{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:UGIQG4LMLMDR4CM4VFUXTFFKPM","short_pith_number":"pith:UGIQG4LM","canonical_record":{"source":{"id":"0712.1331","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-12-09T08:28:26Z","cross_cats_sorted":[],"title_canon_sha256":"4541475f9668dd0a36919974fc5d56a75dd8cb20965aac6e195f47eab25e2e8f","abstract_canon_sha256":"273bf30702d1e81a075fd8e0f8c82abcc9ddd08365d28f96d8b414376b4d9eb7"},"schema_version":"1.0"},"canonical_sha256":"a19103716c5b071e099ca9697994aa7b03f74ff36d7b6c1db1a5baabb2cdb337","source":{"kind":"arxiv","id":"0712.1331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1331","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1331v1","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1331","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"UGIQG4LMLMDR","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"pith_short_16","alias_value":"UGIQG4LMLMDR4CM4","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"pith_short_8","alias_value":"UGIQG4LM","created_at":"2026-07-04T15:06:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:UGIQG4LMLMDR4CM4VFUXTFFKPM","target":"record","payload":{"canonical_record":{"source":{"id":"0712.1331","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-12-09T08:28:26Z","cross_cats_sorted":[],"title_canon_sha256":"4541475f9668dd0a36919974fc5d56a75dd8cb20965aac6e195f47eab25e2e8f","abstract_canon_sha256":"273bf30702d1e81a075fd8e0f8c82abcc9ddd08365d28f96d8b414376b4d9eb7"},"schema_version":"1.0"},"canonical_sha256":"a19103716c5b071e099ca9697994aa7b03f74ff36d7b6c1db1a5baabb2cdb337","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:06:09.090379Z","signature_b64":"uf2Hv7Mxu+xbm9Uf75ILtxm3CIWe+esk99SV/FkRu4bLxYPR6Kn27ZeMdBv8ywIR9oxQLMG8/gL+wksjuauyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a19103716c5b071e099ca9697994aa7b03f74ff36d7b6c1db1a5baabb2cdb337","last_reissued_at":"2026-07-04T15:06:09.090041Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:06:09.090041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.1331","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":"2026-07-04T15:06:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bb6kNHiUdMDgMJvwq9PKF22t67RuFxOcuYlgo5C2bjz25HiqWhmXBSdJAEn/UBO3RRoDFE30M0hjaJMFz+/HBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T03:18:03.687238Z"},"content_sha256":"401905f203428fcc704ac7cf173d7aedc51fd341a069d82f8eb50c57a1e0fe65","schema_version":"1.0","event_id":"sha256:401905f203428fcc704ac7cf173d7aedc51fd341a069d82f8eb50c57a1e0fe65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:UGIQG4LMLMDR4CM4VFUXTFFKPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Super-linear elliptic equation for the Pucci operator without growth restrictions for the data","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Maria J. Esteban (CEREMADE), Patricio Felmer (CMM)","submitted_at":"2007-12-09T08:28:26Z","abstract_excerpt":"In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: $$ -\\M^+(D^2u)+|u|^{s-1}u=f(x) \\quad {in} \\RR^n, $$ where $s>1$ and $f$ satisfies only local integrability conditions. This result is well known when, instead of the Pucci operator, the Laplacian or a divergence form operator is considered. Our existence results use the Alexandroff-Bakelman-Pucci inequality since we cannot use any variational formulation. For radially symmetric $f$ we can prove our results under less local integrability assumptions, taking advantage of an appropriat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1331","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0712.1331/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:06:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qOXIEedqAR9H5V4ajRa7vWrIVDVl61ken2dqWjznj7lMBz+GhY4Q94vazr02sOwsY+RcG6cZ3ulPW33uogZ3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T03:18:03.687631Z"},"content_sha256":"4400596a891212a178c8c9f3bbdbbea3368767ac73a302a7b4de3c9303d4df68","schema_version":"1.0","event_id":"sha256:4400596a891212a178c8c9f3bbdbbea3368767ac73a302a7b4de3c9303d4df68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UGIQG4LMLMDR4CM4VFUXTFFKPM/bundle.json","state_url":"https://pith.science/pith/UGIQG4LMLMDR4CM4VFUXTFFKPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UGIQG4LMLMDR4CM4VFUXTFFKPM/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":"2026-07-05T03:18:03Z","links":{"resolver":"https://pith.science/pith/UGIQG4LMLMDR4CM4VFUXTFFKPM","bundle":"https://pith.science/pith/UGIQG4LMLMDR4CM4VFUXTFFKPM/bundle.json","state":"https://pith.science/pith/UGIQG4LMLMDR4CM4VFUXTFFKPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UGIQG4LMLMDR4CM4VFUXTFFKPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UGIQG4LMLMDR4CM4VFUXTFFKPM","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":"273bf30702d1e81a075fd8e0f8c82abcc9ddd08365d28f96d8b414376b4d9eb7","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-12-09T08:28:26Z","title_canon_sha256":"4541475f9668dd0a36919974fc5d56a75dd8cb20965aac6e195f47eab25e2e8f"},"schema_version":"1.0","source":{"id":"0712.1331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1331","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1331v1","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1331","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"UGIQG4LMLMDR","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"pith_short_16","alias_value":"UGIQG4LMLMDR4CM4","created_at":"2026-07-04T15:06:09Z"},{"alias_kind":"pith_short_8","alias_value":"UGIQG4LM","created_at":"2026-07-04T15:06:09Z"}],"graph_snapshots":[{"event_id":"sha256:4400596a891212a178c8c9f3bbdbbea3368767ac73a302a7b4de3c9303d4df68","target":"graph","created_at":"2026-07-04T15:06:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0712.1331/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: $$ -\\M^+(D^2u)+|u|^{s-1}u=f(x) \\quad {in} \\RR^n, $$ where $s>1$ and $f$ satisfies only local integrability conditions. This result is well known when, instead of the Pucci operator, the Laplacian or a divergence form operator is considered. Our existence results use the Alexandroff-Bakelman-Pucci inequality since we cannot use any variational formulation. For radially symmetric $f$ we can prove our results under less local integrability assumptions, taking advantage of an appropriat","authors_text":"Alexander Quaas, Maria J. Esteban (CEREMADE), Patricio Felmer (CMM)","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-12-09T08:28:26Z","title":"Super-linear elliptic equation for the Pucci operator without growth restrictions for the data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1331","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":"sha256:401905f203428fcc704ac7cf173d7aedc51fd341a069d82f8eb50c57a1e0fe65","target":"record","created_at":"2026-07-04T15:06:09Z","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":"273bf30702d1e81a075fd8e0f8c82abcc9ddd08365d28f96d8b414376b4d9eb7","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-12-09T08:28:26Z","title_canon_sha256":"4541475f9668dd0a36919974fc5d56a75dd8cb20965aac6e195f47eab25e2e8f"},"schema_version":"1.0","source":{"id":"0712.1331","kind":"arxiv","version":1}},"canonical_sha256":"a19103716c5b071e099ca9697994aa7b03f74ff36d7b6c1db1a5baabb2cdb337","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a19103716c5b071e099ca9697994aa7b03f74ff36d7b6c1db1a5baabb2cdb337","first_computed_at":"2026-07-04T15:06:09.090041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:06:09.090041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uf2Hv7Mxu+xbm9Uf75ILtxm3CIWe+esk99SV/FkRu4bLxYPR6Kn27ZeMdBv8ywIR9oxQLMG8/gL+wksjuauyDw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:06:09.090379Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.1331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:401905f203428fcc704ac7cf173d7aedc51fd341a069d82f8eb50c57a1e0fe65","sha256:4400596a891212a178c8c9f3bbdbbea3368767ac73a302a7b4de3c9303d4df68"],"state_sha256":"26a4f74b189c05fc5bc917b0be459e026105369f2c3ae57a20d2cda8902b9e12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wirSunJMRmYBBplcI2ra6OJNTfUKcXSbHt5Xw2v3lRTEb3YyZH1tO/xJzjGqIM1J5Y2A7uElmHwsxlWEbXY+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T03:18:03.689566Z","bundle_sha256":"52692040c8709da4cac48a4c36de6d8f37dbac9d577ab1d46c30e2c7cb0aec9c"}}