{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:73K573VEHZGWYZ6YOYJYDOUT6L","short_pith_number":"pith:73K573VE","canonical_record":{"source":{"id":"1205.2414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-11T01:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"2f24410c5924ab7975d3a53ed0b71bb008b6cbe7cb184e1dce4c687949207a86","abstract_canon_sha256":"ef7b42fcfae508e40362226df6f32ffff96836594f47857fa3e325cc0d9e6e09"},"schema_version":"1.0"},"canonical_sha256":"fed5dfeea43e4d6c67d8761381ba93f2e4f5ce284a3a468d174a5c64d3207b37","source":{"kind":"arxiv","id":"1205.2414","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2414","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2414v2","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2414","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"73K573VEHZGW","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"73K573VEHZGWYZ6Y","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"73K573VE","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:73K573VEHZGWYZ6YOYJYDOUT6L","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-11T01:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"2f24410c5924ab7975d3a53ed0b71bb008b6cbe7cb184e1dce4c687949207a86","abstract_canon_sha256":"ef7b42fcfae508e40362226df6f32ffff96836594f47857fa3e325cc0d9e6e09"},"schema_version":"1.0"},"canonical_sha256":"fed5dfeea43e4d6c67d8761381ba93f2e4f5ce284a3a468d174a5c64d3207b37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:58.208200Z","signature_b64":"8GTLgmEixYBu8kZdzZk7pfXi6WpL9dGQ1d3tjGsfE9juCCVLpwqxQ27ZyG9cJ6eGy5LxSR6wkEjAVb9od4BICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fed5dfeea43e4d6c67d8761381ba93f2e4f5ce284a3a468d174a5c64d3207b37","last_reissued_at":"2026-05-18T03:11:58.207399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:58.207399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2414","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zWjHb62SuTVM6t8xA7ChnyO4QgYICtZgb5KlglxnbIYumo3Y1ArWTXyLBPe0qmjiRLrfCJfu/yMJjXl4Cxf9Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:15:59.280565Z"},"content_sha256":"4af6516bc0f4eae3f6a400a7603bd0a8cd8a20ed489173ceb573d8fd85682feb","schema_version":"1.0","event_id":"sha256:4af6516bc0f4eae3f6a400a7603bd0a8cd8a20ed489173ceb573d8fd85682feb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:73K573VEHZGWYZ6YOYJYDOUT6L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved estimates for the discrete Fourier restriction to the higher dimensional sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ciprian Demeter, Jean Bourgain","submitted_at":"2012-05-11T01:47:50Z","abstract_excerpt":"We improve the exponent for the discrete Fourier restriction to the $n$ dimensional sphere, from $p=\\frac{2(n+1)}{n-3}$ to $p=\\frac{2n}{n-3}$, when $n\\ge 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2414","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5oErljRbGKrr+NBell+I1eItKQUxw5AIcWTTXqDU50MZbNUJumm6BHLrjWzF1y+ME/NMxqpFm6AV6EsdMpscDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:15:59.280919Z"},"content_sha256":"2bbffedf927f7f4d3e34ad549e6e0ede42d2804a396906c94643abe2abe17b86","schema_version":"1.0","event_id":"sha256:2bbffedf927f7f4d3e34ad549e6e0ede42d2804a396906c94643abe2abe17b86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/73K573VEHZGWYZ6YOYJYDOUT6L/bundle.json","state_url":"https://pith.science/pith/73K573VEHZGWYZ6YOYJYDOUT6L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/73K573VEHZGWYZ6YOYJYDOUT6L/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T20:15:59Z","links":{"resolver":"https://pith.science/pith/73K573VEHZGWYZ6YOYJYDOUT6L","bundle":"https://pith.science/pith/73K573VEHZGWYZ6YOYJYDOUT6L/bundle.json","state":"https://pith.science/pith/73K573VEHZGWYZ6YOYJYDOUT6L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/73K573VEHZGWYZ6YOYJYDOUT6L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:73K573VEHZGWYZ6YOYJYDOUT6L","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":"ef7b42fcfae508e40362226df6f32ffff96836594f47857fa3e325cc0d9e6e09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-11T01:47:50Z","title_canon_sha256":"2f24410c5924ab7975d3a53ed0b71bb008b6cbe7cb184e1dce4c687949207a86"},"schema_version":"1.0","source":{"id":"1205.2414","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2414","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2414v2","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2414","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"73K573VEHZGW","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"73K573VEHZGWYZ6Y","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"73K573VE","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:2bbffedf927f7f4d3e34ad549e6e0ede42d2804a396906c94643abe2abe17b86","target":"graph","created_at":"2026-05-18T03:11:58Z","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 improve the exponent for the discrete Fourier restriction to the $n$ dimensional sphere, from $p=\\frac{2(n+1)}{n-3}$ to $p=\\frac{2n}{n-3}$, when $n\\ge 4$.","authors_text":"Ciprian Demeter, Jean Bourgain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-11T01:47:50Z","title":"Improved estimates for the discrete Fourier restriction to the higher dimensional sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2414","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":"sha256:4af6516bc0f4eae3f6a400a7603bd0a8cd8a20ed489173ceb573d8fd85682feb","target":"record","created_at":"2026-05-18T03:11:58Z","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":"ef7b42fcfae508e40362226df6f32ffff96836594f47857fa3e325cc0d9e6e09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-11T01:47:50Z","title_canon_sha256":"2f24410c5924ab7975d3a53ed0b71bb008b6cbe7cb184e1dce4c687949207a86"},"schema_version":"1.0","source":{"id":"1205.2414","kind":"arxiv","version":2}},"canonical_sha256":"fed5dfeea43e4d6c67d8761381ba93f2e4f5ce284a3a468d174a5c64d3207b37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fed5dfeea43e4d6c67d8761381ba93f2e4f5ce284a3a468d174a5c64d3207b37","first_computed_at":"2026-05-18T03:11:58.207399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:58.207399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8GTLgmEixYBu8kZdzZk7pfXi6WpL9dGQ1d3tjGsfE9juCCVLpwqxQ27ZyG9cJ6eGy5LxSR6wkEjAVb9od4BICw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:58.208200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2414","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4af6516bc0f4eae3f6a400a7603bd0a8cd8a20ed489173ceb573d8fd85682feb","sha256:2bbffedf927f7f4d3e34ad549e6e0ede42d2804a396906c94643abe2abe17b86"],"state_sha256":"2040b377daf57c5f41f80c75253cc55b6fcc53e5999fb07ab8bd27639ebfa053"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4dK2JEn9NHDXsxcWJPW/Mz8a51xf5ZBnLj7WDbl2iFYauQKRrFOem6U1D6/WOZlMJEZPT4a8EabBw+5Jz15yAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:15:59.283260Z","bundle_sha256":"44d62b5ba399edfaf31e7da3239a3373feb08e7fa7950190e1e7807dc3f266f8"}}