{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IH3KP7V3AYKNRUB36FLLY47HVV","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":"69668e8468bc9880b5669d83a5adb315b9e73ff936134d9811a28a29f4004313","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-03-13T11:18:40Z","title_canon_sha256":"894dedb54f6880c4d0a725c26bf4a72893909704635e2d63b627b2995d38879e"},"schema_version":"1.0","source":{"id":"1003.2699","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.2699","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1003.2699v1","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2699","created_at":"2026-05-18T02:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"IH3KP7V3AYKN","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IH3KP7V3AYKNRUB3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IH3KP7V3","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:3873830df5c2a5e70273f8ad77a872fa4fbf307b727fb0458a524915c7839816","target":"graph","created_at":"2026-05-18T02:56:11Z","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 find an explicit integral formula for the eigenfunctions of a fourth order differential operator against the kernel involving two Bessel functions. Our formula establishes the relation between K-types in two different realizations of the minimal representation of the indefinite orthogonal group, namely the L^2-model and the conformal model.","authors_text":"Jan M\\\"ollers, Toshiyuki Kobayashi","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-03-13T11:18:40Z","title":"An integral formula for L^2-eigenfunctions of a fourth order Bessel-type differential operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2699","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:fb830524754c75c00dcb956e4fab8ad05a24bfd15724dbbdbe492578a41617f5","target":"record","created_at":"2026-05-18T02:56:11Z","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":"69668e8468bc9880b5669d83a5adb315b9e73ff936134d9811a28a29f4004313","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-03-13T11:18:40Z","title_canon_sha256":"894dedb54f6880c4d0a725c26bf4a72893909704635e2d63b627b2995d38879e"},"schema_version":"1.0","source":{"id":"1003.2699","kind":"arxiv","version":1}},"canonical_sha256":"41f6a7febb0614d8d03bf156bc73e7ad64046894b22b3d2aa13ec5f1121d74e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41f6a7febb0614d8d03bf156bc73e7ad64046894b22b3d2aa13ec5f1121d74e8","first_computed_at":"2026-05-18T02:56:11.921351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:11.921351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"51rFaw2wb+LzLUU6BbLsd9N/Kcg2tOX+pOi+3CYZn8xTmUuRiS+iRZezCR5PcoODZ6DBbjk92jMo19yS4axmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:11.921741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.2699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb830524754c75c00dcb956e4fab8ad05a24bfd15724dbbdbe492578a41617f5","sha256:3873830df5c2a5e70273f8ad77a872fa4fbf307b727fb0458a524915c7839816"],"state_sha256":"925a0412fe18f78840c9bdc4ed334793ea841cdc0ca38d4d63d3952f2864f90f"}