{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZLSXALZGPGO5N5J7SXDX3JLQF2","short_pith_number":"pith:ZLSXALZG","canonical_record":{"source":{"id":"1301.1872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-09T14:46:17Z","cross_cats_sorted":[],"title_canon_sha256":"410d7c829d62b06eaca8ac00bc9d48e43ea1c2a015da296a76f173755b06e609","abstract_canon_sha256":"5a1a8add794886baf2a687b133409b01fa7dcf6cc26559c26b443450b103cdf2"},"schema_version":"1.0"},"canonical_sha256":"cae5702f26799dd6f53f95c77da5702eb15c64833dd96519a5857ab8a599573f","source":{"kind":"arxiv","id":"1301.1872","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1872","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1872v2","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1872","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZLSXALZGPGO5","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZLSXALZGPGO5N5J7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZLSXALZG","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZLSXALZGPGO5N5J7SXDX3JLQF2","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-09T14:46:17Z","cross_cats_sorted":[],"title_canon_sha256":"410d7c829d62b06eaca8ac00bc9d48e43ea1c2a015da296a76f173755b06e609","abstract_canon_sha256":"5a1a8add794886baf2a687b133409b01fa7dcf6cc26559c26b443450b103cdf2"},"schema_version":"1.0"},"canonical_sha256":"cae5702f26799dd6f53f95c77da5702eb15c64833dd96519a5857ab8a599573f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:49.696993Z","signature_b64":"OkmyzoLXU4fQCNuQAY3fMxu/Yu1WvCJxcOCwqjv5n37mujdNmxiR4eGNa1b9+BuKgW1+hVXQ7nMismvW4AEdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cae5702f26799dd6f53f95c77da5702eb15c64833dd96519a5857ab8a599573f","last_reissued_at":"2026-05-18T03:34:49.696506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:49.696506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1872","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":"2026-05-18T03:34:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hipqd3JwGdAkYg/R5JTBU7rktJOvChMuiu2YauWz7xv8WCaAHwS+S+b1RHLltnCKw1pAxmbiVgNMZGJrM32SDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:46:26.680678Z"},"content_sha256":"b0d58fb8857f8a68c108ba7f8ce28ece26d08b176de348a7a3decf88e199d2ef","schema_version":"1.0","event_id":"sha256:b0d58fb8857f8a68c108ba7f8ce28ece26d08b176de348a7a3decf88e199d2ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZLSXALZGPGO5N5J7SXDX3JLQF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global estimates for nonlinear parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnese Di Castro, Giampiero Palatucci, Paolo Baroni","submitted_at":"2013-01-09T14:46:17Z","abstract_excerpt":"We consider nonlinear parabolic equations of the type $$ u_t - div a(x, t, Du)= f(x,t) on \\Omega_T = \\Omega\\times (-T,0), $$ under standard growth conditions on $a$, with $f$ only assumed to be integrable. We prove general decay estimates up to the boundary for level sets of the solutions $u$ and the gradient $Du$ which imply very general estimates in Lebesgue and Lorentz spaces. Assuming only that the involved domains satisfy a mild exterior capacity density condition, we provide global regularity results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1872","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":"2026-05-18T03:34:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IHeONrTUUgJVuieJyp+0AAjfjyW+l7ij6CYzh53/AuTnfZWQNExBTBRjJD3YQTrUxesq3HI6Mc6PMbbvO/j+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:46:26.681269Z"},"content_sha256":"e15a3a060b765077f883c0bcece6fc5094517512f676fcb7744ca65a2e66774e","schema_version":"1.0","event_id":"sha256:e15a3a060b765077f883c0bcece6fc5094517512f676fcb7744ca65a2e66774e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZLSXALZGPGO5N5J7SXDX3JLQF2/bundle.json","state_url":"https://pith.science/pith/ZLSXALZGPGO5N5J7SXDX3JLQF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZLSXALZGPGO5N5J7SXDX3JLQF2/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":"2026-05-31T15:46:26Z","links":{"resolver":"https://pith.science/pith/ZLSXALZGPGO5N5J7SXDX3JLQF2","bundle":"https://pith.science/pith/ZLSXALZGPGO5N5J7SXDX3JLQF2/bundle.json","state":"https://pith.science/pith/ZLSXALZGPGO5N5J7SXDX3JLQF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZLSXALZGPGO5N5J7SXDX3JLQF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZLSXALZGPGO5N5J7SXDX3JLQF2","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":"5a1a8add794886baf2a687b133409b01fa7dcf6cc26559c26b443450b103cdf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-09T14:46:17Z","title_canon_sha256":"410d7c829d62b06eaca8ac00bc9d48e43ea1c2a015da296a76f173755b06e609"},"schema_version":"1.0","source":{"id":"1301.1872","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1872","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1872v2","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1872","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZLSXALZGPGO5","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZLSXALZGPGO5N5J7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZLSXALZG","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:e15a3a060b765077f883c0bcece6fc5094517512f676fcb7744ca65a2e66774e","target":"graph","created_at":"2026-05-18T03:34:49Z","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 consider nonlinear parabolic equations of the type $$ u_t - div a(x, t, Du)= f(x,t) on \\Omega_T = \\Omega\\times (-T,0), $$ under standard growth conditions on $a$, with $f$ only assumed to be integrable. We prove general decay estimates up to the boundary for level sets of the solutions $u$ and the gradient $Du$ which imply very general estimates in Lebesgue and Lorentz spaces. Assuming only that the involved domains satisfy a mild exterior capacity density condition, we provide global regularity results.","authors_text":"Agnese Di Castro, Giampiero Palatucci, Paolo Baroni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-09T14:46:17Z","title":"Global estimates for nonlinear parabolic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1872","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:b0d58fb8857f8a68c108ba7f8ce28ece26d08b176de348a7a3decf88e199d2ef","target":"record","created_at":"2026-05-18T03:34:49Z","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":"5a1a8add794886baf2a687b133409b01fa7dcf6cc26559c26b443450b103cdf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-09T14:46:17Z","title_canon_sha256":"410d7c829d62b06eaca8ac00bc9d48e43ea1c2a015da296a76f173755b06e609"},"schema_version":"1.0","source":{"id":"1301.1872","kind":"arxiv","version":2}},"canonical_sha256":"cae5702f26799dd6f53f95c77da5702eb15c64833dd96519a5857ab8a599573f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cae5702f26799dd6f53f95c77da5702eb15c64833dd96519a5857ab8a599573f","first_computed_at":"2026-05-18T03:34:49.696506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:49.696506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OkmyzoLXU4fQCNuQAY3fMxu/Yu1WvCJxcOCwqjv5n37mujdNmxiR4eGNa1b9+BuKgW1+hVXQ7nMismvW4AEdAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:49.696993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1872","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0d58fb8857f8a68c108ba7f8ce28ece26d08b176de348a7a3decf88e199d2ef","sha256:e15a3a060b765077f883c0bcece6fc5094517512f676fcb7744ca65a2e66774e"],"state_sha256":"8983033fab90e157299fc8c77648268fe16e1ccd849cdf0c84c4c00993e94ee7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+VtYBh+9phl4FdZ7hvi2PXZo+NVL5NV/ggBoVvFqx45Xv0huK9zDcWXz5j3WF8iy6ZYHL4Zq4V1w6auaufPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:46:26.684396Z","bundle_sha256":"107bd803c7863e790d957176ab41d337be9898ff2e40f0b29ad6e0ba05c7de89"}}