{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CHCJJRW6B6KXLK2GF6YLNUXU43","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":"32df10d27deb80343529963cfb8c5e749229a26e371e551b8e917c9b08574d22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-20T02:38:38Z","title_canon_sha256":"499a35a0fc5d2916a141ef7dc4559efcb0805abdf523e9ba6be04ce7de1a583e"},"schema_version":"1.0","source":{"id":"1409.5847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5847","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5847v1","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5847","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"pith_short_12","alias_value":"CHCJJRW6B6KX","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CHCJJRW6B6KXLK2G","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CHCJJRW6","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:120ff3c301e95af8c0099fef8b276048ce41a276ba49efc31cb64fdbcc786ed0","target":"graph","created_at":"2026-05-18T02:42:15Z","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 all extremisers for the trace theorem on the sphere. We also provide a sharp extension for functions belonging to certain Sobolev spaces with angular regularity.","authors_text":"Mitsuru Sugimoto, Neal Bez, Shuji Machihara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-20T02:38:38Z","title":"Extremisers for the trace theorem on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5847","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":"sha256:4011035cf39242b8e3a20cd8acd22a0c93fb038762ba049860d37291cea06886","target":"record","created_at":"2026-05-18T02:42:15Z","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":"32df10d27deb80343529963cfb8c5e749229a26e371e551b8e917c9b08574d22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-20T02:38:38Z","title_canon_sha256":"499a35a0fc5d2916a141ef7dc4559efcb0805abdf523e9ba6be04ce7de1a583e"},"schema_version":"1.0","source":{"id":"1409.5847","kind":"arxiv","version":1}},"canonical_sha256":"11c494c6de0f9575ab462fb0b6d2f4e6ee448f3c50a51d398703a7f7bac4f64f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11c494c6de0f9575ab462fb0b6d2f4e6ee448f3c50a51d398703a7f7bac4f64f","first_computed_at":"2026-05-18T02:42:15.835768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:15.835768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nkrHA+RRLUWt7hwRZzcZJkKp6egtTWURaFuokCIly86BYFEhHseSIwOouknK+TandKa0WDlqxLqofAQbUPBBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:15.836554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4011035cf39242b8e3a20cd8acd22a0c93fb038762ba049860d37291cea06886","sha256:120ff3c301e95af8c0099fef8b276048ce41a276ba49efc31cb64fdbcc786ed0"],"state_sha256":"e3fd43334955a9fa31aaeff2fe0153199f86514517c9d4b979cec1d119ec55cb"}