{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MBSQXMN7DYI2ZRHJ6HSRZU6PWS","short_pith_number":"pith:MBSQXMN7","canonical_record":{"source":{"id":"2512.03412","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-03T03:39:27Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c58565719f2b02c9f8693168ce46ea65fa613754f21635150ef06cc860876d7b","abstract_canon_sha256":"1d23fced5dd872e214585c20195044f3bf7940efd8f83f7dc5d4b462afe66d3f"},"schema_version":"1.0"},"canonical_sha256":"60650bb1bf1e11acc4e9f1e51cd3cfb497361a614351bb2a46ec6a970e527374","source":{"kind":"arxiv","id":"2512.03412","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.03412","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"arxiv_version","alias_value":"2512.03412v5","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.03412","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"pith_short_12","alias_value":"MBSQXMN7DYI2","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"pith_short_16","alias_value":"MBSQXMN7DYI2ZRHJ","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"pith_short_8","alias_value":"MBSQXMN7","created_at":"2026-06-03T02:05:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MBSQXMN7DYI2ZRHJ6HSRZU6PWS","target":"record","payload":{"canonical_record":{"source":{"id":"2512.03412","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-03T03:39:27Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c58565719f2b02c9f8693168ce46ea65fa613754f21635150ef06cc860876d7b","abstract_canon_sha256":"1d23fced5dd872e214585c20195044f3bf7940efd8f83f7dc5d4b462afe66d3f"},"schema_version":"1.0"},"canonical_sha256":"60650bb1bf1e11acc4e9f1e51cd3cfb497361a614351bb2a46ec6a970e527374","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T02:05:43.860126Z","signature_b64":"Vtnto5C4WNSzi8QF2hrQnG0p+HiBR0VZNlYS51qnUOHy4GiTcA4k0R/RI7W2LMSMy2s8OhN3LRFPMXB9sKNzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60650bb1bf1e11acc4e9f1e51cd3cfb497361a614351bb2a46ec6a970e527374","last_reissued_at":"2026-06-03T02:05:43.859669Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T02:05:43.859669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.03412","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T02:05:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+uFYdVYZflS6Gmo7uBj9GbBBq5qSnY7aoHkdXoDQR4YaE8iLDkdTyyxrZdMx/dhmSXW3e1zV2eoq20aAZysjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:16:59.474614Z"},"content_sha256":"8cc38017231a7ab93e6dc70b96033fee76830cea2226bb3058f093fd1e62ab22","schema_version":"1.0","event_id":"sha256:8cc38017231a7ab93e6dc70b96033fee76830cea2226bb3058f093fd1e62ab22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MBSQXMN7DYI2ZRHJ6HSRZU6PWS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourier coefficients of Eisenstein series on ${\\rm SO}(3,n+1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Henry H. Kim, Takuya Yamauchi","submitted_at":"2025-12-03T03:39:27Z","abstract_excerpt":"We explicitly compute Fourier coefficients of Eisenstein series on the special orthogonal group $G={\\rm SO}(3,n+1)$ over $\\mathbb{Q}$ with $n\\ge 2$ which splits everywhere at finite places. We show that it has a bounded denominator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.03412","kind":"arxiv","version":5},"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/2512.03412/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":"2026-06-03T02:05:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OvQDzJhuCKg0Z0Vt4JGXcPcYsGvO1pmxL7Xvkfcc2POD359T18uF8JDlK33dnGcwgsZW1qsGigbWYVlIsFn1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:16:59.475007Z"},"content_sha256":"b1664f39da515e2479cb2b7d4a3577891222e418c4435451c0c71efe0ff31791","schema_version":"1.0","event_id":"sha256:b1664f39da515e2479cb2b7d4a3577891222e418c4435451c0c71efe0ff31791"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MBSQXMN7DYI2ZRHJ6HSRZU6PWS/bundle.json","state_url":"https://pith.science/pith/MBSQXMN7DYI2ZRHJ6HSRZU6PWS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MBSQXMN7DYI2ZRHJ6HSRZU6PWS/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":"2026-06-22T10:16:59Z","links":{"resolver":"https://pith.science/pith/MBSQXMN7DYI2ZRHJ6HSRZU6PWS","bundle":"https://pith.science/pith/MBSQXMN7DYI2ZRHJ6HSRZU6PWS/bundle.json","state":"https://pith.science/pith/MBSQXMN7DYI2ZRHJ6HSRZU6PWS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MBSQXMN7DYI2ZRHJ6HSRZU6PWS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MBSQXMN7DYI2ZRHJ6HSRZU6PWS","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":"1d23fced5dd872e214585c20195044f3bf7940efd8f83f7dc5d4b462afe66d3f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-03T03:39:27Z","title_canon_sha256":"c58565719f2b02c9f8693168ce46ea65fa613754f21635150ef06cc860876d7b"},"schema_version":"1.0","source":{"id":"2512.03412","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.03412","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"arxiv_version","alias_value":"2512.03412v5","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.03412","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"pith_short_12","alias_value":"MBSQXMN7DYI2","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"pith_short_16","alias_value":"MBSQXMN7DYI2ZRHJ","created_at":"2026-06-03T02:05:43Z"},{"alias_kind":"pith_short_8","alias_value":"MBSQXMN7","created_at":"2026-06-03T02:05:43Z"}],"graph_snapshots":[{"event_id":"sha256:b1664f39da515e2479cb2b7d4a3577891222e418c4435451c0c71efe0ff31791","target":"graph","created_at":"2026-06-03T02:05:43Z","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/2512.03412/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explicitly compute Fourier coefficients of Eisenstein series on the special orthogonal group $G={\\rm SO}(3,n+1)$ over $\\mathbb{Q}$ with $n\\ge 2$ which splits everywhere at finite places. We show that it has a bounded denominator.","authors_text":"Henry H. Kim, Takuya Yamauchi","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-03T03:39:27Z","title":"Fourier coefficients of Eisenstein series on ${\\rm SO}(3,n+1)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.03412","kind":"arxiv","version":5},"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":"sha256:8cc38017231a7ab93e6dc70b96033fee76830cea2226bb3058f093fd1e62ab22","target":"record","created_at":"2026-06-03T02:05:43Z","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":"1d23fced5dd872e214585c20195044f3bf7940efd8f83f7dc5d4b462afe66d3f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-03T03:39:27Z","title_canon_sha256":"c58565719f2b02c9f8693168ce46ea65fa613754f21635150ef06cc860876d7b"},"schema_version":"1.0","source":{"id":"2512.03412","kind":"arxiv","version":5}},"canonical_sha256":"60650bb1bf1e11acc4e9f1e51cd3cfb497361a614351bb2a46ec6a970e527374","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60650bb1bf1e11acc4e9f1e51cd3cfb497361a614351bb2a46ec6a970e527374","first_computed_at":"2026-06-03T02:05:43.859669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T02:05:43.859669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vtnto5C4WNSzi8QF2hrQnG0p+HiBR0VZNlYS51qnUOHy4GiTcA4k0R/RI7W2LMSMy2s8OhN3LRFPMXB9sKNzCQ==","signature_status":"signed_v1","signed_at":"2026-06-03T02:05:43.860126Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.03412","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cc38017231a7ab93e6dc70b96033fee76830cea2226bb3058f093fd1e62ab22","sha256:b1664f39da515e2479cb2b7d4a3577891222e418c4435451c0c71efe0ff31791"],"state_sha256":"3358c2233557959cab66b072519446d2b5ef0473fa987ee094a93d9ca5ae23bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ovUcBeT3/HonuW9cKROrwnaR8ZWTs4cFuqerxOy0iTdY4l02lteiEkOmo5rbsAfHRulV+Eb+RKJM6bkkPZg0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:16:59.477088Z","bundle_sha256":"8872e3c7ea1348b1c1303125ab41cb5490aa21a68a693fe302f961160e6f91ed"}}