{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:T2JR2V3Z3NRHS7D5NA5FYIWYA2","short_pith_number":"pith:T2JR2V3Z","canonical_record":{"source":{"id":"1712.02671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-07T15:37:36Z","cross_cats_sorted":[],"title_canon_sha256":"154787ea916b3f5955deb8a096db3ae3319383814fce4bc6ff3f600cc74eb17f","abstract_canon_sha256":"ea44811ea475eb3c2a2c737684dbb3cc5ae732c36069e3f1dcd864c0cbe81a53"},"schema_version":"1.0"},"canonical_sha256":"9e931d5779db62797c7d683a5c22d8069f6b3831902891df14fcc6258cf5db0a","source":{"kind":"arxiv","id":"1712.02671","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02671","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02671v1","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02671","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"T2JR2V3Z3NRH","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T2JR2V3Z3NRHS7D5","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T2JR2V3Z","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:T2JR2V3Z3NRHS7D5NA5FYIWYA2","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-07T15:37:36Z","cross_cats_sorted":[],"title_canon_sha256":"154787ea916b3f5955deb8a096db3ae3319383814fce4bc6ff3f600cc74eb17f","abstract_canon_sha256":"ea44811ea475eb3c2a2c737684dbb3cc5ae732c36069e3f1dcd864c0cbe81a53"},"schema_version":"1.0"},"canonical_sha256":"9e931d5779db62797c7d683a5c22d8069f6b3831902891df14fcc6258cf5db0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:33.227302Z","signature_b64":"6u6jM5kySmF7tVdi+ufMKujqEn6UsinoNQxVj5OqHivbyZW1+nGd614JXoHvDxrti9siSu9s2GcbUwxSgdxlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e931d5779db62797c7d683a5c22d8069f6b3831902891df14fcc6258cf5db0a","last_reissued_at":"2026-05-18T00:28:33.226595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:33.226595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02671","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":"2026-05-18T00:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+dhwY0eo/NpXaBWqJNi/DrSDO448OR5W/utB0vyt04rzOTvjZ5DgoMnpD0EyfR364Oim4FFBghKP/VHmNxv/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:22:20.078204Z"},"content_sha256":"05643732edaad3e76498632dc599307b2b831e7b16ba4f5df032907ad286a782","schema_version":"1.0","event_id":"sha256:05643732edaad3e76498632dc599307b2b831e7b16ba4f5df032907ad286a782"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:T2JR2V3Z3NRHS7D5NA5FYIWYA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodic pairs for singular or degenerate fully nonlinear operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabiana Leoni, Francoise Demengel, Isabeau Birindelli","submitted_at":"2017-12-07T15:37:36Z","abstract_excerpt":"We study the ergodic problem for fully nonlinear operators which may be singular or degenerate when the gradient of solutions vanishes. We prove the convergence of both explosive solutions and solutions of Dirichlet problems for approximating equations. We further characterize the ergodic constant as the infimum of constants for which there exist bounded sub solutions. As intermediate results of independent interest, we prove a priori Lipschitz estimates depending only on the norm of the zeroth order term, and a comparison principle for equations having no zero order terms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02671","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":"2026-05-18T00:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gv3nxyTZH9cHRNrkxKYpSaenvAiQ2UahnxWkGsz+Q/NGMU4Rh9aUaCnCX+weuMsA+v2tk3WfWtg2BC1jeHgtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:22:20.078939Z"},"content_sha256":"d053933b12c2468f8fc1764e0b8c3e96b513d766ff4376b56e4778d8bd2f868e","schema_version":"1.0","event_id":"sha256:d053933b12c2468f8fc1764e0b8c3e96b513d766ff4376b56e4778d8bd2f868e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T2JR2V3Z3NRHS7D5NA5FYIWYA2/bundle.json","state_url":"https://pith.science/pith/T2JR2V3Z3NRHS7D5NA5FYIWYA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T2JR2V3Z3NRHS7D5NA5FYIWYA2/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":"2026-05-31T12:22:20Z","links":{"resolver":"https://pith.science/pith/T2JR2V3Z3NRHS7D5NA5FYIWYA2","bundle":"https://pith.science/pith/T2JR2V3Z3NRHS7D5NA5FYIWYA2/bundle.json","state":"https://pith.science/pith/T2JR2V3Z3NRHS7D5NA5FYIWYA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T2JR2V3Z3NRHS7D5NA5FYIWYA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T2JR2V3Z3NRHS7D5NA5FYIWYA2","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":"ea44811ea475eb3c2a2c737684dbb3cc5ae732c36069e3f1dcd864c0cbe81a53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-07T15:37:36Z","title_canon_sha256":"154787ea916b3f5955deb8a096db3ae3319383814fce4bc6ff3f600cc74eb17f"},"schema_version":"1.0","source":{"id":"1712.02671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02671","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02671v1","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02671","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"T2JR2V3Z3NRH","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T2JR2V3Z3NRHS7D5","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T2JR2V3Z","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:d053933b12c2468f8fc1764e0b8c3e96b513d766ff4376b56e4778d8bd2f868e","target":"graph","created_at":"2026-05-18T00:28:33Z","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 the ergodic problem for fully nonlinear operators which may be singular or degenerate when the gradient of solutions vanishes. We prove the convergence of both explosive solutions and solutions of Dirichlet problems for approximating equations. We further characterize the ergodic constant as the infimum of constants for which there exist bounded sub solutions. As intermediate results of independent interest, we prove a priori Lipschitz estimates depending only on the norm of the zeroth order term, and a comparison principle for equations having no zero order terms.","authors_text":"Fabiana Leoni, Francoise Demengel, Isabeau Birindelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-07T15:37:36Z","title":"Ergodic pairs for singular or degenerate fully nonlinear operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02671","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":"sha256:05643732edaad3e76498632dc599307b2b831e7b16ba4f5df032907ad286a782","target":"record","created_at":"2026-05-18T00:28:33Z","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":"ea44811ea475eb3c2a2c737684dbb3cc5ae732c36069e3f1dcd864c0cbe81a53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-07T15:37:36Z","title_canon_sha256":"154787ea916b3f5955deb8a096db3ae3319383814fce4bc6ff3f600cc74eb17f"},"schema_version":"1.0","source":{"id":"1712.02671","kind":"arxiv","version":1}},"canonical_sha256":"9e931d5779db62797c7d683a5c22d8069f6b3831902891df14fcc6258cf5db0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e931d5779db62797c7d683a5c22d8069f6b3831902891df14fcc6258cf5db0a","first_computed_at":"2026-05-18T00:28:33.226595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:33.226595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6u6jM5kySmF7tVdi+ufMKujqEn6UsinoNQxVj5OqHivbyZW1+nGd614JXoHvDxrti9siSu9s2GcbUwxSgdxlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:33.227302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05643732edaad3e76498632dc599307b2b831e7b16ba4f5df032907ad286a782","sha256:d053933b12c2468f8fc1764e0b8c3e96b513d766ff4376b56e4778d8bd2f868e"],"state_sha256":"0489e4fc06d501c08c492437431ee9259dd2f8547da2a792a3f34f70434444be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"acMch4NgOFMYSbq5+CgTuU/51+dDzBIlzP4ZtgLX4byV7kZnIZVz7vnsrN/fgtUWnh+tXSZwtDNmz4uBbWpiCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:22:20.082832Z","bundle_sha256":"d600dc37795aa931ae7dd0cf085ffc31d67fc0a89b75c4cb5e8602f40acba2ea"}}