81ca39d6a403c0378d2968dcd4f75c0b0ec4c8e848655c159ace093181b78e80"},"schema_version":"1.0"},"canonical_sha256":"51857b55caaab916c882c151fbc4e2c21c8d287d52171c1fc3e8123f407c5360","source":{"kind":"arxiv","id":"1712.06370","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06370","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06370v2","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06370","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"KGCXWVOKVK4R","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KGCXWVOKVK4RNSEC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KGCXWVOK","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KGCXWVOKVK4RNSECYFI7XRHCYI","target":"record","payload":{"canonical_record":{"source":{"id":"1712.06370","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-18T12:37:46Z","cross_cats_sorted":[],"title_canon_sha256":"7b31ebcd028d887637c68beb0288a3b57621f978bae21a5f8ffa15b7d769e552","abstract_canon_sha256":"81ca39d6a403c0378d2968dcd4f75c0b0ec4c8e848655c159ace093181b78e80"},"schema_version":"1.0"},"canonical_sha256":"51857b55caaab916c882c151fbc4e2c21c8d287d52171c1fc3e8123f407c5360","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:24.795440Z","signature_b64":"qQLrd/7vEg8+aOjcvPExrKlOtvUc/5l7wCiuLcv+fAlxWSWnvc22t364VfjXNpdMp6f7Gx2LaIfvcLMKhMuBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51857b55caaab916c882c151fbc4e2c21c8d287d52171c1fc3e8123f407c5360","last_reissued_at":"2026-05-18T00:03:24.794762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:24.794762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.06370","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":"2026-05-18T00:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwWE32rz6u4sMiCWOIqcyjHTgfZIt2xu1XX3Jq19K7mgCiA95c+k0qBbUvVi0T2NiK0KMyU0Z5CXQITml9gTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:58:11.543691Z"},"content_sha256":"aedeef709663b7cbed313bf123ffa296516314da294253d446950ec15dd3e0e8","schema_version":"1.0","event_id":"sha256:aedeef709663b7cbed313bf123ffa296516314da294253d446950ec15dd3e0e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KGCXWVOKVK4RNSECYFI7XRHCYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exceptional poles of local $L$-functions for $GSp(4)$ with respect to split Bessel models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rainer Weissauer","submitted_at":"2017-12-18T12:37:46Z","abstract_excerpt":"Piateskii-Shapiro defined local $L$-factors $L^{PS}(s,\\Pi,\\Lambda)$ attached to irreducible admissible representations $\\Pi$ of the group $GSp(4)$ over local fields and Bessel models of $\\Pi$ attached to Bessel data $\\Lambda$. These local $L$-factors decompose into a product $L^{PS}(s,\\Pi,\\Lambda)= L^{PS}_{ex}(s,\\Pi,\\Lambda) L^{PS}_{reg}(s,\\Pi,\\Lambda)$ of an exceptional and a regular $L$-factor. In this paper we compute the exceptional factors $L^{PS}_{ex}(s,\\Pi,\\Lambda)$ for split Bessel models of $\\Pi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06370","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":"2026-05-18T00:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LgAFH5sqaWSTX/MWyDZvDQSJYyUEBQZb9oDvrIMiUp2JpeqLnrrVRRN30Wu88R2jlt3LfnmRm4TcfcUk79XACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:58:11.544037Z"},"content_sha256":"8089dcc682434c414109ccd45e97e961f8c8b1efa50830777c9c417c4c40cd0c","schema_version":"1.0","event_id":"sha256:8089dcc682434c414109ccd45e97e961f8c8b1efa50830777c9c417c4c40cd0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KGCXWVOKVK4RNSECYFI7XRHCYI/bundle.json","state_url":"https://pith.science/pith/KGCXWVOKVK4RNSECYFI7XRHCYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KGCXWVOKVK4RNSECYFI7XRHCYI/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":"2026-06-12T07:58:11Z","links":{"resolver":"https://pith.science/pith/KGCXWVOKVK4RNSECYFI7XRHCYI","bundle":"https://pith.science/pith/KGCXWVOKVK4RNSECYFI7XRHCYI/bundle.json","state":"https://pith.science/pith/KGCXWVOKVK4RNSECYFI7XRHCYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KGCXWVOKVK4RNSECYFI7XRHCYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KGCXWVOKVK4RNSECYFI7XRHCYI","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":"81ca39d6a403c0378d2968dcd4f75c0b0ec4c8e848655c159ace093181b78e80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-18T12:37:46Z","title_canon_sha256":"7b31ebcd028d887637c68beb0288a3b57621f978bae21a5f8ffa15b7d769e552"},"schema_version":"1.0","source":{"id":"1712.06370","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06370","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06370v2","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06370","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"KGCXWVOKVK4R","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KGCXWVOKVK4RNSEC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KGCXWVOK","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:8089dcc682434c414109ccd45e97e961f8c8b1efa50830777c9c417c4c40cd0c","target":"graph","created_at":"2026-05-18T00:03:24Z","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":"Piateskii-Shapiro defined local $L$-factors $L^{PS}(s,\\Pi,\\Lambda)$ attached to irreducible admissible representations $\\Pi$ of the group $GSp(4)$ over local fields and Bessel models of $\\Pi$ attached to Bessel data $\\Lambda$. These local $L$-factors decompose into a product $L^{PS}(s,\\Pi,\\Lambda)= L^{PS}_{ex}(s,\\Pi,\\Lambda) L^{PS}_{reg}(s,\\Pi,\\Lambda)$ of an exceptional and a regular $L$-factor. In this paper we compute the exceptional factors $L^{PS}_{ex}(s,\\Pi,\\Lambda)$ for split Bessel models of $\\Pi$.","authors_text":"Rainer Weissauer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-18T12:37:46Z","title":"Exceptional poles of local $L$-functions for $GSp(4)$ with respect to split Bessel models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06370","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:aedeef709663b7cbed313bf123ffa296516314da294253d446950ec15dd3e0e8","target":"record","created_at":"2026-05-18T00:03:24Z","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":"81ca39d6a403c0378d2968dcd4f75c0b0ec4c8e848655c159ace093181b78e80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-18T12:37:46Z","title_canon_sha256":"7b31ebcd028d887637c68beb0288a3b57621f978bae21a5f8ffa15b7d769e552"},"schema_version":"1.0","source":{"id":"1712.06370","kind":"arxiv","version":2}},"canonical_sha256":"51857b55caaab916c882c151fbc4e2c21c8d287d52171c1fc3e8123f407c5360","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51857b55caaab916c882c151fbc4e2c21c8d287d52171c1fc3e8123f407c5360","first_computed_at":"2026-05-18T00:03:24.794762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:24.794762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qQLrd/7vEg8+aOjcvPExrKlOtvUc/5l7wCiuLcv+fAlxWSWnvc22t364VfjXNpdMp6f7Gx2LaIfvcLMKhMuBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:24.795440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06370","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aedeef709663b7cbed313bf123ffa296516314da294253d446950ec15dd3e0e8","sha256:8089dcc682434c414109ccd45e97e961f8c8b1efa50830777c9c417c4c40cd0c"],"state_sha256":"130d01963867e69b67dab878f39d1e08a4fe712b41caaa81eb1c73cb264eca77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3Hw+l/rr5IwkH7I0g354w2J6h+VPbvgA04xu/iRvoQhpQTV3XcZZHyV8jM/HBptvDhGPIbKv6O1H7dlNcd6Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:58:11.545988Z","bundle_sha256":"9cd6c564386f0bcc2e280fca3e0ff215d0454889300d46e41d335d20b1161617"}}