{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:L7LVUW5VO3EELDOEA7VSZJA2PT","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":"5f9a6c4ad1a21c6e2adc46f8c63ceec2ffe3dec0c9bdc6a6e4e3860da040cff5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-31T14:22:14Z","title_canon_sha256":"72616900c58a3379f96f012df075b772b383970b791fef161ddfc4407bfbf6b5"},"schema_version":"1.0","source":{"id":"1608.00219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00219","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00219v1","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00219","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"pith_short_12","alias_value":"L7LVUW5VO3EE","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L7LVUW5VO3EELDOE","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L7LVUW5V","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:e2807070e7ed837dfff7c66f0dfbafc293734eb68b2051ced24d796d9145a731","target":"graph","created_at":"2026-05-18T01:02:20Z","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":"Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We generalize iterated spherical means to weighted ones based on generalized translation operators and consider applications to B-hyperbolic equations and transmission tomography problems.","authors_text":"E.L. Shishkina, S.M. Sitnik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-31T14:22:14Z","title":"On an equality for the iterated weighted spherical mean and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00219","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:e8f2b30ce6de21bb75164dbd639850c70f0890722cf5c3b96487b8978c674995","target":"record","created_at":"2026-05-18T01:02:20Z","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":"5f9a6c4ad1a21c6e2adc46f8c63ceec2ffe3dec0c9bdc6a6e4e3860da040cff5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-31T14:22:14Z","title_canon_sha256":"72616900c58a3379f96f012df075b772b383970b791fef161ddfc4407bfbf6b5"},"schema_version":"1.0","source":{"id":"1608.00219","kind":"arxiv","version":1}},"canonical_sha256":"5fd75a5bb576c8458dc407eb2ca41a7cd906e1dc58afb755b46e4aece512aa6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fd75a5bb576c8458dc407eb2ca41a7cd906e1dc58afb755b46e4aece512aa6c","first_computed_at":"2026-05-18T01:02:20.550261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:20.550261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HiH5eTdxcy3bPG7Kvu+FCyoKDOlTMKMpLK/+2iK9m+fJjAs2lWDhzKJN8VYlHIey2vg5ziBcAAo6FjVzPEc3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:20.550902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8f2b30ce6de21bb75164dbd639850c70f0890722cf5c3b96487b8978c674995","sha256:e2807070e7ed837dfff7c66f0dfbafc293734eb68b2051ced24d796d9145a731"],"state_sha256":"bcad6ef370a4ac23a90a51ef322d1429c73369aa740cf8a7bd6a48a38b60a348"}