{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EXJGWG2WVL5RGZ2UKK3HZK75DA","short_pith_number":"pith:EXJGWG2W","canonical_record":{"source":{"id":"1709.08387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T09:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"3d2732c2d37afc3fd542fa788d834b4765cefa8b38663d66f18aed96ad3e8848","abstract_canon_sha256":"6a9add3d8702cd2a23d5ba3fc752157f7d298ca44f1ebd31a52ad5c4a6a55030"},"schema_version":"1.0"},"canonical_sha256":"25d26b1b56aafb13675452b67cabfd18095062c090758bfd2522b0fd3e1ea0d0","source":{"kind":"arxiv","id":"1709.08387","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08387","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08387v2","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08387","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"EXJGWG2WVL5R","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EXJGWG2WVL5RGZ2U","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EXJGWG2W","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EXJGWG2WVL5RGZ2UKK3HZK75DA","target":"record","payload":{"canonical_record":{"source":{"id":"1709.08387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T09:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"3d2732c2d37afc3fd542fa788d834b4765cefa8b38663d66f18aed96ad3e8848","abstract_canon_sha256":"6a9add3d8702cd2a23d5ba3fc752157f7d298ca44f1ebd31a52ad5c4a6a55030"},"schema_version":"1.0"},"canonical_sha256":"25d26b1b56aafb13675452b67cabfd18095062c090758bfd2522b0fd3e1ea0d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:30.540748Z","signature_b64":"rsKdAmztLdmha6DvNDmExd+kpkNASpCKayZN5i5KZistk9w6PZHkjG/UbnUZFiNd28QEr8QgG73kM4XS2LFHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25d26b1b56aafb13675452b67cabfd18095062c090758bfd2522b0fd3e1ea0d0","last_reissued_at":"2026-05-18T00:15:30.540006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:30.540006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.08387","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"THiTLNci14EeXB5407nm+wr42n/NgEPB5V+XDjKV7LG6x+MgF0q6XvMLhz4K+ozrqnfcWV5KWF+qz389Uxk2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:49:47.966173Z"},"content_sha256":"b2c7a0c6fce6f1dcbd84c3f187f5cd3b65356ba7ffaa456a86040773af8dc2aa","schema_version":"1.0","event_id":"sha256:b2c7a0c6fce6f1dcbd84c3f187f5cd3b65356ba7ffaa456a86040773af8dc2aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EXJGWG2WVL5RGZ2UKK3HZK75DA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large time behavior of unbounded solutions of first-order Hamilton-Jacobi equations in the whole space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guy Barles (LMPT), Olivier Ley (IRMAR), Thanh Phan, Thi-Tuyen Nguyen","submitted_at":"2017-09-25T09:08:56Z","abstract_excerpt":"We study the large time behavior of solutions of first-order convex Hamilton-Jacobi Equations of Eikonal type set in the whole space. We assume that the solutions may have arbitrary growth.  A complete study of the structure of solutions of the ergodic problem is provided : contrarily to the periodic setting, the ergodic constant is not anymore unique, leading to different large time behavior for the solutions. We establish the ergodic behavior of the solutions of the Cauchy problem (i) when starting with a bounded from below initial condition and (ii) for some particular unbounded from below "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08387","kind":"arxiv","version":2},"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":"2026-05-18T00:15:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FoNlL4claPnC7E/bIUPMPyF69hWHHtDw3EnXkxrJE0f69q1YNuVrb+ChNV5hisBSDSauQsnw+9t7LTI5Atl0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:49:47.966559Z"},"content_sha256":"dee5e8cd8e148c2415d1f0b7c55fa82b8e80df6708e5038c3d0cdb0d212681fc","schema_version":"1.0","event_id":"sha256:dee5e8cd8e148c2415d1f0b7c55fa82b8e80df6708e5038c3d0cdb0d212681fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXJGWG2WVL5RGZ2UKK3HZK75DA/bundle.json","state_url":"https://pith.science/pith/EXJGWG2WVL5RGZ2UKK3HZK75DA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXJGWG2WVL5RGZ2UKK3HZK75DA/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":"2026-06-20T21:49:47Z","links":{"resolver":"https://pith.science/pith/EXJGWG2WVL5RGZ2UKK3HZK75DA","bundle":"https://pith.science/pith/EXJGWG2WVL5RGZ2UKK3HZK75DA/bundle.json","state":"https://pith.science/pith/EXJGWG2WVL5RGZ2UKK3HZK75DA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXJGWG2WVL5RGZ2UKK3HZK75DA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EXJGWG2WVL5RGZ2UKK3HZK75DA","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":"6a9add3d8702cd2a23d5ba3fc752157f7d298ca44f1ebd31a52ad5c4a6a55030","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T09:08:56Z","title_canon_sha256":"3d2732c2d37afc3fd542fa788d834b4765cefa8b38663d66f18aed96ad3e8848"},"schema_version":"1.0","source":{"id":"1709.08387","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08387","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08387v2","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08387","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"EXJGWG2WVL5R","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EXJGWG2WVL5RGZ2U","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EXJGWG2W","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:dee5e8cd8e148c2415d1f0b7c55fa82b8e80df6708e5038c3d0cdb0d212681fc","target":"graph","created_at":"2026-05-18T00:15:30Z","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 large time behavior of solutions of first-order convex Hamilton-Jacobi Equations of Eikonal type set in the whole space. We assume that the solutions may have arbitrary growth.  A complete study of the structure of solutions of the ergodic problem is provided : contrarily to the periodic setting, the ergodic constant is not anymore unique, leading to different large time behavior for the solutions. We establish the ergodic behavior of the solutions of the Cauchy problem (i) when starting with a bounded from below initial condition and (ii) for some particular unbounded from below ","authors_text":"Guy Barles (LMPT), Olivier Ley (IRMAR), Thanh Phan, Thi-Tuyen Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T09:08:56Z","title":"Large time behavior of unbounded solutions of first-order Hamilton-Jacobi equations in the whole space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08387","kind":"arxiv","version":2},"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:b2c7a0c6fce6f1dcbd84c3f187f5cd3b65356ba7ffaa456a86040773af8dc2aa","target":"record","created_at":"2026-05-18T00:15:30Z","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":"6a9add3d8702cd2a23d5ba3fc752157f7d298ca44f1ebd31a52ad5c4a6a55030","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-25T09:08:56Z","title_canon_sha256":"3d2732c2d37afc3fd542fa788d834b4765cefa8b38663d66f18aed96ad3e8848"},"schema_version":"1.0","source":{"id":"1709.08387","kind":"arxiv","version":2}},"canonical_sha256":"25d26b1b56aafb13675452b67cabfd18095062c090758bfd2522b0fd3e1ea0d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25d26b1b56aafb13675452b67cabfd18095062c090758bfd2522b0fd3e1ea0d0","first_computed_at":"2026-05-18T00:15:30.540006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:30.540006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rsKdAmztLdmha6DvNDmExd+kpkNASpCKayZN5i5KZistk9w6PZHkjG/UbnUZFiNd28QEr8QgG73kM4XS2LFHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:30.540748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08387","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2c7a0c6fce6f1dcbd84c3f187f5cd3b65356ba7ffaa456a86040773af8dc2aa","sha256:dee5e8cd8e148c2415d1f0b7c55fa82b8e80df6708e5038c3d0cdb0d212681fc"],"state_sha256":"75912e7de949a4daddaba8d5de91f73efb34cce3711d604094b338473985ce3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dzDGf+HVvvIkcuZyQql0J312Mj4umWdt0OaeONObI3Jp+OdXhiGJ2nfPUUH4TdBYNe/6fdN6UUKKGzVRaxGcDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T21:49:47.968482Z","bundle_sha256":"3a4fa0a5713867a00ffe9f8130347509de1ba3196965c82890cea278b5f6595b"}}