{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XQNR55HU5OCN6QR2SUKANUNYPA","short_pith_number":"pith:XQNR55HU","canonical_record":{"source":{"id":"1201.4573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-22T16:57:23Z","cross_cats_sorted":[],"title_canon_sha256":"b1b428ebf3c9b76b592d03e549d737e54d57417b463754c0c3df9cbb2d03ed42","abstract_canon_sha256":"ba466b8ca37177d176ba27b2fd8863123e4e27d386090a1e3b8c26c6ee0216ff"},"schema_version":"1.0"},"canonical_sha256":"bc1b1ef4f4eb84df423a951406d1b87820e2dec1dcbff100a1634ae0eacbf864","source":{"kind":"arxiv","id":"1201.4573","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4573","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4573v1","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4573","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"XQNR55HU5OCN","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XQNR55HU5OCN6QR2","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XQNR55HU","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XQNR55HU5OCN6QR2SUKANUNYPA","target":"record","payload":{"canonical_record":{"source":{"id":"1201.4573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-22T16:57:23Z","cross_cats_sorted":[],"title_canon_sha256":"b1b428ebf3c9b76b592d03e549d737e54d57417b463754c0c3df9cbb2d03ed42","abstract_canon_sha256":"ba466b8ca37177d176ba27b2fd8863123e4e27d386090a1e3b8c26c6ee0216ff"},"schema_version":"1.0"},"canonical_sha256":"bc1b1ef4f4eb84df423a951406d1b87820e2dec1dcbff100a1634ae0eacbf864","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:05.689748Z","signature_b64":"goiYy+A2knWi2XvsAWCtpaIRHjg7kSdla/bmqz63+goC5TVg1tbIFMeFb5SsVLlghOx64AC53UIlsOe6MND8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc1b1ef4f4eb84df423a951406d1b87820e2dec1dcbff100a1634ae0eacbf864","last_reissued_at":"2026-05-18T04:04:05.688810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:05.688810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.4573","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":"2026-05-18T04:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y3Mjs4bnXbaFfC0GMwYUwp2Gm2justWRaXwvb5ziBL1FvueQClZyNPgZAZa2UUcCQ64p3jwlHZpFnFXPQPj2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:15:42.862008Z"},"content_sha256":"b46fc4d2267448f2cbb101ff5f6c7f68462509bb9bc96ed76ceab5634668dea1","schema_version":"1.0","event_id":"sha256:b46fc4d2267448f2cbb101ff5f6c7f68462509bb9bc96ed76ceab5634668dea1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XQNR55HU5OCN6QR2SUKANUNYPA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some $L_{p}$-estimates for elliptic and parabolic operators with measurable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"N. V. Krylov","submitted_at":"2012-01-22T16:57:23Z","abstract_excerpt":"We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order equations in \\cite{DKL}. The first type is an estimate of the $\\gamma$th norm of the second-order derivatives, where $\\gamma\\in(0,1)$, and the second type deals with estimates of the resolvent operators in $L_{p}$ when the first-order coefficients are summable to an appropriate power."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4573","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":"2026-05-18T04:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hS1qO6KcI8oYzQJkj0mmIEfvIl78+FTH4FNDlXIFYibDl8l+FlVl/nuPk9P2wtZ+KzLD1XeOgq0lrCJsn8IPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:15:42.862355Z"},"content_sha256":"5247e945b1eefe90d2f4f1e67f52a33cee254269b2b15fa5294d8fa069e9ebbe","schema_version":"1.0","event_id":"sha256:5247e945b1eefe90d2f4f1e67f52a33cee254269b2b15fa5294d8fa069e9ebbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XQNR55HU5OCN6QR2SUKANUNYPA/bundle.json","state_url":"https://pith.science/pith/XQNR55HU5OCN6QR2SUKANUNYPA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XQNR55HU5OCN6QR2SUKANUNYPA/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":"2026-06-09T11:15:42Z","links":{"resolver":"https://pith.science/pith/XQNR55HU5OCN6QR2SUKANUNYPA","bundle":"https://pith.science/pith/XQNR55HU5OCN6QR2SUKANUNYPA/bundle.json","state":"https://pith.science/pith/XQNR55HU5OCN6QR2SUKANUNYPA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XQNR55HU5OCN6QR2SUKANUNYPA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XQNR55HU5OCN6QR2SUKANUNYPA","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":"ba466b8ca37177d176ba27b2fd8863123e4e27d386090a1e3b8c26c6ee0216ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-22T16:57:23Z","title_canon_sha256":"b1b428ebf3c9b76b592d03e549d737e54d57417b463754c0c3df9cbb2d03ed42"},"schema_version":"1.0","source":{"id":"1201.4573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4573","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4573v1","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4573","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"XQNR55HU5OCN","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XQNR55HU5OCN6QR2","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XQNR55HU","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:5247e945b1eefe90d2f4f1e67f52a33cee254269b2b15fa5294d8fa069e9ebbe","target":"graph","created_at":"2026-05-18T04:04:05Z","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 linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order equations in \\cite{DKL}. The first type is an estimate of the $\\gamma$th norm of the second-order derivatives, where $\\gamma\\in(0,1)$, and the second type deals with estimates of the resolvent operators in $L_{p}$ when the first-order coefficients are summable to an appropriate power.","authors_text":"N. V. Krylov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-22T16:57:23Z","title":"Some $L_{p}$-estimates for elliptic and parabolic operators with measurable coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4573","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:b46fc4d2267448f2cbb101ff5f6c7f68462509bb9bc96ed76ceab5634668dea1","target":"record","created_at":"2026-05-18T04:04:05Z","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":"ba466b8ca37177d176ba27b2fd8863123e4e27d386090a1e3b8c26c6ee0216ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-22T16:57:23Z","title_canon_sha256":"b1b428ebf3c9b76b592d03e549d737e54d57417b463754c0c3df9cbb2d03ed42"},"schema_version":"1.0","source":{"id":"1201.4573","kind":"arxiv","version":1}},"canonical_sha256":"bc1b1ef4f4eb84df423a951406d1b87820e2dec1dcbff100a1634ae0eacbf864","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc1b1ef4f4eb84df423a951406d1b87820e2dec1dcbff100a1634ae0eacbf864","first_computed_at":"2026-05-18T04:04:05.688810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:05.688810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"goiYy+A2knWi2XvsAWCtpaIRHjg7kSdla/bmqz63+goC5TVg1tbIFMeFb5SsVLlghOx64AC53UIlsOe6MND8Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:05.689748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b46fc4d2267448f2cbb101ff5f6c7f68462509bb9bc96ed76ceab5634668dea1","sha256:5247e945b1eefe90d2f4f1e67f52a33cee254269b2b15fa5294d8fa069e9ebbe"],"state_sha256":"c877a51b3c2773313fca5994c3fbdfbf22b44fa28af0c1192fa8c13d7b866752"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBz2vKmJK+KbQYUPbfgB7Hm4nSGBdxcTmFnHstJw+MXDNAxCG+xYea1qsYwPtGcyJ8RYS1+8w9qlBa1vPFhHAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:15:42.864164Z","bundle_sha256":"e033cc73e0732ab5e2dd259020252b8ab9c593db524cd40533095b92d3fce671"}}