{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PSKEX6WH6FK35IRAWWDLXJBN3M","short_pith_number":"pith:PSKEX6WH","canonical_record":{"source":{"id":"1507.06100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-22T08:34:53Z","cross_cats_sorted":[],"title_canon_sha256":"f8dc9d2398fe0225572a86b2e104e292fee4128f63789f3eabe4e2db097f0868","abstract_canon_sha256":"fd3c4b9100135dcc77c53f2d167684e95bf370b9e6b5b97b8b200dc03c0cf8e6"},"schema_version":"1.0"},"canonical_sha256":"7c944bfac7f155bea220b586bba42ddb17968342b86599ffcef21e82b9eb9c6a","source":{"kind":"arxiv","id":"1507.06100","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06100","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06100v2","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06100","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"PSKEX6WH6FK3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PSKEX6WH6FK35IRA","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PSKEX6WH","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PSKEX6WH6FK35IRAWWDLXJBN3M","target":"record","payload":{"canonical_record":{"source":{"id":"1507.06100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-22T08:34:53Z","cross_cats_sorted":[],"title_canon_sha256":"f8dc9d2398fe0225572a86b2e104e292fee4128f63789f3eabe4e2db097f0868","abstract_canon_sha256":"fd3c4b9100135dcc77c53f2d167684e95bf370b9e6b5b97b8b200dc03c0cf8e6"},"schema_version":"1.0"},"canonical_sha256":"7c944bfac7f155bea220b586bba42ddb17968342b86599ffcef21e82b9eb9c6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:43.611907Z","signature_b64":"sqNtoPxbiCDJ88UZKD8CsNrmaP3shzp1S2Enro7EZI5zi8g/OEuXftN8oL/Q0h4XFLfP0iHY7pkD42nm8Y6RCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c944bfac7f155bea220b586bba42ddb17968342b86599ffcef21e82b9eb9c6a","last_reissued_at":"2026-05-17T23:43:43.611328Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:43.611328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.06100","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":"2026-05-17T23:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VeijSXHvqnlP/DWv8IvGL7PEEfn45n+VnEbzPmQ3AaITzDdwpzyHH4GTX+MJZLBV8reM93cJTdwXtD9eMfhyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:20:06.367873Z"},"content_sha256":"12416b10cc09ef1846eb074b9643967b2e4bd30c660136792e60ffe08c9ab9b6","schema_version":"1.0","event_id":"sha256:12416b10cc09ef1846eb074b9643967b2e4bd30c660136792e60ffe08c9ab9b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PSKEX6WH6FK35IRAWWDLXJBN3M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear adjoint restriction estimates for paraboloid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Jiqiang Zheng, Junyong Zhang","submitted_at":"2015-07-22T08:34:53Z","abstract_excerpt":"We prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes the paraboloid restriction estimate in radial case from [Shao, Rev. Mat. Iberoam. 25(2009), 1127-1168], as well as the result from [Miao et al. Proc. AMS 140(2012), 2091-2102]. As an application, we show a local smoothing estimate for a solution of the linear Schr\\\"odinger equation under the assumption that the initial datum has additional angular regularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06100","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":"2026-05-17T23:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rgS6iI440y7Tb1Oa20rPG8W0m06deNNr9YZa3Q0xwEfPERCmzt4QEgc2f71Nxx2smMHAk1mARKpNbJ+5d+HGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:20:06.368526Z"},"content_sha256":"ade3d783127c2a9b28666aa3398b12a201047a945ffcbf866368fdd9d1274237","schema_version":"1.0","event_id":"sha256:ade3d783127c2a9b28666aa3398b12a201047a945ffcbf866368fdd9d1274237"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PSKEX6WH6FK35IRAWWDLXJBN3M/bundle.json","state_url":"https://pith.science/pith/PSKEX6WH6FK35IRAWWDLXJBN3M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PSKEX6WH6FK35IRAWWDLXJBN3M/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":"2026-05-27T11:20:06Z","links":{"resolver":"https://pith.science/pith/PSKEX6WH6FK35IRAWWDLXJBN3M","bundle":"https://pith.science/pith/PSKEX6WH6FK35IRAWWDLXJBN3M/bundle.json","state":"https://pith.science/pith/PSKEX6WH6FK35IRAWWDLXJBN3M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PSKEX6WH6FK35IRAWWDLXJBN3M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PSKEX6WH6FK35IRAWWDLXJBN3M","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":"fd3c4b9100135dcc77c53f2d167684e95bf370b9e6b5b97b8b200dc03c0cf8e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-22T08:34:53Z","title_canon_sha256":"f8dc9d2398fe0225572a86b2e104e292fee4128f63789f3eabe4e2db097f0868"},"schema_version":"1.0","source":{"id":"1507.06100","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06100","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06100v2","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06100","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"PSKEX6WH6FK3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PSKEX6WH6FK35IRA","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PSKEX6WH","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:ade3d783127c2a9b28666aa3398b12a201047a945ffcbf866368fdd9d1274237","target":"graph","created_at":"2026-05-17T23:43:43Z","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 prove a class of modified paraboloid restriction estimates with a loss of angular derivatives for the full set of paraboloid restriction conjecture indices. This result generalizes the paraboloid restriction estimate in radial case from [Shao, Rev. Mat. Iberoam. 25(2009), 1127-1168], as well as the result from [Miao et al. Proc. AMS 140(2012), 2091-2102]. As an application, we show a local smoothing estimate for a solution of the linear Schr\\\"odinger equation under the assumption that the initial datum has additional angular regularity.","authors_text":"Changxing Miao, Jiqiang Zheng, Junyong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-22T08:34:53Z","title":"Linear adjoint restriction estimates for paraboloid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06100","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":"sha256:12416b10cc09ef1846eb074b9643967b2e4bd30c660136792e60ffe08c9ab9b6","target":"record","created_at":"2026-05-17T23:43:43Z","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":"fd3c4b9100135dcc77c53f2d167684e95bf370b9e6b5b97b8b200dc03c0cf8e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-22T08:34:53Z","title_canon_sha256":"f8dc9d2398fe0225572a86b2e104e292fee4128f63789f3eabe4e2db097f0868"},"schema_version":"1.0","source":{"id":"1507.06100","kind":"arxiv","version":2}},"canonical_sha256":"7c944bfac7f155bea220b586bba42ddb17968342b86599ffcef21e82b9eb9c6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c944bfac7f155bea220b586bba42ddb17968342b86599ffcef21e82b9eb9c6a","first_computed_at":"2026-05-17T23:43:43.611328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:43.611328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sqNtoPxbiCDJ88UZKD8CsNrmaP3shzp1S2Enro7EZI5zi8g/OEuXftN8oL/Q0h4XFLfP0iHY7pkD42nm8Y6RCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:43.611907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06100","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12416b10cc09ef1846eb074b9643967b2e4bd30c660136792e60ffe08c9ab9b6","sha256:ade3d783127c2a9b28666aa3398b12a201047a945ffcbf866368fdd9d1274237"],"state_sha256":"22fb1f2a61a641782bf5da26dba5d97c4090f9a4ed50cacce7802516a830d1dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IMUSlNJOaAFmLLXJ/IUFYWWVjR7lSAvIOCXQHpVEboGakIkHS8gCmO9jeuAky1gvj7Z0zFcMvOxftUQKGYLPCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:20:06.372120Z","bundle_sha256":"bbece71c2e9fd49a70a1477e0dfa74014d91a362c2becfed08b8568ef7ca3f3c"}}