{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QBTDLUND6E4QOB4QJC65HW3YYN","short_pith_number":"pith:QBTDLUND","canonical_record":{"source":{"id":"1801.06329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-19T08:14:22Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"822f41b220042001725090170e42624e5ac54dea33473d3164d3bd86e619c3c2","abstract_canon_sha256":"fcfdf95c84eb1a11cb1379095a69d8ed17f107b1624132bcdcb509e177243c9f"},"schema_version":"1.0"},"canonical_sha256":"806635d1a3f13907079048bdd3db78c37008b5f94476a012096df4a5e5ffe2a4","source":{"kind":"arxiv","id":"1801.06329","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06329","created_at":"2026-05-18T00:25:30Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06329v1","created_at":"2026-05-18T00:25:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06329","created_at":"2026-05-18T00:25:30Z"},{"alias_kind":"pith_short_12","alias_value":"QBTDLUND6E4Q","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QBTDLUND6E4QOB4Q","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QBTDLUND","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QBTDLUND6E4QOB4QJC65HW3YYN","target":"record","payload":{"canonical_record":{"source":{"id":"1801.06329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-19T08:14:22Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"822f41b220042001725090170e42624e5ac54dea33473d3164d3bd86e619c3c2","abstract_canon_sha256":"fcfdf95c84eb1a11cb1379095a69d8ed17f107b1624132bcdcb509e177243c9f"},"schema_version":"1.0"},"canonical_sha256":"806635d1a3f13907079048bdd3db78c37008b5f94476a012096df4a5e5ffe2a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:30.484711Z","signature_b64":"+hWeCckybkRfJASKXcpze9KBR1foVfIrk+442oOpS37Gu7xdMwkNs6cZS9Y0jcWtjRbdgpmvPx5d0mUkA/vACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"806635d1a3f13907079048bdd3db78c37008b5f94476a012096df4a5e5ffe2a4","last_reissued_at":"2026-05-18T00:25:30.484172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:30.484172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.06329","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":"2026-05-18T00:25:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"171AZgn4ZIMpikuPTiK3goABsgoNm8wQn2rINUEcwV/K6LRu/oy8GtEvQTkSsGs0D0+GfR1QU/RI92RTQqQWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T15:38:58.056565Z"},"content_sha256":"9bf2bfdfccc098c20d492d2601e139d05f086640db1a527a78feef790262b457","schema_version":"1.0","event_id":"sha256:9bf2bfdfccc098c20d492d2601e139d05f086640db1a527a78feef790262b457"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QBTDLUND6E4QOB4QJC65HW3YYN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Hardy and Caffarelli-Kohn-Nirenberg inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Hoai-Minh Nguyen, Marco Squassina","submitted_at":"2018-01-19T08:14:22Z","abstract_excerpt":"We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps from a sphere into itself and characterizations of Sobolev spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06329","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":"2026-05-18T00:25:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rfX5fWgfvsOKmBnVrOjJMHuHA/VwockBXBC01FiCFbLYsevgBlzYy9LU0pxdP9pX/+tjLJkEJ40kF/3Y6mtJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T15:38:58.056899Z"},"content_sha256":"fac34101a043af045c7b04607ad4da306704b0b44981c1869c0bff165e406f7c","schema_version":"1.0","event_id":"sha256:fac34101a043af045c7b04607ad4da306704b0b44981c1869c0bff165e406f7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBTDLUND6E4QOB4QJC65HW3YYN/bundle.json","state_url":"https://pith.science/pith/QBTDLUND6E4QOB4QJC65HW3YYN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBTDLUND6E4QOB4QJC65HW3YYN/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":"2026-06-20T15:38:58Z","links":{"resolver":"https://pith.science/pith/QBTDLUND6E4QOB4QJC65HW3YYN","bundle":"https://pith.science/pith/QBTDLUND6E4QOB4QJC65HW3YYN/bundle.json","state":"https://pith.science/pith/QBTDLUND6E4QOB4QJC65HW3YYN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBTDLUND6E4QOB4QJC65HW3YYN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QBTDLUND6E4QOB4QJC65HW3YYN","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":"fcfdf95c84eb1a11cb1379095a69d8ed17f107b1624132bcdcb509e177243c9f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-19T08:14:22Z","title_canon_sha256":"822f41b220042001725090170e42624e5ac54dea33473d3164d3bd86e619c3c2"},"schema_version":"1.0","source":{"id":"1801.06329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06329","created_at":"2026-05-18T00:25:30Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06329v1","created_at":"2026-05-18T00:25:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06329","created_at":"2026-05-18T00:25:30Z"},{"alias_kind":"pith_short_12","alias_value":"QBTDLUND6E4Q","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QBTDLUND6E4QOB4Q","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QBTDLUND","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:fac34101a043af045c7b04607ad4da306704b0b44981c1869c0bff165e406f7c","target":"graph","created_at":"2026-05-18T00:25:30Z","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 establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps from a sphere into itself and characterizations of Sobolev spaces.","authors_text":"Hoai-Minh Nguyen, Marco Squassina","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-19T08:14:22Z","title":"On Hardy and Caffarelli-Kohn-Nirenberg inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06329","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":"sha256:9bf2bfdfccc098c20d492d2601e139d05f086640db1a527a78feef790262b457","target":"record","created_at":"2026-05-18T00:25:30Z","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":"fcfdf95c84eb1a11cb1379095a69d8ed17f107b1624132bcdcb509e177243c9f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-19T08:14:22Z","title_canon_sha256":"822f41b220042001725090170e42624e5ac54dea33473d3164d3bd86e619c3c2"},"schema_version":"1.0","source":{"id":"1801.06329","kind":"arxiv","version":1}},"canonical_sha256":"806635d1a3f13907079048bdd3db78c37008b5f94476a012096df4a5e5ffe2a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"806635d1a3f13907079048bdd3db78c37008b5f94476a012096df4a5e5ffe2a4","first_computed_at":"2026-05-18T00:25:30.484172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:30.484172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+hWeCckybkRfJASKXcpze9KBR1foVfIrk+442oOpS37Gu7xdMwkNs6cZS9Y0jcWtjRbdgpmvPx5d0mUkA/vACA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:30.484711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.06329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bf2bfdfccc098c20d492d2601e139d05f086640db1a527a78feef790262b457","sha256:fac34101a043af045c7b04607ad4da306704b0b44981c1869c0bff165e406f7c"],"state_sha256":"151c231989615f520f12946540acd0abebbf3d73012092b5bb9301bced4b2ae4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"enf7rgRGBRWP6qrdLy5zi4ZvF5eyzplaCdJQd1AwT0Xu4kvGyCYeRhq+ibEBai0gIorWtajjfBTOap9QlLH/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T15:38:58.058678Z","bundle_sha256":"9fb56d97d69a85e2426216096a9fea9c3d43a0165d1abbc49d31956ca30f4d5e"}}