{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ST7WN2J2KZ5RMCXZVD6DSHHGWJ","short_pith_number":"pith:ST7WN2J2","canonical_record":{"source":{"id":"1311.1230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-05T21:51:00Z","cross_cats_sorted":[],"title_canon_sha256":"ae212ef4ec984e6866026d62c3e9f5139ef51b4f0c699eb55b0452b46c696c75","abstract_canon_sha256":"6ab5675305e5a6ad7c8bbb73677c558b0235e041912c0d4c6a42e44a7c58d706"},"schema_version":"1.0"},"canonical_sha256":"94ff66e93a567b160af9a8fc391ce6b26d62df94c1feb603e38b1cb374f63759","source":{"kind":"arxiv","id":"1311.1230","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1230","created_at":"2026-05-18T03:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1230v1","created_at":"2026-05-18T03:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1230","created_at":"2026-05-18T03:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"ST7WN2J2KZ5R","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"ST7WN2J2KZ5RMCXZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"ST7WN2J2","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ST7WN2J2KZ5RMCXZVD6DSHHGWJ","target":"record","payload":{"canonical_record":{"source":{"id":"1311.1230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-05T21:51:00Z","cross_cats_sorted":[],"title_canon_sha256":"ae212ef4ec984e6866026d62c3e9f5139ef51b4f0c699eb55b0452b46c696c75","abstract_canon_sha256":"6ab5675305e5a6ad7c8bbb73677c558b0235e041912c0d4c6a42e44a7c58d706"},"schema_version":"1.0"},"canonical_sha256":"94ff66e93a567b160af9a8fc391ce6b26d62df94c1feb603e38b1cb374f63759","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:53.966219Z","signature_b64":"hrJHSadohL8UX1zgTwBpUW+1QQwdgF7p/L1/cGHJaUZijTQJgeABGmYQLvG9AcgDRBs44RrYMz7LzDsT9AFrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94ff66e93a567b160af9a8fc391ce6b26d62df94c1feb603e38b1cb374f63759","last_reissued_at":"2026-05-18T03:07:53.965494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:53.965494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.1230","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":"2026-05-18T03:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3TCTJdaXQEobbUqQQ/I63zaQfSMk49kW/DDEsxSCpXUxfhzkcI82taxVnXIcA98feIdwyaVeU39LeFkZuBWbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:21:57.763019Z"},"content_sha256":"8cdaa609660b723c374367f66ccbd45f0cc91365d4331e8d1babd8ffec3dd76f","schema_version":"1.0","event_id":"sha256:8cdaa609660b723c374367f66ccbd45f0cc91365d4331e8d1babd8ffec3dd76f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ST7WN2J2KZ5RMCXZVD6DSHHGWJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lorentz estimates for obstacle parabolic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paolo Baroni","submitted_at":"2013-11-05T21:51:00Z","abstract_excerpt":"We prove that the spatial gradient of (variational) solutions to parabolic obstacle problems of p-Laplacian type enjoys the same regularity of the data and of the derivatives of the obstacle in the scale of Lorentz spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1230","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":"2026-05-18T03:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwR0ByuZXqN3iCzHBJ6Dx/NKh/O2HWnNoOyMBtReCIzXdsZLeh+O5BK7KB2xHs/hcvybUc5Y5IkVtnOnDmDICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:21:57.763676Z"},"content_sha256":"f9a562d1e8f57986b0cf96ad2a7e2b3270b30f27e0dc966716a714bf437a633f","schema_version":"1.0","event_id":"sha256:f9a562d1e8f57986b0cf96ad2a7e2b3270b30f27e0dc966716a714bf437a633f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ST7WN2J2KZ5RMCXZVD6DSHHGWJ/bundle.json","state_url":"https://pith.science/pith/ST7WN2J2KZ5RMCXZVD6DSHHGWJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ST7WN2J2KZ5RMCXZVD6DSHHGWJ/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":"2026-05-31T19:21:57Z","links":{"resolver":"https://pith.science/pith/ST7WN2J2KZ5RMCXZVD6DSHHGWJ","bundle":"https://pith.science/pith/ST7WN2J2KZ5RMCXZVD6DSHHGWJ/bundle.json","state":"https://pith.science/pith/ST7WN2J2KZ5RMCXZVD6DSHHGWJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ST7WN2J2KZ5RMCXZVD6DSHHGWJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ST7WN2J2KZ5RMCXZVD6DSHHGWJ","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":"6ab5675305e5a6ad7c8bbb73677c558b0235e041912c0d4c6a42e44a7c58d706","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-05T21:51:00Z","title_canon_sha256":"ae212ef4ec984e6866026d62c3e9f5139ef51b4f0c699eb55b0452b46c696c75"},"schema_version":"1.0","source":{"id":"1311.1230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1230","created_at":"2026-05-18T03:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1230v1","created_at":"2026-05-18T03:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1230","created_at":"2026-05-18T03:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"ST7WN2J2KZ5R","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"ST7WN2J2KZ5RMCXZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"ST7WN2J2","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:f9a562d1e8f57986b0cf96ad2a7e2b3270b30f27e0dc966716a714bf437a633f","target":"graph","created_at":"2026-05-18T03:07:53Z","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 prove that the spatial gradient of (variational) solutions to parabolic obstacle problems of p-Laplacian type enjoys the same regularity of the data and of the derivatives of the obstacle in the scale of Lorentz spaces.","authors_text":"Paolo Baroni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-05T21:51:00Z","title":"Lorentz estimates for obstacle parabolic problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1230","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":"sha256:8cdaa609660b723c374367f66ccbd45f0cc91365d4331e8d1babd8ffec3dd76f","target":"record","created_at":"2026-05-18T03:07:53Z","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":"6ab5675305e5a6ad7c8bbb73677c558b0235e041912c0d4c6a42e44a7c58d706","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-05T21:51:00Z","title_canon_sha256":"ae212ef4ec984e6866026d62c3e9f5139ef51b4f0c699eb55b0452b46c696c75"},"schema_version":"1.0","source":{"id":"1311.1230","kind":"arxiv","version":1}},"canonical_sha256":"94ff66e93a567b160af9a8fc391ce6b26d62df94c1feb603e38b1cb374f63759","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94ff66e93a567b160af9a8fc391ce6b26d62df94c1feb603e38b1cb374f63759","first_computed_at":"2026-05-18T03:07:53.965494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:53.965494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hrJHSadohL8UX1zgTwBpUW+1QQwdgF7p/L1/cGHJaUZijTQJgeABGmYQLvG9AcgDRBs44RrYMz7LzDsT9AFrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:53.966219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cdaa609660b723c374367f66ccbd45f0cc91365d4331e8d1babd8ffec3dd76f","sha256:f9a562d1e8f57986b0cf96ad2a7e2b3270b30f27e0dc966716a714bf437a633f"],"state_sha256":"9ae3e66ff40eec0e421016562302688a5f42809153083fef61c4ed9e1cbaad22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hejRS2bHk9uQSGpjiFoZ1H43+V7b0MDMfe2EIkwb/Tu66TsKW0qkhi8aVAmgGRi8SrBqMGpvR4BZPW/fxAwRBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:21:57.767412Z","bundle_sha256":"2f4548437aeb1931c86108ea229c43ad0d5adbe0b0be4139c3e02c07d298d3ae"}}