{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ML62EAFLLWVSZN76ITR6HUFIUA","short_pith_number":"pith:ML62EAFL","canonical_record":{"source":{"id":"1710.07537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-20T14:10:58Z","cross_cats_sorted":[],"title_canon_sha256":"5fa0d9c2e663a24e0959e7e502b24786ff344629932295c2061104e0923472f2","abstract_canon_sha256":"df49ff3ed37601c0d039fc82bce2d6990bf81d389163ca7125e585856b474852"},"schema_version":"1.0"},"canonical_sha256":"62fda200ab5dab2cb7fe44e3e3d0a8a035af46c63f74d797de143124df18a04b","source":{"kind":"arxiv","id":"1710.07537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07537","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07537v1","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07537","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"pith_short_12","alias_value":"ML62EAFLLWVS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"ML62EAFLLWVSZN76","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"ML62EAFL","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ML62EAFLLWVSZN76ITR6HUFIUA","target":"record","payload":{"canonical_record":{"source":{"id":"1710.07537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-20T14:10:58Z","cross_cats_sorted":[],"title_canon_sha256":"5fa0d9c2e663a24e0959e7e502b24786ff344629932295c2061104e0923472f2","abstract_canon_sha256":"df49ff3ed37601c0d039fc82bce2d6990bf81d389163ca7125e585856b474852"},"schema_version":"1.0"},"canonical_sha256":"62fda200ab5dab2cb7fe44e3e3d0a8a035af46c63f74d797de143124df18a04b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:24.588999Z","signature_b64":"EFkfTs78UI780ShmijHZk3BaJvg0o5fAAZ6Rq/SIM/pV5RcLPVBWYdoYLRppSWfEdxuJ6JzhhiV3ia3+cryVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62fda200ab5dab2cb7fe44e3e3d0a8a035af46c63f74d797de143124df18a04b","last_reissued_at":"2026-05-18T00:32:24.588227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:24.588227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.07537","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nnZAXP3xZr5eus3jOOZ/UJelxGMfHue4hkPbWHFPb9r6+i4I//QjGG0UFhL/1u65t5T8T4nK2mDq+tTsfl69Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:21:05.365802Z"},"content_sha256":"e7a41af89f530549a9ddc702a6479bd7283323a663ec5c559eea01ca3783ce1e","schema_version":"1.0","event_id":"sha256:e7a41af89f530549a9ddc702a6479bd7283323a663ec5c559eea01ca3783ce1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ML62EAFLLWVSZN76ITR6HUFIUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bilinear restriction estimates for surfaces of codimension bigger than one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jong-Guk Bak, Jungjin Lee, Sanghyuk Lee","submitted_at":"2017-10-20T14:10:58Z","abstract_excerpt":"In connection with the restriction problem in $\\mathbb R^n$ for hypersurfaces including the sphere and paraboloid, the bilinear (adjoint) restriction estimates have been extensively studied. However, not much is known about such estimates for surfaces with codimension (and dimension) larger than one. In this paper we show sharp bilinear $L^2 \\times L^2 \\to L^q$ restriction estimates for general surfaces of higher codimension. In some special cases, we can apply these results to obtain the corresponding linear estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07537","kind":"arxiv","version":1},"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":"2026-05-18T00:32:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H69n5QphsE86kYgDwxxKAuEAFBl1itaRpkYuj3s6AwCDcpn5lOh5EQi4+DPkgjcC9sulV7HzF160LJezGn3mDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:21:05.366452Z"},"content_sha256":"6178def3c1c25bdb04c90a9ebbaee2a358cdabe4f04168f7717eaa4e91f47182","schema_version":"1.0","event_id":"sha256:6178def3c1c25bdb04c90a9ebbaee2a358cdabe4f04168f7717eaa4e91f47182"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ML62EAFLLWVSZN76ITR6HUFIUA/bundle.json","state_url":"https://pith.science/pith/ML62EAFLLWVSZN76ITR6HUFIUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ML62EAFLLWVSZN76ITR6HUFIUA/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":"2026-05-30T07:21:05Z","links":{"resolver":"https://pith.science/pith/ML62EAFLLWVSZN76ITR6HUFIUA","bundle":"https://pith.science/pith/ML62EAFLLWVSZN76ITR6HUFIUA/bundle.json","state":"https://pith.science/pith/ML62EAFLLWVSZN76ITR6HUFIUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ML62EAFLLWVSZN76ITR6HUFIUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ML62EAFLLWVSZN76ITR6HUFIUA","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":"df49ff3ed37601c0d039fc82bce2d6990bf81d389163ca7125e585856b474852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-20T14:10:58Z","title_canon_sha256":"5fa0d9c2e663a24e0959e7e502b24786ff344629932295c2061104e0923472f2"},"schema_version":"1.0","source":{"id":"1710.07537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07537","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07537v1","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07537","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"pith_short_12","alias_value":"ML62EAFLLWVS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"ML62EAFLLWVSZN76","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"ML62EAFL","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:6178def3c1c25bdb04c90a9ebbaee2a358cdabe4f04168f7717eaa4e91f47182","target":"graph","created_at":"2026-05-18T00:32:24Z","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":"In connection with the restriction problem in $\\mathbb R^n$ for hypersurfaces including the sphere and paraboloid, the bilinear (adjoint) restriction estimates have been extensively studied. However, not much is known about such estimates for surfaces with codimension (and dimension) larger than one. In this paper we show sharp bilinear $L^2 \\times L^2 \\to L^q$ restriction estimates for general surfaces of higher codimension. In some special cases, we can apply these results to obtain the corresponding linear estimates.","authors_text":"Jong-Guk Bak, Jungjin Lee, Sanghyuk Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-20T14:10:58Z","title":"Bilinear restriction estimates for surfaces of codimension bigger than one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07537","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:e7a41af89f530549a9ddc702a6479bd7283323a663ec5c559eea01ca3783ce1e","target":"record","created_at":"2026-05-18T00:32:24Z","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":"df49ff3ed37601c0d039fc82bce2d6990bf81d389163ca7125e585856b474852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-20T14:10:58Z","title_canon_sha256":"5fa0d9c2e663a24e0959e7e502b24786ff344629932295c2061104e0923472f2"},"schema_version":"1.0","source":{"id":"1710.07537","kind":"arxiv","version":1}},"canonical_sha256":"62fda200ab5dab2cb7fe44e3e3d0a8a035af46c63f74d797de143124df18a04b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62fda200ab5dab2cb7fe44e3e3d0a8a035af46c63f74d797de143124df18a04b","first_computed_at":"2026-05-18T00:32:24.588227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:24.588227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EFkfTs78UI780ShmijHZk3BaJvg0o5fAAZ6Rq/SIM/pV5RcLPVBWYdoYLRppSWfEdxuJ6JzhhiV3ia3+cryVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:24.588999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.07537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7a41af89f530549a9ddc702a6479bd7283323a663ec5c559eea01ca3783ce1e","sha256:6178def3c1c25bdb04c90a9ebbaee2a358cdabe4f04168f7717eaa4e91f47182"],"state_sha256":"72476af4f919c2eb6741a04a00d19ad9e81ac4cc32158ee39567a0739c907841"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sw7ihUpFBvuhhl7/UH9r6VzEsjUFUWRY6uYdOZJixgoGyLV3KN+CoR4i/JF3yWnugMXLo+x4vFuowJ9GxTG5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:21:05.369334Z","bundle_sha256":"814c70697d56d44e057e8e48b3e3306eec46ba7e1baa29219e98b7fbfcfc2205"}}