{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:B7HSKSNW72AQZ6DS2KFKPVTH64","short_pith_number":"pith:B7HSKSNW","canonical_record":{"source":{"id":"1805.04738","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-12T15:37:29Z","cross_cats_sorted":[],"title_canon_sha256":"d24e2a2df4b57f1295f52eb75060678084b599197552b8ffca129fa73aee76d0","abstract_canon_sha256":"58c5e5818a39e0bb5f135669660c0cffe964ae7ba75bdb579757061be1dc6312"},"schema_version":"1.0"},"canonical_sha256":"0fcf2549b6fe810cf872d28aa7d667f706fb0a304bcec5f188dbf8f4c45a9ffd","source":{"kind":"arxiv","id":"1805.04738","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04738","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04738v2","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04738","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"pith_short_12","alias_value":"B7HSKSNW72AQ","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"pith_short_16","alias_value":"B7HSKSNW72AQZ6DS","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"pith_short_8","alias_value":"B7HSKSNW","created_at":"2026-07-05T01:06:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:B7HSKSNW72AQZ6DS2KFKPVTH64","target":"record","payload":{"canonical_record":{"source":{"id":"1805.04738","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-12T15:37:29Z","cross_cats_sorted":[],"title_canon_sha256":"d24e2a2df4b57f1295f52eb75060678084b599197552b8ffca129fa73aee76d0","abstract_canon_sha256":"58c5e5818a39e0bb5f135669660c0cffe964ae7ba75bdb579757061be1dc6312"},"schema_version":"1.0"},"canonical_sha256":"0fcf2549b6fe810cf872d28aa7d667f706fb0a304bcec5f188dbf8f4c45a9ffd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:06:46.125038Z","signature_b64":"9pecZO2Rtn+dCgGhkn3m9XF3IW0qa1Qb5EMbsUaOYnHA8uGw8F+tkh7ikAZvpfLRfoThHY9Dl743ArxGknKsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fcf2549b6fe810cf872d28aa7d667f706fb0a304bcec5f188dbf8f4c45a9ffd","last_reissued_at":"2026-07-05T01:06:46.124588Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:06:46.124588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.04738","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":"2026-07-05T01:06:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i4fSdTOj7rdf+MRzdswkKQ9kZWnSFU2c8576odTOHT704g+rjJSJdahK1w1HEurmA2MeKkalH8ZxIbLDT81BAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:03:25.081753Z"},"content_sha256":"9627ff36a90d34562d4eac5613ad337d89815fb9318e40564f80733ec722ce5c","schema_version":"1.0","event_id":"sha256:9627ff36a90d34562d4eac5613ad337d89815fb9318e40564f80733ec722ce5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:B7HSKSNW72AQZ6DS2KFKPVTH64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak KAM solutions of Hamilton-Jacobi equations with decreasing dependence on unknown functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jun Yan, Kaizhi Wang, Lin Wang","submitted_at":"2018-05-12T15:37:29Z","abstract_excerpt":"We consider the Hamilton-Jacobi equation \\[{H}(x,u,Du)=0,\\quad x\\in M, \\] where $M$ is a connected, closed and smooth Riemannian manifold, ${H}(x,u,p)$ satisfies Tonelli conditions with respect to $p$ and certain decreasing condition with respect to $u$. Based on a dynamical approach developed in \\cite{WWY,WWY1,WWY2}, we obtain a series of properties for weak KAM solutions (equivalently, viscosity solutions) of the stationary equation and the long time behavior of viscosity solutions of the evolutionary equation on the Cauchy problem \\begin{equation*}\n  \\begin{cases} w_t+{H}(x,w,w_x)=0,\\quad ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04738","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1805.04738/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":"2026-07-05T01:06:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k1iy9GhZaxDQqnUsjjAhTYWCVB50YOH1ep5ZShQ+MA9TUrRglbnH/dQjZvQP48SAi6+bNpF8i0bRshcI93KkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:03:25.082144Z"},"content_sha256":"63881c488ec62d2cb2360c5beec427661e180f2698bab28178fadac5f9d80a38","schema_version":"1.0","event_id":"sha256:63881c488ec62d2cb2360c5beec427661e180f2698bab28178fadac5f9d80a38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B7HSKSNW72AQZ6DS2KFKPVTH64/bundle.json","state_url":"https://pith.science/pith/B7HSKSNW72AQZ6DS2KFKPVTH64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B7HSKSNW72AQZ6DS2KFKPVTH64/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":"2026-07-07T05:03:25Z","links":{"resolver":"https://pith.science/pith/B7HSKSNW72AQZ6DS2KFKPVTH64","bundle":"https://pith.science/pith/B7HSKSNW72AQZ6DS2KFKPVTH64/bundle.json","state":"https://pith.science/pith/B7HSKSNW72AQZ6DS2KFKPVTH64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B7HSKSNW72AQZ6DS2KFKPVTH64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:B7HSKSNW72AQZ6DS2KFKPVTH64","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":"58c5e5818a39e0bb5f135669660c0cffe964ae7ba75bdb579757061be1dc6312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-12T15:37:29Z","title_canon_sha256":"d24e2a2df4b57f1295f52eb75060678084b599197552b8ffca129fa73aee76d0"},"schema_version":"1.0","source":{"id":"1805.04738","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04738","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04738v2","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04738","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"pith_short_12","alias_value":"B7HSKSNW72AQ","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"pith_short_16","alias_value":"B7HSKSNW72AQZ6DS","created_at":"2026-07-05T01:06:46Z"},{"alias_kind":"pith_short_8","alias_value":"B7HSKSNW","created_at":"2026-07-05T01:06:46Z"}],"graph_snapshots":[{"event_id":"sha256:63881c488ec62d2cb2360c5beec427661e180f2698bab28178fadac5f9d80a38","target":"graph","created_at":"2026-07-05T01:06:46Z","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/1805.04738/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the Hamilton-Jacobi equation \\[{H}(x,u,Du)=0,\\quad x\\in M, \\] where $M$ is a connected, closed and smooth Riemannian manifold, ${H}(x,u,p)$ satisfies Tonelli conditions with respect to $p$ and certain decreasing condition with respect to $u$. Based on a dynamical approach developed in \\cite{WWY,WWY1,WWY2}, we obtain a series of properties for weak KAM solutions (equivalently, viscosity solutions) of the stationary equation and the long time behavior of viscosity solutions of the evolutionary equation on the Cauchy problem \\begin{equation*}\n  \\begin{cases} w_t+{H}(x,w,w_x)=0,\\quad (","authors_text":"Jun Yan, Kaizhi Wang, Lin Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-12T15:37:29Z","title":"Weak KAM solutions of Hamilton-Jacobi equations with decreasing dependence on unknown functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04738","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":"sha256:9627ff36a90d34562d4eac5613ad337d89815fb9318e40564f80733ec722ce5c","target":"record","created_at":"2026-07-05T01:06:46Z","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":"58c5e5818a39e0bb5f135669660c0cffe964ae7ba75bdb579757061be1dc6312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-12T15:37:29Z","title_canon_sha256":"d24e2a2df4b57f1295f52eb75060678084b599197552b8ffca129fa73aee76d0"},"schema_version":"1.0","source":{"id":"1805.04738","kind":"arxiv","version":2}},"canonical_sha256":"0fcf2549b6fe810cf872d28aa7d667f706fb0a304bcec5f188dbf8f4c45a9ffd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fcf2549b6fe810cf872d28aa7d667f706fb0a304bcec5f188dbf8f4c45a9ffd","first_computed_at":"2026-07-05T01:06:46.124588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:06:46.124588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9pecZO2Rtn+dCgGhkn3m9XF3IW0qa1Qb5EMbsUaOYnHA8uGw8F+tkh7ikAZvpfLRfoThHY9Dl743ArxGknKsAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:06:46.125038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04738","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9627ff36a90d34562d4eac5613ad337d89815fb9318e40564f80733ec722ce5c","sha256:63881c488ec62d2cb2360c5beec427661e180f2698bab28178fadac5f9d80a38"],"state_sha256":"e0c921862a2588b342e97e0f7826702a508bcbbdce59442c3c9369cb74142d01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkzHYjRDW3yGJXtW8ZOsEL6no23XmSuI+MdyEVKJz+FjINw12deS1nze90roIwGQqFbR0RRhlTQ3npigruyKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T05:03:25.084753Z","bundle_sha256":"5a58937df4c33ac86c64e51054e204a2c00fdf513d092adf8b84948756e9927e"}}