{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NJWHM37DGW7R3MQAZXRHXL63J2","short_pith_number":"pith:NJWHM37D","canonical_record":{"source":{"id":"1601.03336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-13T18:09:57Z","cross_cats_sorted":[],"title_canon_sha256":"23466ff760a4ffde6fc73a3e220a86e2c8d028fa1aed90ed2aee659ca19d4c54","abstract_canon_sha256":"7a536573a145b7d9ae68cbce6df9a77b200c4498afb7d381d5bf33b886a06dfc"},"schema_version":"1.0"},"canonical_sha256":"6a6c766fe335bf1db200cde27bafdb4e8dba657e194644a154525522249ce262","source":{"kind":"arxiv","id":"1601.03336","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03336","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03336v1","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03336","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"pith_short_12","alias_value":"NJWHM37DGW7R","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJWHM37DGW7R3MQA","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJWHM37D","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NJWHM37DGW7R3MQAZXRHXL63J2","target":"record","payload":{"canonical_record":{"source":{"id":"1601.03336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-13T18:09:57Z","cross_cats_sorted":[],"title_canon_sha256":"23466ff760a4ffde6fc73a3e220a86e2c8d028fa1aed90ed2aee659ca19d4c54","abstract_canon_sha256":"7a536573a145b7d9ae68cbce6df9a77b200c4498afb7d381d5bf33b886a06dfc"},"schema_version":"1.0"},"canonical_sha256":"6a6c766fe335bf1db200cde27bafdb4e8dba657e194644a154525522249ce262","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:54.760413Z","signature_b64":"V7DNzX5uv/EIuJPca6XilmGrNxCWfoerSBEtNJV3YEbtvum50pjbBxEcOyZ6h2QCN99qpGm3sn6Ejj1BeAEcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a6c766fe335bf1db200cde27bafdb4e8dba657e194644a154525522249ce262","last_reissued_at":"2026-05-18T01:22:54.759765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:54.759765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.03336","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":"2026-05-18T01:22:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KiV8wMs0MoqTf/LaGDWEv37IHnfzYZOCEDWp3YH+JtgarjRXs47WZdPTqlKQmWiRF3+J0pj1LI5stQdumJMwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:36:38.549555Z"},"content_sha256":"34f1b8b57a65bb75076da60a96897fca2df8ebd2336e097b0eca91922e37be6a","schema_version":"1.0","event_id":"sha256:34f1b8b57a65bb75076da60a96897fca2df8ebd2336e097b0eca91922e37be6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NJWHM37DGW7R3MQAZXRHXL63J2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The multilinear restriction estimate: a short proof and a refinement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioan Bejenaru","submitted_at":"2016-01-13T18:09:57Z","abstract_excerpt":"We provide an alternative and self contained proof of the main result of Bennett, Carbery, Tao regarding the multilinear restriction estimate. The approach is inspired by the recent result of Guth about the Kakeya version of multilinear restriction estimate. At lower levels of multilinearity we provide a refined estimate in the context of small support for one of the terms involved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03336","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":"2026-05-18T01:22:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ebg7+pKYrAfqRfTyuCfb8HU9MqPOwgViwW6KfKEu/ZDEu7rLb7TX9cMR+M/PwsPMRQAHwX4wkZ6cDtmR+BgJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:36:38.549909Z"},"content_sha256":"3b8f6ae3c015f262c102826b92951639489dd7615ae9d5490673994cfda19bf8","schema_version":"1.0","event_id":"sha256:3b8f6ae3c015f262c102826b92951639489dd7615ae9d5490673994cfda19bf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJWHM37DGW7R3MQAZXRHXL63J2/bundle.json","state_url":"https://pith.science/pith/NJWHM37DGW7R3MQAZXRHXL63J2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJWHM37DGW7R3MQAZXRHXL63J2/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":"2026-05-30T22:36:38Z","links":{"resolver":"https://pith.science/pith/NJWHM37DGW7R3MQAZXRHXL63J2","bundle":"https://pith.science/pith/NJWHM37DGW7R3MQAZXRHXL63J2/bundle.json","state":"https://pith.science/pith/NJWHM37DGW7R3MQAZXRHXL63J2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJWHM37DGW7R3MQAZXRHXL63J2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NJWHM37DGW7R3MQAZXRHXL63J2","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":"7a536573a145b7d9ae68cbce6df9a77b200c4498afb7d381d5bf33b886a06dfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-13T18:09:57Z","title_canon_sha256":"23466ff760a4ffde6fc73a3e220a86e2c8d028fa1aed90ed2aee659ca19d4c54"},"schema_version":"1.0","source":{"id":"1601.03336","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03336","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03336v1","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03336","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"pith_short_12","alias_value":"NJWHM37DGW7R","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJWHM37DGW7R3MQA","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJWHM37D","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:3b8f6ae3c015f262c102826b92951639489dd7615ae9d5490673994cfda19bf8","target":"graph","created_at":"2026-05-18T01:22:54Z","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 provide an alternative and self contained proof of the main result of Bennett, Carbery, Tao regarding the multilinear restriction estimate. The approach is inspired by the recent result of Guth about the Kakeya version of multilinear restriction estimate. At lower levels of multilinearity we provide a refined estimate in the context of small support for one of the terms involved.","authors_text":"Ioan Bejenaru","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-13T18:09:57Z","title":"The multilinear restriction estimate: a short proof and a refinement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03336","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":"sha256:34f1b8b57a65bb75076da60a96897fca2df8ebd2336e097b0eca91922e37be6a","target":"record","created_at":"2026-05-18T01:22:54Z","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":"7a536573a145b7d9ae68cbce6df9a77b200c4498afb7d381d5bf33b886a06dfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-01-13T18:09:57Z","title_canon_sha256":"23466ff760a4ffde6fc73a3e220a86e2c8d028fa1aed90ed2aee659ca19d4c54"},"schema_version":"1.0","source":{"id":"1601.03336","kind":"arxiv","version":1}},"canonical_sha256":"6a6c766fe335bf1db200cde27bafdb4e8dba657e194644a154525522249ce262","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a6c766fe335bf1db200cde27bafdb4e8dba657e194644a154525522249ce262","first_computed_at":"2026-05-18T01:22:54.759765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:54.759765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V7DNzX5uv/EIuJPca6XilmGrNxCWfoerSBEtNJV3YEbtvum50pjbBxEcOyZ6h2QCN99qpGm3sn6Ejj1BeAEcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:54.760413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.03336","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34f1b8b57a65bb75076da60a96897fca2df8ebd2336e097b0eca91922e37be6a","sha256:3b8f6ae3c015f262c102826b92951639489dd7615ae9d5490673994cfda19bf8"],"state_sha256":"ad30151da4374cc7ce469bc76a1d07660cfd4278f18b196f964052dc2e77beff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63hi1INk5xDjplkJGGOZ6Owt+qaPPZdNVbgodamtF5NMPMky1jf4P6rQTNweq0CAgyagCXhog9Ej4dMYSFdLDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:36:38.552573Z","bundle_sha256":"d28750dadf8e3ba70fd85abcd907a227067226c89ff25a8679f780d0bca97751"}}