{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:N5FXNFDPDAMVFKZFRJJFCK7WQA","short_pith_number":"pith:N5FXNFDP","canonical_record":{"source":{"id":"2402.02524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-02-04T15:14:25Z","cross_cats_sorted":[],"title_canon_sha256":"3a6cdd8e0f14b73af7ede97b6e43bfdd1d419fddcba4b6146b51e44a6ddade1b","abstract_canon_sha256":"6031ffcba9ed41b6906badd7053bec036cb1f8b19028ac776d65b8006073be91"},"schema_version":"1.0"},"canonical_sha256":"6f4b76946f181952ab258a52512bf6801dab919983ab7c4a9b124fffbaeda31d","source":{"kind":"arxiv","id":"2402.02524","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.02524","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"2402.02524v1","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.02524","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"N5FXNFDPDAMV","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"pith_short_16","alias_value":"N5FXNFDPDAMVFKZF","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"pith_short_8","alias_value":"N5FXNFDP","created_at":"2026-07-05T07:41:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:N5FXNFDPDAMVFKZFRJJFCK7WQA","target":"record","payload":{"canonical_record":{"source":{"id":"2402.02524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-02-04T15:14:25Z","cross_cats_sorted":[],"title_canon_sha256":"3a6cdd8e0f14b73af7ede97b6e43bfdd1d419fddcba4b6146b51e44a6ddade1b","abstract_canon_sha256":"6031ffcba9ed41b6906badd7053bec036cb1f8b19028ac776d65b8006073be91"},"schema_version":"1.0"},"canonical_sha256":"6f4b76946f181952ab258a52512bf6801dab919983ab7c4a9b124fffbaeda31d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:41:15.524040Z","signature_b64":"+Dos47CyiEaZpfpCOhv3w1h230W/s4RtQozEiURniNAS4GrFB+OyGOT2lscSlO+ritL/YzZIHCKqVziGom+yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f4b76946f181952ab258a52512bf6801dab919983ab7c4a9b124fffbaeda31d","last_reissued_at":"2026-07-05T07:41:15.523619Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:41:15.523619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.02524","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":"2026-07-05T07:41:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dsKPGLER/6G9pZ0wxIdBmucTqrA6bQI6JtwaNPXjMGAyjKybk//CGA9owZEf7JbEAdxKvTsYuHbZslcTNtUcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:44:52.437419Z"},"content_sha256":"6dbed1da62bb8ea3b0f776e594428f432002fe50724863aecb9be80aa7c80f1f","schema_version":"1.0","event_id":"sha256:6dbed1da62bb8ea3b0f776e594428f432002fe50724863aecb9be80aa7c80f1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:N5FXNFDPDAMVFKZFRJJFCK7WQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A theta operator for the group $\\mathrm{GSp}_4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Leonardo Fiore","submitted_at":"2024-02-04T15:14:25Z","abstract_excerpt":"We construct a differential operator on sheaves of $p$-adic modular forms defined over the locus of $p$-rank $\\ge 1$ of the Siegel threefold, by applying a revisited version of the approach that Sean Howe recently introduced in his paper \"A unipotent circle action on $p$-adic modular forms\" (2020, Trans. Am. Math. Soc.) to construct the theta operator in the elliptic case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.02524","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.02524/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:41:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LD1sbdodm/PAvdNVL/4ImXAGuBMeRTVAD3mZ+qX4S1n+L7CCKbAg9xdKXGbLLuLCTPUdffQQ/5aI7aNwn+oPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:44:52.438248Z"},"content_sha256":"c9ebea5c0c56bf1792612c350ab883d175b48bb215c6e6e15e5f89fca91eb6ec","schema_version":"1.0","event_id":"sha256:c9ebea5c0c56bf1792612c350ab883d175b48bb215c6e6e15e5f89fca91eb6ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N5FXNFDPDAMVFKZFRJJFCK7WQA/bundle.json","state_url":"https://pith.science/pith/N5FXNFDPDAMVFKZFRJJFCK7WQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N5FXNFDPDAMVFKZFRJJFCK7WQA/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":"2026-08-09T13:44:52Z","links":{"resolver":"https://pith.science/pith/N5FXNFDPDAMVFKZFRJJFCK7WQA","bundle":"https://pith.science/pith/N5FXNFDPDAMVFKZFRJJFCK7WQA/bundle.json","state":"https://pith.science/pith/N5FXNFDPDAMVFKZFRJJFCK7WQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N5FXNFDPDAMVFKZFRJJFCK7WQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:N5FXNFDPDAMVFKZFRJJFCK7WQA","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":"6031ffcba9ed41b6906badd7053bec036cb1f8b19028ac776d65b8006073be91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-02-04T15:14:25Z","title_canon_sha256":"3a6cdd8e0f14b73af7ede97b6e43bfdd1d419fddcba4b6146b51e44a6ddade1b"},"schema_version":"1.0","source":{"id":"2402.02524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.02524","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"2402.02524v1","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.02524","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"N5FXNFDPDAMV","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"pith_short_16","alias_value":"N5FXNFDPDAMVFKZF","created_at":"2026-07-05T07:41:15Z"},{"alias_kind":"pith_short_8","alias_value":"N5FXNFDP","created_at":"2026-07-05T07:41:15Z"}],"graph_snapshots":[{"event_id":"sha256:c9ebea5c0c56bf1792612c350ab883d175b48bb215c6e6e15e5f89fca91eb6ec","target":"graph","created_at":"2026-07-05T07:41:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.02524/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a differential operator on sheaves of $p$-adic modular forms defined over the locus of $p$-rank $\\ge 1$ of the Siegel threefold, by applying a revisited version of the approach that Sean Howe recently introduced in his paper \"A unipotent circle action on $p$-adic modular forms\" (2020, Trans. Am. Math. Soc.) to construct the theta operator in the elliptic case.","authors_text":"Leonardo Fiore","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-02-04T15:14:25Z","title":"A theta operator for the group $\\mathrm{GSp}_4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.02524","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":"sha256:6dbed1da62bb8ea3b0f776e594428f432002fe50724863aecb9be80aa7c80f1f","target":"record","created_at":"2026-07-05T07:41:15Z","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":"6031ffcba9ed41b6906badd7053bec036cb1f8b19028ac776d65b8006073be91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-02-04T15:14:25Z","title_canon_sha256":"3a6cdd8e0f14b73af7ede97b6e43bfdd1d419fddcba4b6146b51e44a6ddade1b"},"schema_version":"1.0","source":{"id":"2402.02524","kind":"arxiv","version":1}},"canonical_sha256":"6f4b76946f181952ab258a52512bf6801dab919983ab7c4a9b124fffbaeda31d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f4b76946f181952ab258a52512bf6801dab919983ab7c4a9b124fffbaeda31d","first_computed_at":"2026-07-05T07:41:15.523619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:41:15.523619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Dos47CyiEaZpfpCOhv3w1h230W/s4RtQozEiURniNAS4GrFB+OyGOT2lscSlO+ritL/YzZIHCKqVziGom+yDA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:41:15.524040Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.02524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dbed1da62bb8ea3b0f776e594428f432002fe50724863aecb9be80aa7c80f1f","sha256:c9ebea5c0c56bf1792612c350ab883d175b48bb215c6e6e15e5f89fca91eb6ec"],"state_sha256":"940b1bd04988ee05aa15f198227f071e325ebb66d0a2835bfe904d8877108689"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pkigk/Xke2GaD6i1hMHVu2Ry0AoNDeFK0FZCMq9NQNudHB6MNlEsFtEdX6z5ozluId1uGaEjn50aqIgaFHtVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T13:44:52.442717Z","bundle_sha256":"b1ad403543a3bbb22284bb1835654e468c00c2e391b6fce29934b8e764e74efe"}}