{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BWTPIPZZYY6X6UKKWYSBE752VM","short_pith_number":"pith:BWTPIPZZ","canonical_record":{"source":{"id":"1605.00819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:58:23Z","cross_cats_sorted":[],"title_canon_sha256":"cdbb408b5a8fc68bfcf57b7d26d6484d6399104343da86fd9d6b70f5a39f65f6","abstract_canon_sha256":"629a8023999119453094b644a1f89ea2a2ca142b136881690638c9bde9c6a6a0"},"schema_version":"1.0"},"canonical_sha256":"0da6f43f39c63d7f514ab624127fbaab3ecf7bc321746b01df9b9faa019d16e4","source":{"kind":"arxiv","id":"1605.00819","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00819","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00819v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00819","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"BWTPIPZZYY6X","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BWTPIPZZYY6X6UKK","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BWTPIPZZ","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BWTPIPZZYY6X6UKKWYSBE752VM","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:58:23Z","cross_cats_sorted":[],"title_canon_sha256":"cdbb408b5a8fc68bfcf57b7d26d6484d6399104343da86fd9d6b70f5a39f65f6","abstract_canon_sha256":"629a8023999119453094b644a1f89ea2a2ca142b136881690638c9bde9c6a6a0"},"schema_version":"1.0"},"canonical_sha256":"0da6f43f39c63d7f514ab624127fbaab3ecf7bc321746b01df9b9faa019d16e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:47.956110Z","signature_b64":"pVFRYUscqZnwqlw55ngEHLF0oidq+6KmXVZ6ldBlili5BaHMDFPgkCInqrMD+UzOPjuPdqh6SM3uxBAHgJlkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0da6f43f39c63d7f514ab624127fbaab3ecf7bc321746b01df9b9faa019d16e4","last_reissued_at":"2026-05-18T01:15:47.955612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:47.955612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00819","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gHvCiXkUROwDTDv9Xo9Bi3pZhSRSNkpZIrAzUM/Mc+1YIQj2wjymFOcAPh6Eb5AbGYDF43kjv1CntX0OHC77Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:40:30.576858Z"},"content_sha256":"c7c46a614948a85b20494889c269b16f082981b85baee3434c86530ac3db5931","schema_version":"1.0","event_id":"sha256:c7c46a614948a85b20494889c269b16f082981b85baee3434c86530ac3db5931"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BWTPIPZZYY6X6UKKWYSBE752VM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eisenstein congruences for SO(4,3), SO(4,4), spinor and triple product L-values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jonas Bergstr\\\"om, Neil Dummigan, Thomas M\\'egarban\\'e","submitted_at":"2016-05-03T09:58:23Z","abstract_excerpt":"We work out instances of a general conjecture on congruences between Hecke eigenvalues of induced and cuspidal automorphic representations of a reductive group, modulo divisors of certain critical L-values, in the case that the group is a split orthogonal group. We provide some numerical evidence in the case that the group is SO(4,3) and the L-function is the spinor L-function of a genus 2, vector-valued, Siegel cusp form. We also consider the case that the group is SO(4,4) and the L-function is a triple product L-function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00819","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VdeXHO4I5Pzl1zafbu9EXdLLRp6mciOC+m3Nygkk7g2wQcOXtGmeI5/Xrc6vJdz5nTKktDC1Y3UynPi7hltLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:40:30.577508Z"},"content_sha256":"53969026de15645fa4a186541fc45b0fc622313b88fd5e50d320158d01aab449","schema_version":"1.0","event_id":"sha256:53969026de15645fa4a186541fc45b0fc622313b88fd5e50d320158d01aab449"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BWTPIPZZYY6X6UKKWYSBE752VM/bundle.json","state_url":"https://pith.science/pith/BWTPIPZZYY6X6UKKWYSBE752VM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BWTPIPZZYY6X6UKKWYSBE752VM/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":"2026-06-05T02:40:30Z","links":{"resolver":"https://pith.science/pith/BWTPIPZZYY6X6UKKWYSBE752VM","bundle":"https://pith.science/pith/BWTPIPZZYY6X6UKKWYSBE752VM/bundle.json","state":"https://pith.science/pith/BWTPIPZZYY6X6UKKWYSBE752VM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BWTPIPZZYY6X6UKKWYSBE752VM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BWTPIPZZYY6X6UKKWYSBE752VM","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":"629a8023999119453094b644a1f89ea2a2ca142b136881690638c9bde9c6a6a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:58:23Z","title_canon_sha256":"cdbb408b5a8fc68bfcf57b7d26d6484d6399104343da86fd9d6b70f5a39f65f6"},"schema_version":"1.0","source":{"id":"1605.00819","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00819","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00819v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00819","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"BWTPIPZZYY6X","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BWTPIPZZYY6X6UKK","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BWTPIPZZ","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:53969026de15645fa4a186541fc45b0fc622313b88fd5e50d320158d01aab449","target":"graph","created_at":"2026-05-18T01:15:47Z","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 work out instances of a general conjecture on congruences between Hecke eigenvalues of induced and cuspidal automorphic representations of a reductive group, modulo divisors of certain critical L-values, in the case that the group is a split orthogonal group. We provide some numerical evidence in the case that the group is SO(4,3) and the L-function is the spinor L-function of a genus 2, vector-valued, Siegel cusp form. We also consider the case that the group is SO(4,4) and the L-function is a triple product L-function.","authors_text":"Jonas Bergstr\\\"om, Neil Dummigan, Thomas M\\'egarban\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:58:23Z","title":"Eisenstein congruences for SO(4,3), SO(4,4), spinor and triple product L-values"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00819","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:c7c46a614948a85b20494889c269b16f082981b85baee3434c86530ac3db5931","target":"record","created_at":"2026-05-18T01:15:47Z","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":"629a8023999119453094b644a1f89ea2a2ca142b136881690638c9bde9c6a6a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-03T09:58:23Z","title_canon_sha256":"cdbb408b5a8fc68bfcf57b7d26d6484d6399104343da86fd9d6b70f5a39f65f6"},"schema_version":"1.0","source":{"id":"1605.00819","kind":"arxiv","version":1}},"canonical_sha256":"0da6f43f39c63d7f514ab624127fbaab3ecf7bc321746b01df9b9faa019d16e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0da6f43f39c63d7f514ab624127fbaab3ecf7bc321746b01df9b9faa019d16e4","first_computed_at":"2026-05-18T01:15:47.955612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:47.955612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pVFRYUscqZnwqlw55ngEHLF0oidq+6KmXVZ6ldBlili5BaHMDFPgkCInqrMD+UzOPjuPdqh6SM3uxBAHgJlkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:47.956110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00819","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7c46a614948a85b20494889c269b16f082981b85baee3434c86530ac3db5931","sha256:53969026de15645fa4a186541fc45b0fc622313b88fd5e50d320158d01aab449"],"state_sha256":"19d95a61db08668b5bbb8473160b2d6ff8e19fb1cb498420356bbeea87523552"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+JJPLgHy8Qvg4s/KNHf0djHEsseTtJBX6JNXVvAGCcpTRXZFa2r6+LgAkon00v9Z3aAKzOLdgEthD2WgNvxBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:40:30.580895Z","bundle_sha256":"7aab51d078bff11f7c569100b8bf6c8627abcb5b05f15815a66ccf45538c667e"}}