{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XSPATN63XMMG2KRYTK266Q3HOM","short_pith_number":"pith:XSPATN63","canonical_record":{"source":{"id":"1312.1606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-05T16:25:56Z","cross_cats_sorted":["math.AP","math.OC"],"title_canon_sha256":"93e0642a161e5f9f7be5a8dd4d0128367420dc2468c5ad10fa4106a345ebbfce","abstract_canon_sha256":"22c4b4b1c9bf499027a858322f5b2ab36899c763b779213fdcc8dff38f29360c"},"schema_version":"1.0"},"canonical_sha256":"bc9e09b7dbbb186d2a389ab5ef4367731d824ddb486b719fe0b2069a2fb1525a","source":{"kind":"arxiv","id":"1312.1606","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1606","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1606v1","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1606","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"XSPATN63XMMG","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XSPATN63XMMG2KRY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XSPATN63","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XSPATN63XMMG2KRYTK266Q3HOM","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-05T16:25:56Z","cross_cats_sorted":["math.AP","math.OC"],"title_canon_sha256":"93e0642a161e5f9f7be5a8dd4d0128367420dc2468c5ad10fa4106a345ebbfce","abstract_canon_sha256":"22c4b4b1c9bf499027a858322f5b2ab36899c763b779213fdcc8dff38f29360c"},"schema_version":"1.0"},"canonical_sha256":"bc9e09b7dbbb186d2a389ab5ef4367731d824ddb486b719fe0b2069a2fb1525a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:26.753011Z","signature_b64":"HnwL2aMEK7wBHBm9gT0BJiymWKZ7Kx/drpWeyh7Vxht/McFwumJwYSQmIz3r75WdLwulA8jsjra4ERJC25LxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc9e09b7dbbb186d2a389ab5ef4367731d824ddb486b719fe0b2069a2fb1525a","last_reissued_at":"2026-05-18T03:05:26.752527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:26.752527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1606","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":"2026-05-18T03:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Eftl9PDd2JQU1yv3srnFeJvIckr6R//ZbayEW6WF/W16SxZywivZdvXoKXIUryKnBo0yCIHVNJROXpxyxCTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T15:28:18.900427Z"},"content_sha256":"e1c4bd1ca40edb6cbd4b559b762ac0f0d8e167bc37d41ff135e0e01f66f76710","schema_version":"1.0","event_id":"sha256:e1c4bd1ca40edb6cbd4b559b762ac0f0d8e167bc37d41ff135e0e01f66f76710"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XSPATN63XMMG2KRYTK266Q3HOM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak KAM theorem for Hamilton-Jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC"],"primary_cat":"math.DS","authors_text":"Jun Yan, Xifeng SU","submitted_at":"2013-12-05T16:25:56Z","abstract_excerpt":"In this paper, we generalize weak KAM theorem from positive Lagrangian systems to \"proper\" Hamilton-Jacobi equations.\n  We introduce an implicitly defined solution semigroup of evolutionary Hamilton-Jacobi equations. By exploring the properties of the solution semigroup, we prove the convergence of solution semigroup and existence of weak KAM solutions for stationary equations: \\begin{equation*} H(x, u, d_x u)=0. \\end{equation*}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1606","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":"2026-05-18T03:05:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AgK73FhRVFgwlnfDcuSPe8Ci0paM4mTijSY0hDXs2F2gYyItCPRm709i6LuKN4PyUGv1iJBs3bEIiE3/UZMBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T15:28:18.900787Z"},"content_sha256":"d91987fdec5037cc8199456ac15bbabff955fbc482fd95f0ff3abb902f228a72","schema_version":"1.0","event_id":"sha256:d91987fdec5037cc8199456ac15bbabff955fbc482fd95f0ff3abb902f228a72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM/bundle.json","state_url":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSPATN63XMMG2KRYTK266Q3HOM/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":"2026-05-21T15:28:18Z","links":{"resolver":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM","bundle":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM/bundle.json","state":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSPATN63XMMG2KRYTK266Q3HOM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XSPATN63XMMG2KRYTK266Q3HOM","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":"22c4b4b1c9bf499027a858322f5b2ab36899c763b779213fdcc8dff38f29360c","cross_cats_sorted":["math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-05T16:25:56Z","title_canon_sha256":"93e0642a161e5f9f7be5a8dd4d0128367420dc2468c5ad10fa4106a345ebbfce"},"schema_version":"1.0","source":{"id":"1312.1606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1606","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1606v1","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1606","created_at":"2026-05-18T03:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"XSPATN63XMMG","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XSPATN63XMMG2KRY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XSPATN63","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:d91987fdec5037cc8199456ac15bbabff955fbc482fd95f0ff3abb902f228a72","target":"graph","created_at":"2026-05-18T03:05:26Z","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 generalize weak KAM theorem from positive Lagrangian systems to \"proper\" Hamilton-Jacobi equations.\n  We introduce an implicitly defined solution semigroup of evolutionary Hamilton-Jacobi equations. By exploring the properties of the solution semigroup, we prove the convergence of solution semigroup and existence of weak KAM solutions for stationary equations: \\begin{equation*} H(x, u, d_x u)=0. \\end{equation*}","authors_text":"Jun Yan, Xifeng SU","cross_cats":["math.AP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-05T16:25:56Z","title":"Weak KAM theorem for Hamilton-Jacobi equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1606","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:e1c4bd1ca40edb6cbd4b559b762ac0f0d8e167bc37d41ff135e0e01f66f76710","target":"record","created_at":"2026-05-18T03:05:26Z","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":"22c4b4b1c9bf499027a858322f5b2ab36899c763b779213fdcc8dff38f29360c","cross_cats_sorted":["math.AP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-05T16:25:56Z","title_canon_sha256":"93e0642a161e5f9f7be5a8dd4d0128367420dc2468c5ad10fa4106a345ebbfce"},"schema_version":"1.0","source":{"id":"1312.1606","kind":"arxiv","version":1}},"canonical_sha256":"bc9e09b7dbbb186d2a389ab5ef4367731d824ddb486b719fe0b2069a2fb1525a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc9e09b7dbbb186d2a389ab5ef4367731d824ddb486b719fe0b2069a2fb1525a","first_computed_at":"2026-05-18T03:05:26.752527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:26.752527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HnwL2aMEK7wBHBm9gT0BJiymWKZ7Kx/drpWeyh7Vxht/McFwumJwYSQmIz3r75WdLwulA8jsjra4ERJC25LxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:26.753011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1c4bd1ca40edb6cbd4b559b762ac0f0d8e167bc37d41ff135e0e01f66f76710","sha256:d91987fdec5037cc8199456ac15bbabff955fbc482fd95f0ff3abb902f228a72"],"state_sha256":"783f586f5b9531cbec7436cee4d10244cb9298be131cb269f697ddc9be713422"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8uEkx8S6y8lbuf9DfS0lppjlNKcOjqPGfM4xgWVlBKvdn2QJzCnoWSgyeVAygCpuNYWD8SEuqqNjsOZRGUmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T15:28:18.903011Z","bundle_sha256":"c09563db4bbce999e5e5f001f04f50b8ecd8ac09bc96255938bfa6b65db34aec"}}