{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4I54DZIYTHUN67FEQXJ2BN42OQ","short_pith_number":"pith:4I54DZIY","canonical_record":{"source":{"id":"1310.3192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-11T16:41:48Z","cross_cats_sorted":[],"title_canon_sha256":"fb912579861d30169ada22227d2fa3b2f65355ca3ea5c04f4ebd43bc54272c29","abstract_canon_sha256":"68c931dc0ee221a7d7ee439d36c896e61a0b84c0c1e9e8d76c77b2a792f26d12"},"schema_version":"1.0"},"canonical_sha256":"e23bc1e51899e8df7ca485d3a0b79a742328e330bb5a90e408b72fdebe69a0a0","source":{"kind":"arxiv","id":"1310.3192","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3192","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3192v1","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3192","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"pith_short_12","alias_value":"4I54DZIYTHUN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4I54DZIYTHUN67FE","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4I54DZIY","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4I54DZIYTHUN67FEQXJ2BN42OQ","target":"record","payload":{"canonical_record":{"source":{"id":"1310.3192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-11T16:41:48Z","cross_cats_sorted":[],"title_canon_sha256":"fb912579861d30169ada22227d2fa3b2f65355ca3ea5c04f4ebd43bc54272c29","abstract_canon_sha256":"68c931dc0ee221a7d7ee439d36c896e61a0b84c0c1e9e8d76c77b2a792f26d12"},"schema_version":"1.0"},"canonical_sha256":"e23bc1e51899e8df7ca485d3a0b79a742328e330bb5a90e408b72fdebe69a0a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:44.768874Z","signature_b64":"P2OhYuSCWX8w1eTVM5EGiuqBoD4PwJF08Y6nQuiA+gyOACQG3Few8npz31LG6n/uoRNX9AkaVM61RWzS2d7pBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e23bc1e51899e8df7ca485d3a0b79a742328e330bb5a90e408b72fdebe69a0a0","last_reissued_at":"2026-05-18T03:10:44.768389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:44.768389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.3192","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":"2026-05-18T03:10:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sXs/gN41yiljlso846sNc/VdpXtJVULyr/X1JkwCxMltVTBfpGrAPmOMEuik3YyAF8o2/5yCO4O7z+ksq119Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:01:00.665842Z"},"content_sha256":"d8443f58662201f54de696a4571465598ff7128ea677db320463eb887190f8cd","schema_version":"1.0","event_id":"sha256:d8443f58662201f54de696a4571465598ff7128ea677db320463eb887190f8cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4I54DZIYTHUN67FEQXJ2BN42OQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Porretta, Henri Berestycki, Italo Capuzzo Dolcetta, Luca Rossi","submitted_at":"2013-10-11T16:41:48Z","abstract_excerpt":"We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, maximum principle refers to the non-positivity of viscosity subsolutions of the Dirichlet problem. This characterization is derived in terms of a new notion of generalized principal eigenvalue, which is needed because of the possible degeneracy of the operator, admitted in full generality. We further discuss the relations between this notion and other natural generalizations of the classical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3192","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":"2026-05-18T03:10:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvZimyA56v53RYdRkP4l8o2njwFBLFIr4VaFiPt/t7ueJz/E2D0gz3Nrv2WLBX2EpY3GMy3H2ekVsGRUrPuDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:01:00.666200Z"},"content_sha256":"22a4b08a5cad2168aec330986a29fc2f3bd28998f9d46be2be71d586a0c56f46","schema_version":"1.0","event_id":"sha256:22a4b08a5cad2168aec330986a29fc2f3bd28998f9d46be2be71d586a0c56f46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4I54DZIYTHUN67FEQXJ2BN42OQ/bundle.json","state_url":"https://pith.science/pith/4I54DZIYTHUN67FEQXJ2BN42OQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4I54DZIYTHUN67FEQXJ2BN42OQ/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":"2026-05-26T20:01:00Z","links":{"resolver":"https://pith.science/pith/4I54DZIYTHUN67FEQXJ2BN42OQ","bundle":"https://pith.science/pith/4I54DZIYTHUN67FEQXJ2BN42OQ/bundle.json","state":"https://pith.science/pith/4I54DZIYTHUN67FEQXJ2BN42OQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4I54DZIYTHUN67FEQXJ2BN42OQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4I54DZIYTHUN67FEQXJ2BN42OQ","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":"68c931dc0ee221a7d7ee439d36c896e61a0b84c0c1e9e8d76c77b2a792f26d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-11T16:41:48Z","title_canon_sha256":"fb912579861d30169ada22227d2fa3b2f65355ca3ea5c04f4ebd43bc54272c29"},"schema_version":"1.0","source":{"id":"1310.3192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3192","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3192v1","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3192","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"pith_short_12","alias_value":"4I54DZIYTHUN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4I54DZIYTHUN67FE","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4I54DZIY","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:22a4b08a5cad2168aec330986a29fc2f3bd28998f9d46be2be71d586a0c56f46","target":"graph","created_at":"2026-05-18T03:10:44Z","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 characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, maximum principle refers to the non-positivity of viscosity subsolutions of the Dirichlet problem. This characterization is derived in terms of a new notion of generalized principal eigenvalue, which is needed because of the possible degeneracy of the operator, admitted in full generality. We further discuss the relations between this notion and other natural generalizations of the classical","authors_text":"Alessio Porretta, Henri Berestycki, Italo Capuzzo Dolcetta, Luca Rossi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-11T16:41:48Z","title":"Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3192","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:d8443f58662201f54de696a4571465598ff7128ea677db320463eb887190f8cd","target":"record","created_at":"2026-05-18T03:10:44Z","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":"68c931dc0ee221a7d7ee439d36c896e61a0b84c0c1e9e8d76c77b2a792f26d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-11T16:41:48Z","title_canon_sha256":"fb912579861d30169ada22227d2fa3b2f65355ca3ea5c04f4ebd43bc54272c29"},"schema_version":"1.0","source":{"id":"1310.3192","kind":"arxiv","version":1}},"canonical_sha256":"e23bc1e51899e8df7ca485d3a0b79a742328e330bb5a90e408b72fdebe69a0a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e23bc1e51899e8df7ca485d3a0b79a742328e330bb5a90e408b72fdebe69a0a0","first_computed_at":"2026-05-18T03:10:44.768389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:44.768389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P2OhYuSCWX8w1eTVM5EGiuqBoD4PwJF08Y6nQuiA+gyOACQG3Few8npz31LG6n/uoRNX9AkaVM61RWzS2d7pBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:44.768874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8443f58662201f54de696a4571465598ff7128ea677db320463eb887190f8cd","sha256:22a4b08a5cad2168aec330986a29fc2f3bd28998f9d46be2be71d586a0c56f46"],"state_sha256":"8a29dbcaae19bd8a5bdacc7e67458ef418b7127955b6e6ed6379c83a9e990cdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lhfLqOKHVzd4pgZ6zKqpv91nukgBCq34crNMw1rgAoFeeED4hNvf/5Tk+IKxfQMroLP07caBZCVQdoh6UBtiBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:01:00.668410Z","bundle_sha256":"5eebfea2b9dc7d54d529908ec9cd6f1855ab37355375b207d9b056646b22753c"}}