{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RKRB4BOZKLREZIDG64W6ENTD4T","short_pith_number":"pith:RKRB4BOZ","canonical_record":{"source":{"id":"1512.02002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-07T11:59:07Z","cross_cats_sorted":[],"title_canon_sha256":"90bd457d36c05728f82a9e44cae99f38100531c34672693ab464e015adb700b4","abstract_canon_sha256":"fbd51414f5730d22c04abd6a0818917e496d4aa6c41f86a83d02c41192b3ec03"},"schema_version":"1.0"},"canonical_sha256":"8aa21e05d952e24ca066f72de23663e4cee970af8cb8255b7e33f5b784fe1d3e","source":{"kind":"arxiv","id":"1512.02002","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02002","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02002v1","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02002","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"pith_short_12","alias_value":"RKRB4BOZKLRE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RKRB4BOZKLREZIDG","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RKRB4BOZ","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RKRB4BOZKLREZIDG64W6ENTD4T","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-07T11:59:07Z","cross_cats_sorted":[],"title_canon_sha256":"90bd457d36c05728f82a9e44cae99f38100531c34672693ab464e015adb700b4","abstract_canon_sha256":"fbd51414f5730d22c04abd6a0818917e496d4aa6c41f86a83d02c41192b3ec03"},"schema_version":"1.0"},"canonical_sha256":"8aa21e05d952e24ca066f72de23663e4cee970af8cb8255b7e33f5b784fe1d3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:09.818465Z","signature_b64":"JTOTIDgTugL0TWBqnxwZTPAWWrWuS7NIVlO2CERaaTNY6qsZM6+J2+HMqyo4ihWTR464zxi2aQHYkvqxEWnEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8aa21e05d952e24ca066f72de23663e4cee970af8cb8255b7e33f5b784fe1d3e","last_reissued_at":"2026-05-18T01:25:09.818010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:09.818010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02002","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":"2026-05-18T01:25:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0LlXl4w5YrcQ/VkolciOBAzBhYw72Sxmd6eawi8WDZg+eyuBDgUkjAf5XlBgyAoxvBsSSX5nrF3r3Srhz7bNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:46:20.372738Z"},"content_sha256":"a6c4aad7384fc02ccf491abb2bb73b37d610ced84c55a727e862e99dfd5c4d9d","schema_version":"1.0","event_id":"sha256:a6c4aad7384fc02ccf491abb2bb73b37d610ced84c55a727e862e99dfd5c4d9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RKRB4BOZKLREZIDG64W6ENTD4T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cavity problems in discontinuous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Disson dos Prazeres, Eduardo V. Teixeira","submitted_at":"2015-12-07T11:59:07Z","abstract_excerpt":"We study cavitation type equations, $\\text{div}(a_{ij}(X) \\nabla u) \\sim \\delta_0(u)$, for bounded, measurable elliptic media $a_{ij}(X)$. De Giorgi-Nash-Moser theory assures that solutions are $\\alpha$-H\\\"older continuous within its set of positivity, $\\{u>0\\}$, for some exponent $\\alpha$ strictly less than one. Notwithstanding, the key, main result proven in this paper provides a sharp Lipschitz regularity estimate for such solutions along their free boundaries, $\\partial \\{u>0 \\}$. Such a sharp estimate implies geometric-measure constrains for the free boundary. In particular, we show that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02002","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":"2026-05-18T01:25:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8FpwpjYxxXp7+QIRq/QH8bMmxXw1eHb39EvRNq8k6vp8r3V7ivJfchKnCko1uHau9GXTjNkKFwo6/AnwvbrdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:46:20.373105Z"},"content_sha256":"19859487e8c34a927cd1770c3c0edca33973bd1783160ee0a1cc73005bac7320","schema_version":"1.0","event_id":"sha256:19859487e8c34a927cd1770c3c0edca33973bd1783160ee0a1cc73005bac7320"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RKRB4BOZKLREZIDG64W6ENTD4T/bundle.json","state_url":"https://pith.science/pith/RKRB4BOZKLREZIDG64W6ENTD4T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RKRB4BOZKLREZIDG64W6ENTD4T/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":"2026-06-04T02:46:20Z","links":{"resolver":"https://pith.science/pith/RKRB4BOZKLREZIDG64W6ENTD4T","bundle":"https://pith.science/pith/RKRB4BOZKLREZIDG64W6ENTD4T/bundle.json","state":"https://pith.science/pith/RKRB4BOZKLREZIDG64W6ENTD4T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RKRB4BOZKLREZIDG64W6ENTD4T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RKRB4BOZKLREZIDG64W6ENTD4T","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":"fbd51414f5730d22c04abd6a0818917e496d4aa6c41f86a83d02c41192b3ec03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-07T11:59:07Z","title_canon_sha256":"90bd457d36c05728f82a9e44cae99f38100531c34672693ab464e015adb700b4"},"schema_version":"1.0","source":{"id":"1512.02002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02002","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02002v1","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02002","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"pith_short_12","alias_value":"RKRB4BOZKLRE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RKRB4BOZKLREZIDG","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RKRB4BOZ","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:19859487e8c34a927cd1770c3c0edca33973bd1783160ee0a1cc73005bac7320","target":"graph","created_at":"2026-05-18T01:25:09Z","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 study cavitation type equations, $\\text{div}(a_{ij}(X) \\nabla u) \\sim \\delta_0(u)$, for bounded, measurable elliptic media $a_{ij}(X)$. De Giorgi-Nash-Moser theory assures that solutions are $\\alpha$-H\\\"older continuous within its set of positivity, $\\{u>0\\}$, for some exponent $\\alpha$ strictly less than one. Notwithstanding, the key, main result proven in this paper provides a sharp Lipschitz regularity estimate for such solutions along their free boundaries, $\\partial \\{u>0 \\}$. Such a sharp estimate implies geometric-measure constrains for the free boundary. In particular, we show that ","authors_text":"Disson dos Prazeres, Eduardo V. Teixeira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-07T11:59:07Z","title":"Cavity problems in discontinuous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02002","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:a6c4aad7384fc02ccf491abb2bb73b37d610ced84c55a727e862e99dfd5c4d9d","target":"record","created_at":"2026-05-18T01:25:09Z","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":"fbd51414f5730d22c04abd6a0818917e496d4aa6c41f86a83d02c41192b3ec03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-07T11:59:07Z","title_canon_sha256":"90bd457d36c05728f82a9e44cae99f38100531c34672693ab464e015adb700b4"},"schema_version":"1.0","source":{"id":"1512.02002","kind":"arxiv","version":1}},"canonical_sha256":"8aa21e05d952e24ca066f72de23663e4cee970af8cb8255b7e33f5b784fe1d3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8aa21e05d952e24ca066f72de23663e4cee970af8cb8255b7e33f5b784fe1d3e","first_computed_at":"2026-05-18T01:25:09.818010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:09.818010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JTOTIDgTugL0TWBqnxwZTPAWWrWuS7NIVlO2CERaaTNY6qsZM6+J2+HMqyo4ihWTR464zxi2aQHYkvqxEWnEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:09.818465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6c4aad7384fc02ccf491abb2bb73b37d610ced84c55a727e862e99dfd5c4d9d","sha256:19859487e8c34a927cd1770c3c0edca33973bd1783160ee0a1cc73005bac7320"],"state_sha256":"cc5401e9071c6ddeb6a3963c210597a12dfeaa0e6a01240a17c7c75e3f9b2540"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m07PCEwP7RYc2CG8VVGzxjNnlbkm3PhkMS7Boseqt/5uiqSNvDlK8n30Tq6Zf9j6sjBM13aJwDNjkDuKmacfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:46:20.375044Z","bundle_sha256":"c3b1c1bd1e14d8d90a69aa9515ffae726b966d6a34359578ae58cfaee6e698c4"}}