{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MZ4KSOVVXOOXYXFZS5QIJCNQC6","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":"7921e3aaa46416aab43bf11f6d04f14d944cee06422949db2278c1319fb8b372","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-23T13:33:40Z","title_canon_sha256":"6e9288bd14c44e2816383a147c7e717f9c48773d34a4c8850fbbb2e5bbf23c4c"},"schema_version":"1.0","source":{"id":"2606.24565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24565","created_at":"2026-06-24T01:15:34Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24565v1","created_at":"2026-06-24T01:15:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24565","created_at":"2026-06-24T01:15:34Z"},{"alias_kind":"pith_short_12","alias_value":"MZ4KSOVVXOOX","created_at":"2026-06-24T01:15:34Z"},{"alias_kind":"pith_short_16","alias_value":"MZ4KSOVVXOOXYXFZ","created_at":"2026-06-24T01:15:34Z"},{"alias_kind":"pith_short_8","alias_value":"MZ4KSOVV","created_at":"2026-06-24T01:15:34Z"}],"graph_snapshots":[{"event_id":"sha256:49aad93bd55492a07bd1359c620bdf7d8c5a714b1e8fa5398560fc52ec3495f7","target":"graph","created_at":"2026-06-24T01:15:34Z","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/2606.24565/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the inhomogeneous form of the Jordan--von Neumann quadratic functional equation, in which the right-hand side is a prescribed function $g$ of two real variables. We prove that the existence of a $C^{2}$ solution is equivalent to $g$ being itself of class $C^{2}$ and satisfying a single three-variable cocycle identity, and we exhibit the solution as a closed-form integral expression involving the second partial derivative of $g $ along the first coordinate axis. The construction preserves regularity along the standard scale of $C^{k}$, smooth, and polynomial classes.","authors_text":"Alexandra Paicu, Dorian Popa, Mircea Dan Rus","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-23T13:33:40Z","title":"An integral formula for the inhomogeneous Jordan--von Neumann equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24565","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":"sha256:661642180debdb401d0d3963697f76015d9d1ee731da1324552261834e332502","target":"record","created_at":"2026-06-24T01:15:34Z","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":"7921e3aaa46416aab43bf11f6d04f14d944cee06422949db2278c1319fb8b372","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-23T13:33:40Z","title_canon_sha256":"6e9288bd14c44e2816383a147c7e717f9c48773d34a4c8850fbbb2e5bbf23c4c"},"schema_version":"1.0","source":{"id":"2606.24565","kind":"arxiv","version":1}},"canonical_sha256":"6678a93ab5bb9d7c5cb997608489b017a3a5a89eced103afa7d1bd794a52eb5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6678a93ab5bb9d7c5cb997608489b017a3a5a89eced103afa7d1bd794a52eb5e","first_computed_at":"2026-06-24T01:15:34.056092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:34.056092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U5asSQU1M2y+C4YWnNecGAduIH2GaMpdA1mUYv+hwDaHjGdnbhS6isPJoYY/ZGHY2mGqg4zt2XVnCdQQJpAWDg==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:34.056455Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:661642180debdb401d0d3963697f76015d9d1ee731da1324552261834e332502","sha256:49aad93bd55492a07bd1359c620bdf7d8c5a714b1e8fa5398560fc52ec3495f7"],"state_sha256":"2969038360197bc33e9648a5640c7a331ab79ed4dbf24fa853d16d3df032e3ef"}