{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:APK665OS4GBBYCJS76ZAQT26TD","short_pith_number":"pith:APK665OS","canonical_record":{"source":{"id":"1101.3129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-01-17T06:38:46Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"9d7df40fe7819d1ed8da18dabcad531cc38c2c64ff488c0b3ca490a32052bea6","abstract_canon_sha256":"8bad9a850ce6c51171576ba1f52fe7644b4b2ac912c21e6a7e36f1c6068fac66"},"schema_version":"1.0"},"canonical_sha256":"03d5ef75d2e1821c0932ffb2084f5e98cb3bfe142dc05ab3deddaa56b54be7fa","source":{"kind":"arxiv","id":"1101.3129","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3129","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3129v1","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3129","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"APK665OS4GBB","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"APK665OS4GBBYCJS","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"APK665OS","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:APK665OS4GBBYCJS76ZAQT26TD","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-01-17T06:38:46Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"9d7df40fe7819d1ed8da18dabcad531cc38c2c64ff488c0b3ca490a32052bea6","abstract_canon_sha256":"8bad9a850ce6c51171576ba1f52fe7644b4b2ac912c21e6a7e36f1c6068fac66"},"schema_version":"1.0"},"canonical_sha256":"03d5ef75d2e1821c0932ffb2084f5e98cb3bfe142dc05ab3deddaa56b54be7fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:30.448796Z","signature_b64":"qSDfiU/Z2agF6rHq+5eB4MxCpx/7srydGUy97AMLnfXMDQtyf2mNGh//jerlYhnsNoYW24636D/OjM+0EC46CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03d5ef75d2e1821c0932ffb2084f5e98cb3bfe142dc05ab3deddaa56b54be7fa","last_reissued_at":"2026-05-18T04:31:30.448399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:30.448399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3129","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":"2026-05-18T04:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sHalfe+SG4Bow/7XtNVpkxfsNdhLt2ewxDjYpxjqRtHcjh8ybc0G7UV0yP8DgaQcHIdfYyzX9RfcAFNf1vK8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:55:08.600613Z"},"content_sha256":"dfe4dfbfdaf6f003cbdb1e9bc7077330a7d9551796546e2b04ac48fdbaf34252","schema_version":"1.0","event_id":"sha256:dfe4dfbfdaf6f003cbdb1e9bc7077330a7d9551796546e2b04ac48fdbaf34252"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:APK665OS4GBBYCJS76ZAQT26TD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"A. A. Balinsky, T. Umeda, W. D. Evans","submitted_at":"2011-01-17T06:38:46Z","abstract_excerpt":"Dirac-Sobolev and Dirac-Hardy inequalities in $L^1$ are established in which the $L^p$ spaces which feature in the classical Sobolev and Hardy inequalities are replaced by weak $L^p$ spaces. Counter examples to the analogues of the classical inequalities are shown to be provided by zero modes for appropriate Pauli operators constructed by Loss and Yau."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3129","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":"2026-05-18T04:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9lWhh8BPfaR0qO/U7gkJY1ki0hdr2NnWszWCGsMwhMynEhmQ+olbAaMUOGM6Bohet9z9vDnAGpZ5XTCFVpQ+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:55:08.601379Z"},"content_sha256":"74a3add1349aaa05134b96c0d7ac80c201b94040d3df809970fed645af7bb1da","schema_version":"1.0","event_id":"sha256:74a3add1349aaa05134b96c0d7ac80c201b94040d3df809970fed645af7bb1da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/APK665OS4GBBYCJS76ZAQT26TD/bundle.json","state_url":"https://pith.science/pith/APK665OS4GBBYCJS76ZAQT26TD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/APK665OS4GBBYCJS76ZAQT26TD/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":"2026-06-09T16:55:08Z","links":{"resolver":"https://pith.science/pith/APK665OS4GBBYCJS76ZAQT26TD","bundle":"https://pith.science/pith/APK665OS4GBBYCJS76ZAQT26TD/bundle.json","state":"https://pith.science/pith/APK665OS4GBBYCJS76ZAQT26TD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/APK665OS4GBBYCJS76ZAQT26TD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:APK665OS4GBBYCJS76ZAQT26TD","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":"8bad9a850ce6c51171576ba1f52fe7644b4b2ac912c21e6a7e36f1c6068fac66","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-01-17T06:38:46Z","title_canon_sha256":"9d7df40fe7819d1ed8da18dabcad531cc38c2c64ff488c0b3ca490a32052bea6"},"schema_version":"1.0","source":{"id":"1101.3129","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3129","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3129v1","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3129","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"APK665OS4GBB","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"APK665OS4GBBYCJS","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"APK665OS","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:74a3add1349aaa05134b96c0d7ac80c201b94040d3df809970fed645af7bb1da","target":"graph","created_at":"2026-05-18T04:31:30Z","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":"Dirac-Sobolev and Dirac-Hardy inequalities in $L^1$ are established in which the $L^p$ spaces which feature in the classical Sobolev and Hardy inequalities are replaced by weak $L^p$ spaces. Counter examples to the analogues of the classical inequalities are shown to be provided by zero modes for appropriate Pauli operators constructed by Loss and Yau.","authors_text":"A. A. Balinsky, T. Umeda, W. D. Evans","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-01-17T06:38:46Z","title":"The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3129","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:dfe4dfbfdaf6f003cbdb1e9bc7077330a7d9551796546e2b04ac48fdbaf34252","target":"record","created_at":"2026-05-18T04:31:30Z","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":"8bad9a850ce6c51171576ba1f52fe7644b4b2ac912c21e6a7e36f1c6068fac66","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-01-17T06:38:46Z","title_canon_sha256":"9d7df40fe7819d1ed8da18dabcad531cc38c2c64ff488c0b3ca490a32052bea6"},"schema_version":"1.0","source":{"id":"1101.3129","kind":"arxiv","version":1}},"canonical_sha256":"03d5ef75d2e1821c0932ffb2084f5e98cb3bfe142dc05ab3deddaa56b54be7fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03d5ef75d2e1821c0932ffb2084f5e98cb3bfe142dc05ab3deddaa56b54be7fa","first_computed_at":"2026-05-18T04:31:30.448399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:30.448399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qSDfiU/Z2agF6rHq+5eB4MxCpx/7srydGUy97AMLnfXMDQtyf2mNGh//jerlYhnsNoYW24636D/OjM+0EC46CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:30.448796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3129","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfe4dfbfdaf6f003cbdb1e9bc7077330a7d9551796546e2b04ac48fdbaf34252","sha256:74a3add1349aaa05134b96c0d7ac80c201b94040d3df809970fed645af7bb1da"],"state_sha256":"5f85c28b1b7038a3b6b02bc4e57fdeb3f7c61b7feccfdecf5c8c2f7d7b595894"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6X0tBtQre5jpskQNIu/8crxhVwDLnZlbfRZsOhoY3DuSQ1VmEhDSRoj0wQfsOWayzZKauw+8vdjLoZTHlr2Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:55:08.605280Z","bundle_sha256":"6c0858277bc409d22d764e92673e385cb24c23f344b7ad0994456c21e401e483"}}