{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AVC4HC6QXKCV5N4A6UR2UCQQA2","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":"f374ec7fb6c7d5c888b6fc2142949b549ed10a21ecf92fc4f5e9f45357adbe33","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-16T13:47:10Z","title_canon_sha256":"d20bb4efb64a0fe305f41ec28dc5213dfb24b4160206e6015ea257728e650c81"},"schema_version":"1.0","source":{"id":"1708.04894","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04894","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04894v2","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04894","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"pith_short_12","alias_value":"AVC4HC6QXKCV","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AVC4HC6QXKCV5N4A","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AVC4HC6Q","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:26c9715096142fe080eb404616c176999005dfbb92a408e8b58c6507b4c65519","target":"graph","created_at":"2026-05-17T23:44:32Z","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":"Given a complex meromorphic function, it is well defined its Riesz measure in terms of the laplacian of the logarithm of its modulus. Moreover, related to this tool, it is possible to prove the celebrated Jensen formula. In the present paper, using among the other things the fundamental solution for the bilaplacian, we introduce a possible generalization of these two concepts in the space of quaternions, obtaining new interesting Riesz measures and global (i.e. four dimensional), Jensen formulas.","authors_text":"Amedeo Altavilla, Cinzia Bisi","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-16T13:47:10Z","title":"Log-biharmonicity and a Jensen formula in the space of quaternions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04894","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:f3cdebb8886e50e31736ef5c846966034fc68a9c4a731f5f5c227f03e1fe73e6","target":"record","created_at":"2026-05-17T23:44:32Z","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":"f374ec7fb6c7d5c888b6fc2142949b549ed10a21ecf92fc4f5e9f45357adbe33","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-16T13:47:10Z","title_canon_sha256":"d20bb4efb64a0fe305f41ec28dc5213dfb24b4160206e6015ea257728e650c81"},"schema_version":"1.0","source":{"id":"1708.04894","kind":"arxiv","version":2}},"canonical_sha256":"0545c38bd0ba855eb780f523aa0a10069ced70aed1ed5bf7666749848fbb9ae2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0545c38bd0ba855eb780f523aa0a10069ced70aed1ed5bf7666749848fbb9ae2","first_computed_at":"2026-05-17T23:44:32.951284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:32.951284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TLLWFl5BYtgPpbuE178hKbbw81qONekz+VF/07DNDObeVEq1Qq1mYRdWSBle/uo7RjHlKYR5gI6fNTt+7h21DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:32.951985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04894","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3cdebb8886e50e31736ef5c846966034fc68a9c4a731f5f5c227f03e1fe73e6","sha256:26c9715096142fe080eb404616c176999005dfbb92a408e8b58c6507b4c65519"],"state_sha256":"a3f9572e6cc6791285d2b0f613b83a89b11ffe9c4412ecfc7a214f3f749eb911"}