{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6SJCBU3QZC7H3GCVELYXCFY7QO","short_pith_number":"pith:6SJCBU3Q","canonical_record":{"source":{"id":"1109.4768","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-22T10:59:21Z","cross_cats_sorted":[],"title_canon_sha256":"bc9a6d2215c89ca77091e7da85b6dbaea7a87006996bd393ed449d78a98a4665","abstract_canon_sha256":"07f0aa3bdba275aeb2df65e53ebad21c8d5a73ce66f29f307d8c0eac608a46eb"},"schema_version":"1.0"},"canonical_sha256":"f49220d370c8be7d985522f171171f838a2d6cb5243493b276a3d0fa68f855ae","source":{"kind":"arxiv","id":"1109.4768","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4768","created_at":"2026-05-18T03:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4768v3","created_at":"2026-05-18T03:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4768","created_at":"2026-05-18T03:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"6SJCBU3QZC7H","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6SJCBU3QZC7H3GCV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6SJCBU3Q","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6SJCBU3QZC7H3GCVELYXCFY7QO","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4768","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-22T10:59:21Z","cross_cats_sorted":[],"title_canon_sha256":"bc9a6d2215c89ca77091e7da85b6dbaea7a87006996bd393ed449d78a98a4665","abstract_canon_sha256":"07f0aa3bdba275aeb2df65e53ebad21c8d5a73ce66f29f307d8c0eac608a46eb"},"schema_version":"1.0"},"canonical_sha256":"f49220d370c8be7d985522f171171f838a2d6cb5243493b276a3d0fa68f855ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:00.392014Z","signature_b64":"G3HxtBsFA8L/kZBN0Odq2cnVh2uf5EvOwSvZ+C1Y2iGY40/EPOf9SiPZG3kFAzDnCYfmVzlkh+/LbwIZbWhZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f49220d370c8be7d985522f171171f838a2d6cb5243493b276a3d0fa68f855ae","last_reissued_at":"2026-05-18T03:57:00.391148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:00.391148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4768","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PK96t/SrHZAjbpIXeSXc4N/nbCZr+BbEx8ybi2cvt8sugV/iqDB2TsEIEwi3ndz3Pv8g2CvJ6gv9qflNk8O4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:56:21.951684Z"},"content_sha256":"4eff504161028919f74c0d04baf7bf4455aa1c1f66d7c726b97c194cdf2ba59b","schema_version":"1.0","event_id":"sha256:4eff504161028919f74c0d04baf7bf4455aa1c1f66d7c726b97c194cdf2ba59b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6SJCBU3QZC7H3GCVELYXCFY7QO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp regularity for general Poisson equations with borderline sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eduardo V. Teixeira","submitted_at":"2011-09-22T10:59:21Z","abstract_excerpt":"This article concerns optimal estimates for non-homogeneous degenerate elliptic equation with source functions in borderline spaces of integrability. We deliver sharp H\\\"older continuity estimates for solutions to $p$-degenerate elliptic equations in rough media with sources in the weak Lebesgue space $L_\\text{weak}^{\\frac{n}{p} + \\epsilon}$. For the borderline case, $f \\in L_\\text{weak}^{\\frac{n}{p}}$, solutions may not be bounded; nevertheless we show that solutions have bounded mean oscillation, in particular John-Nirenberg's exponential integrability estimates can be employed. All the resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4768","kind":"arxiv","version":3},"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":"2026-05-18T03:57:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YPd9hQGkhEggmvlqQdlO7KiW4oObH4J0375bAck2nOZAV+ItOvJ4UqrKmdwAs6z0DdOakG5cKYo41+cNyJ4uAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:56:21.952034Z"},"content_sha256":"f3418331df6d0043840e66e8f2ea6b8f9224ca501612ec2465e3789af14fdd97","schema_version":"1.0","event_id":"sha256:f3418331df6d0043840e66e8f2ea6b8f9224ca501612ec2465e3789af14fdd97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6SJCBU3QZC7H3GCVELYXCFY7QO/bundle.json","state_url":"https://pith.science/pith/6SJCBU3QZC7H3GCVELYXCFY7QO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6SJCBU3QZC7H3GCVELYXCFY7QO/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":"2026-06-03T22:56:21Z","links":{"resolver":"https://pith.science/pith/6SJCBU3QZC7H3GCVELYXCFY7QO","bundle":"https://pith.science/pith/6SJCBU3QZC7H3GCVELYXCFY7QO/bundle.json","state":"https://pith.science/pith/6SJCBU3QZC7H3GCVELYXCFY7QO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6SJCBU3QZC7H3GCVELYXCFY7QO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6SJCBU3QZC7H3GCVELYXCFY7QO","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":"07f0aa3bdba275aeb2df65e53ebad21c8d5a73ce66f29f307d8c0eac608a46eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-22T10:59:21Z","title_canon_sha256":"bc9a6d2215c89ca77091e7da85b6dbaea7a87006996bd393ed449d78a98a4665"},"schema_version":"1.0","source":{"id":"1109.4768","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4768","created_at":"2026-05-18T03:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4768v3","created_at":"2026-05-18T03:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4768","created_at":"2026-05-18T03:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"6SJCBU3QZC7H","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6SJCBU3QZC7H3GCV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6SJCBU3Q","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:f3418331df6d0043840e66e8f2ea6b8f9224ca501612ec2465e3789af14fdd97","target":"graph","created_at":"2026-05-18T03:57:00Z","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":"This article concerns optimal estimates for non-homogeneous degenerate elliptic equation with source functions in borderline spaces of integrability. We deliver sharp H\\\"older continuity estimates for solutions to $p$-degenerate elliptic equations in rough media with sources in the weak Lebesgue space $L_\\text{weak}^{\\frac{n}{p} + \\epsilon}$. For the borderline case, $f \\in L_\\text{weak}^{\\frac{n}{p}}$, solutions may not be bounded; nevertheless we show that solutions have bounded mean oscillation, in particular John-Nirenberg's exponential integrability estimates can be employed. All the resu","authors_text":"Eduardo V. Teixeira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-22T10:59:21Z","title":"Sharp regularity for general Poisson equations with borderline sources"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4768","kind":"arxiv","version":3},"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":"sha256:4eff504161028919f74c0d04baf7bf4455aa1c1f66d7c726b97c194cdf2ba59b","target":"record","created_at":"2026-05-18T03:57:00Z","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":"07f0aa3bdba275aeb2df65e53ebad21c8d5a73ce66f29f307d8c0eac608a46eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-22T10:59:21Z","title_canon_sha256":"bc9a6d2215c89ca77091e7da85b6dbaea7a87006996bd393ed449d78a98a4665"},"schema_version":"1.0","source":{"id":"1109.4768","kind":"arxiv","version":3}},"canonical_sha256":"f49220d370c8be7d985522f171171f838a2d6cb5243493b276a3d0fa68f855ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f49220d370c8be7d985522f171171f838a2d6cb5243493b276a3d0fa68f855ae","first_computed_at":"2026-05-18T03:57:00.391148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:00.391148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G3HxtBsFA8L/kZBN0Odq2cnVh2uf5EvOwSvZ+C1Y2iGY40/EPOf9SiPZG3kFAzDnCYfmVzlkh+/LbwIZbWhZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:00.392014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4768","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eff504161028919f74c0d04baf7bf4455aa1c1f66d7c726b97c194cdf2ba59b","sha256:f3418331df6d0043840e66e8f2ea6b8f9224ca501612ec2465e3789af14fdd97"],"state_sha256":"b4a77e02948d3bd861d9854d16ecadee2250fd6a1098615d19be2333a66af2a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vKCqo2mFCP6huf3xqJzI3//7HAvijfLvYkGANfvyxhtYKl+MJaGRi3piCd280utXwnkuIxryI0kBgZIwDwwxDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T22:56:21.953896Z","bundle_sha256":"030d7b86c08e6d8eb04a1be2c14aa6c3917ebca02321122e9d3aad14c8e13433"}}