{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:T2JOFORPW7PNAAZ27PRTSPMW2E","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":"3c87602a77601c6e70f206d43c29545838133a667be85a0e8ca5a09f38b00db7","cross_cats_sorted":["math.AP"],"license":"","primary_cat":"math.CA","submitted_at":"2004-07-01T07:11:08Z","title_canon_sha256":"cbd05387f43c79673881cf36bc33fb6d288df26249bf8bb81659a0031c2b3ea0"},"schema_version":"1.0","source":{"id":"math/0407013","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407013","created_at":"2026-05-18T03:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407013v4","created_at":"2026-05-18T03:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407013","created_at":"2026-05-18T03:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"T2JOFORPW7PN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"T2JOFORPW7PNAAZ2","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"T2JOFORP","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:2beae9a6e1e379d8a0ee23fab619ac98b05e0c467078723098e29606dabc3374","target":"graph","created_at":"2026-05-18T03:37:53Z","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":"For $f\\in {\\frak S}({\\Bbb R}^d)$, we consider the Bochner-Riesz operator ${\\frak R}^{\\delta}$ of index $\\delta>0$ defined by $$\\hat {{\\frak R}^{\\delta}f}(\\xi)=(1-|\\xi|^2)^{\\delta}_+ \\hat f (\\xi).$$ Then we prove the Bochner-Riesz conjecture which states that if $\\delta>\\max\\{d|1/p-1/2|-1/2,0\\}$ and $p>1$ then ${\\frak R}^{\\delta}$ is a bounded operator from $L^p({\\Bbb R}^d)$ into $L^p({\\Bbb R}^d)$; moreover, if $\\delta(p)=d(1/p-1/2)-1/2$ and $1<p<2d/(d+1)$, then ${\\frak R}^{\\delta(p)}$ is a bounded operator from $L^p({\\Bbb R}^d)$ into $L^{p,\\infty}({\\Bbb R}^d)$.","authors_text":"Yong-Cheol Kim","cross_cats":["math.AP"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2004-07-01T07:11:08Z","title":"A proof of the Bochner-Riesz conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407013","kind":"arxiv","version":4},"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:c65e7ca5153c15e92263afd63a90fb9c8f6e59721414800d81927a1069ba290f","target":"record","created_at":"2026-05-18T03:37:53Z","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":"3c87602a77601c6e70f206d43c29545838133a667be85a0e8ca5a09f38b00db7","cross_cats_sorted":["math.AP"],"license":"","primary_cat":"math.CA","submitted_at":"2004-07-01T07:11:08Z","title_canon_sha256":"cbd05387f43c79673881cf36bc33fb6d288df26249bf8bb81659a0031c2b3ea0"},"schema_version":"1.0","source":{"id":"math/0407013","kind":"arxiv","version":4}},"canonical_sha256":"9e92e2ba2fb7ded0033afbe3393d96d10963c62f39caee641edb578f0f38ce16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e92e2ba2fb7ded0033afbe3393d96d10963c62f39caee641edb578f0f38ce16","first_computed_at":"2026-05-18T03:37:53.892166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:53.892166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0hj5uCOxHm4GDd/m5yDZMoLx7T2WhhFaTkGwdA/POV1vx6SsPH91/Tw8JJwPoATW9ye4MVK/0ikh/o1ykizAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:53.892858Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0407013","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c65e7ca5153c15e92263afd63a90fb9c8f6e59721414800d81927a1069ba290f","sha256:2beae9a6e1e379d8a0ee23fab619ac98b05e0c467078723098e29606dabc3374"],"state_sha256":"b10b0075ffcf8ec76a714db50de5a90674564a6924b9aaa47283e441d2f1926c"}