{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UTRPFEHW4C4QKGGPWFYSA7P5NG","short_pith_number":"pith:UTRPFEHW","canonical_record":{"source":{"id":"1610.00503","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-03T11:45:59Z","cross_cats_sorted":["math.CA","math.DG"],"title_canon_sha256":"749a2ce5c3aa69b31fa51d9ed118ad851382c1cc925d9320f0099cfd9d7b7b31","abstract_canon_sha256":"ce6424d5c7898dbff86b13598fe650c6cdb641d0a201623122dca8f9f2646c42"},"schema_version":"1.0"},"canonical_sha256":"a4e2f290f6e0b90518cfb171207dfd6984c124a8885912c9f173948677c38218","source":{"kind":"arxiv","id":"1610.00503","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00503","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00503v2","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00503","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"pith_short_12","alias_value":"UTRPFEHW4C4Q","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UTRPFEHW4C4QKGGP","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UTRPFEHW","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UTRPFEHW4C4QKGGPWFYSA7P5NG","target":"record","payload":{"canonical_record":{"source":{"id":"1610.00503","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-03T11:45:59Z","cross_cats_sorted":["math.CA","math.DG"],"title_canon_sha256":"749a2ce5c3aa69b31fa51d9ed118ad851382c1cc925d9320f0099cfd9d7b7b31","abstract_canon_sha256":"ce6424d5c7898dbff86b13598fe650c6cdb641d0a201623122dca8f9f2646c42"},"schema_version":"1.0"},"canonical_sha256":"a4e2f290f6e0b90518cfb171207dfd6984c124a8885912c9f173948677c38218","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:07.831993Z","signature_b64":"+z6Z+nhL7d6v52M0OpI9sjkLDYFVksvKWhJDJpVeoem3JUOfqI/gJmbc2dq9LOv0obl9RujicLza6u1SGRvtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4e2f290f6e0b90518cfb171207dfd6984c124a8885912c9f173948677c38218","last_reissued_at":"2026-05-18T00:41:07.831374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:07.831374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.00503","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":"2026-05-18T00:41:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5IJcrNC988JZ3yg55ORS4LMiWijgLC7yNwlaa6wE0eWAjGV7BO7l/yCCKS4A+Kd/dDUO7TLpO/8aVwD8C2gkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:28:21.681179Z"},"content_sha256":"58d0128c6e2f248362d7da01d9cae32f32c298156b2c4c2387fc3c78e2561c43","schema_version":"1.0","event_id":"sha256:58d0128c6e2f248362d7da01d9cae32f32c298156b2c4c2387fc3c78e2561c43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UTRPFEHW4C4QKGGPWFYSA7P5NG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DG"],"primary_cat":"math.AP","authors_text":"Jean Van Schaftingen, Po-Lam Yung, Sagun Chanillo","submitted_at":"2016-10-03T11:45:59Z","abstract_excerpt":"Let M be a globally Riemannian symmetric space. We prove a duality estimate between pairings of vector fields with divergence zero and and in L^1 with vector fields in a critical Sobolev space on M. As a consequence we get a sharp Calderon-Zygmund estimate for solutions to Poisson's equation on M, where the right side data is manufactured from divergence free vector fields which are in L^1. Such a result was proved earlier by Jean Bourgain and Haim Brezis on Euclidean space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00503","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":"2026-05-18T00:41:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d3Oss6ZXVedpR5O5/XxszGGqevrtk/YF+B3DPArMVsyd8ApZp80hFORHiEDe96n3FBwbJw04wN/6YUOWcaFsDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:28:21.681845Z"},"content_sha256":"c4a0a48c66a8ca6d24c8c45a275d8580675f7dd77e52651f7a8a07a4d6624a4f","schema_version":"1.0","event_id":"sha256:c4a0a48c66a8ca6d24c8c45a275d8580675f7dd77e52651f7a8a07a4d6624a4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UTRPFEHW4C4QKGGPWFYSA7P5NG/bundle.json","state_url":"https://pith.science/pith/UTRPFEHW4C4QKGGPWFYSA7P5NG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UTRPFEHW4C4QKGGPWFYSA7P5NG/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":"2026-05-30T14:28:21Z","links":{"resolver":"https://pith.science/pith/UTRPFEHW4C4QKGGPWFYSA7P5NG","bundle":"https://pith.science/pith/UTRPFEHW4C4QKGGPWFYSA7P5NG/bundle.json","state":"https://pith.science/pith/UTRPFEHW4C4QKGGPWFYSA7P5NG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UTRPFEHW4C4QKGGPWFYSA7P5NG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UTRPFEHW4C4QKGGPWFYSA7P5NG","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":"ce6424d5c7898dbff86b13598fe650c6cdb641d0a201623122dca8f9f2646c42","cross_cats_sorted":["math.CA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-03T11:45:59Z","title_canon_sha256":"749a2ce5c3aa69b31fa51d9ed118ad851382c1cc925d9320f0099cfd9d7b7b31"},"schema_version":"1.0","source":{"id":"1610.00503","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00503","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00503v2","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00503","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"pith_short_12","alias_value":"UTRPFEHW4C4Q","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UTRPFEHW4C4QKGGP","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UTRPFEHW","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:c4a0a48c66a8ca6d24c8c45a275d8580675f7dd77e52651f7a8a07a4d6624a4f","target":"graph","created_at":"2026-05-18T00:41:07Z","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":"Let M be a globally Riemannian symmetric space. We prove a duality estimate between pairings of vector fields with divergence zero and and in L^1 with vector fields in a critical Sobolev space on M. As a consequence we get a sharp Calderon-Zygmund estimate for solutions to Poisson's equation on M, where the right side data is manufactured from divergence free vector fields which are in L^1. Such a result was proved earlier by Jean Bourgain and Haim Brezis on Euclidean space.","authors_text":"Jean Van Schaftingen, Po-Lam Yung, Sagun Chanillo","cross_cats":["math.CA","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-03T11:45:59Z","title":"Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00503","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":"sha256:58d0128c6e2f248362d7da01d9cae32f32c298156b2c4c2387fc3c78e2561c43","target":"record","created_at":"2026-05-18T00:41:07Z","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":"ce6424d5c7898dbff86b13598fe650c6cdb641d0a201623122dca8f9f2646c42","cross_cats_sorted":["math.CA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-03T11:45:59Z","title_canon_sha256":"749a2ce5c3aa69b31fa51d9ed118ad851382c1cc925d9320f0099cfd9d7b7b31"},"schema_version":"1.0","source":{"id":"1610.00503","kind":"arxiv","version":2}},"canonical_sha256":"a4e2f290f6e0b90518cfb171207dfd6984c124a8885912c9f173948677c38218","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4e2f290f6e0b90518cfb171207dfd6984c124a8885912c9f173948677c38218","first_computed_at":"2026-05-18T00:41:07.831374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:07.831374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+z6Z+nhL7d6v52M0OpI9sjkLDYFVksvKWhJDJpVeoem3JUOfqI/gJmbc2dq9LOv0obl9RujicLza6u1SGRvtAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:07.831993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00503","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58d0128c6e2f248362d7da01d9cae32f32c298156b2c4c2387fc3c78e2561c43","sha256:c4a0a48c66a8ca6d24c8c45a275d8580675f7dd77e52651f7a8a07a4d6624a4f"],"state_sha256":"433703e5bd9915e25fb4cad62278f1f37e8d88fc0f0a2bebaa5e613348ffc007"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YU0vlKt70WS+gq4xc3fnOoU0FTH+01nlmSHNFha0EY5ZbEzFQdI5GiA7jGHnEfc10pirPPp1tREdBCYaY6oJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:28:21.685110Z","bundle_sha256":"cd15da9d6635b389696544b7027d3422f6a052282f08fd4edb9406953a28804b"}}