{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PC2XK3FGOHWIZRPL2XWTFJYVCE","short_pith_number":"pith:PC2XK3FG","canonical_record":{"source":{"id":"1506.06994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-23T13:46:26Z","cross_cats_sorted":[],"title_canon_sha256":"12806b4196496283c186a39d855c968594050e9653ec12b229351d8a4d831b33","abstract_canon_sha256":"92b1400b1f025ecd0b45db063429551e0ad7b656ac469eaac7d6067ff1c2a414"},"schema_version":"1.0"},"canonical_sha256":"78b5756ca671ec8cc5ebd5ed32a715111dfd14b4d4e9224b5d830376b7656ebd","source":{"kind":"arxiv","id":"1506.06994","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06994","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06994v1","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06994","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"PC2XK3FGOHWI","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PC2XK3FGOHWIZRPL","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PC2XK3FG","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PC2XK3FGOHWIZRPL2XWTFJYVCE","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-23T13:46:26Z","cross_cats_sorted":[],"title_canon_sha256":"12806b4196496283c186a39d855c968594050e9653ec12b229351d8a4d831b33","abstract_canon_sha256":"92b1400b1f025ecd0b45db063429551e0ad7b656ac469eaac7d6067ff1c2a414"},"schema_version":"1.0"},"canonical_sha256":"78b5756ca671ec8cc5ebd5ed32a715111dfd14b4d4e9224b5d830376b7656ebd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:55.371762Z","signature_b64":"aEqhpohRwrBdep14fxa2dkaoqNkAJ2u1L5u90R4SKKSlqQkcd5wG0GvB5UiWzke6ihkf+pNxxTly5UFyQkqqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78b5756ca671ec8cc5ebd5ed32a715111dfd14b4d4e9224b5d830376b7656ebd","last_reissued_at":"2026-05-18T01:40:55.371072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:55.371072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06994","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":"2026-05-18T01:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GqE6fEEhg9pjH0pkPkA7ZtYsmRt4g9B782c4N89bItVwJzfrscL/4wsnvbgoSZLLFzR4qbNglOZi3E9m4B6CCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:03:12.945133Z"},"content_sha256":"c2eb192183269da352a9cb76fb06e4ebcf12c2949ac0dae4e93bf6bb294c68f0","schema_version":"1.0","event_id":"sha256:c2eb192183269da352a9cb76fb06e4ebcf12c2949ac0dae4e93bf6bb294c68f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PC2XK3FGOHWIZRPL2XWTFJYVCE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Vitolo, Giulio Galise, Olivier Ley (IRMAR), Shigeaki Koike","submitted_at":"2015-06-23T13:46:26Z","abstract_excerpt":"In this paper we consider second order fully nonlinear operators with an additive superlinear gradient term. Like in the pioneering paper of Brezis for the semilinear case, we obtain the existence of entire viscosity solutions, defined in all the space, without assuming global bounds. A uniqueness result is also obtained for special gradient terms, subject to a convexity/concavity type assumption where superlinearity is essential and has to be handled in a different way from the linear case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06994","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":"2026-05-18T01:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZKhsdt716dRW83X3+EW3/LYIGNSd838XdN1iCSsEsdsNq41xV0cS3GBeZeb5lGIRMxftlKTraDs1bKPQc86YAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:03:12.945789Z"},"content_sha256":"d986d61800a66e38544a8e5eeb0e180698b76998b20ca7a11aac1079d10752c7","schema_version":"1.0","event_id":"sha256:d986d61800a66e38544a8e5eeb0e180698b76998b20ca7a11aac1079d10752c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PC2XK3FGOHWIZRPL2XWTFJYVCE/bundle.json","state_url":"https://pith.science/pith/PC2XK3FGOHWIZRPL2XWTFJYVCE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PC2XK3FGOHWIZRPL2XWTFJYVCE/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":"2026-05-30T05:03:12Z","links":{"resolver":"https://pith.science/pith/PC2XK3FGOHWIZRPL2XWTFJYVCE","bundle":"https://pith.science/pith/PC2XK3FGOHWIZRPL2XWTFJYVCE/bundle.json","state":"https://pith.science/pith/PC2XK3FGOHWIZRPL2XWTFJYVCE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PC2XK3FGOHWIZRPL2XWTFJYVCE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PC2XK3FGOHWIZRPL2XWTFJYVCE","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":"92b1400b1f025ecd0b45db063429551e0ad7b656ac469eaac7d6067ff1c2a414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-23T13:46:26Z","title_canon_sha256":"12806b4196496283c186a39d855c968594050e9653ec12b229351d8a4d831b33"},"schema_version":"1.0","source":{"id":"1506.06994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06994","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06994v1","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06994","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"PC2XK3FGOHWI","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PC2XK3FGOHWIZRPL","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PC2XK3FG","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:d986d61800a66e38544a8e5eeb0e180698b76998b20ca7a11aac1079d10752c7","target":"graph","created_at":"2026-05-18T01:40:55Z","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":"In this paper we consider second order fully nonlinear operators with an additive superlinear gradient term. Like in the pioneering paper of Brezis for the semilinear case, we obtain the existence of entire viscosity solutions, defined in all the space, without assuming global bounds. A uniqueness result is also obtained for special gradient terms, subject to a convexity/concavity type assumption where superlinearity is essential and has to be handled in a different way from the linear case.","authors_text":"Antonio Vitolo, Giulio Galise, Olivier Ley (IRMAR), Shigeaki Koike","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-23T13:46:26Z","title":"Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06994","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:c2eb192183269da352a9cb76fb06e4ebcf12c2949ac0dae4e93bf6bb294c68f0","target":"record","created_at":"2026-05-18T01:40:55Z","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":"92b1400b1f025ecd0b45db063429551e0ad7b656ac469eaac7d6067ff1c2a414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-23T13:46:26Z","title_canon_sha256":"12806b4196496283c186a39d855c968594050e9653ec12b229351d8a4d831b33"},"schema_version":"1.0","source":{"id":"1506.06994","kind":"arxiv","version":1}},"canonical_sha256":"78b5756ca671ec8cc5ebd5ed32a715111dfd14b4d4e9224b5d830376b7656ebd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78b5756ca671ec8cc5ebd5ed32a715111dfd14b4d4e9224b5d830376b7656ebd","first_computed_at":"2026-05-18T01:40:55.371072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:55.371072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aEqhpohRwrBdep14fxa2dkaoqNkAJ2u1L5u90R4SKKSlqQkcd5wG0GvB5UiWzke6ihkf+pNxxTly5UFyQkqqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:55.371762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2eb192183269da352a9cb76fb06e4ebcf12c2949ac0dae4e93bf6bb294c68f0","sha256:d986d61800a66e38544a8e5eeb0e180698b76998b20ca7a11aac1079d10752c7"],"state_sha256":"1ea54fbeb7459b33db32e91a958cc5dcd5cd5d3c98ca9fb4e70ad8bbaccc18db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8XJpTME4/O8Vs1lFBfSLv64+6fsH7LlmZ5uIJt4lqUpBlMl25kCUm7mDr0363nGZ7XHyJK5e6jRaVYHiA4BCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:03:12.949019Z","bundle_sha256":"f69a6df5bc75b4011ab70e33bf7603e7a203aed7fcea109fe58fd858cb0e2845"}}