{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PYOFTJGPNNVH243KZJ763XHX2W","short_pith_number":"pith:PYOFTJGP","canonical_record":{"source":{"id":"1605.00168","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-30T21:43:28Z","cross_cats_sorted":[],"title_canon_sha256":"1da663e75666ef7055825f0b4cfc3ca1e27b39d2f99905786152b731fcf37ade","abstract_canon_sha256":"6076d97f90c3aeb76d4c50b82eade3cceb78331a57770d367f51aaad61724fed"},"schema_version":"1.0"},"canonical_sha256":"7e1c59a4cf6b6a7d736aca7feddcf7d59b1d3717ec2e08d38072334ca56ddaa6","source":{"kind":"arxiv","id":"1605.00168","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00168","created_at":"2026-05-18T00:38:09Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00168v4","created_at":"2026-05-18T00:38:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00168","created_at":"2026-05-18T00:38:09Z"},{"alias_kind":"pith_short_12","alias_value":"PYOFTJGPNNVH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYOFTJGPNNVH243K","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYOFTJGP","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PYOFTJGPNNVH243KZJ763XHX2W","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00168","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-30T21:43:28Z","cross_cats_sorted":[],"title_canon_sha256":"1da663e75666ef7055825f0b4cfc3ca1e27b39d2f99905786152b731fcf37ade","abstract_canon_sha256":"6076d97f90c3aeb76d4c50b82eade3cceb78331a57770d367f51aaad61724fed"},"schema_version":"1.0"},"canonical_sha256":"7e1c59a4cf6b6a7d736aca7feddcf7d59b1d3717ec2e08d38072334ca56ddaa6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:09.448201Z","signature_b64":"S+za/u3NJC9hyD3oxBdcKVEfwuIfW7WGgi4j0rnzMrxL14s2mUIEXQwEJ4fHEXyLYJ+SSnahSEE4HqVbnSVDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e1c59a4cf6b6a7d736aca7feddcf7d59b1d3717ec2e08d38072334ca56ddaa6","last_reissued_at":"2026-05-18T00:38:09.447551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:09.447551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00168","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:38:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gyF+5wL2E5w17ZyEQ17YUOgypO4IX3SCc4w0vXHG1I8TJ+lr5nakvwd9qSPml/plDw279Qhv0ftfINCL/3doBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:00:03.962654Z"},"content_sha256":"53b69bf8e772d26e4f8eab843fd0840826f0b86640283ec2960c8a9af9569c7c","schema_version":"1.0","event_id":"sha256:53b69bf8e772d26e4f8eab843fd0840826f0b86640283ec2960c8a9af9569c7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PYOFTJGPNNVH243KZJ763XHX2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogenization of pathwise Hamilton-Jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Seeger","submitted_at":"2016-04-30T21:43:28Z","abstract_excerpt":"We present qualitative and quantitative homogenization results for pathwise Hamilton-Jacobi equations with \"rough\" multiplicative driving signals. When there is only one such signal and the Hamiltonian is convex, we show that the equation, as well as equations with smooth approximating paths, homogenize. In the multi-signal setting, we demonstrate that blow-up or homogenization may take place. The paper also includes a new well-posedness result, which gives explicit estimates for the continuity of the solution map and the equicontinuity of solutions in the spatial variable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00168","kind":"arxiv","version":4},"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":"2026-05-18T00:38:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eakUR7QW4W9Aq4c4wjrLST4xn0pX0h8x4rc/4hgzheUfjoOEsHE2ZBsyWSrQyPwR0UBtF1Z4LaaABLzVYxq6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:00:03.963359Z"},"content_sha256":"f5e5dca89f4ef4478657df02d31b31822a929659bc04ec4112b9c5ac44aea0c9","schema_version":"1.0","event_id":"sha256:f5e5dca89f4ef4478657df02d31b31822a929659bc04ec4112b9c5ac44aea0c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYOFTJGPNNVH243KZJ763XHX2W/bundle.json","state_url":"https://pith.science/pith/PYOFTJGPNNVH243KZJ763XHX2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYOFTJGPNNVH243KZJ763XHX2W/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":"2026-05-22T11:00:03Z","links":{"resolver":"https://pith.science/pith/PYOFTJGPNNVH243KZJ763XHX2W","bundle":"https://pith.science/pith/PYOFTJGPNNVH243KZJ763XHX2W/bundle.json","state":"https://pith.science/pith/PYOFTJGPNNVH243KZJ763XHX2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYOFTJGPNNVH243KZJ763XHX2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PYOFTJGPNNVH243KZJ763XHX2W","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":"6076d97f90c3aeb76d4c50b82eade3cceb78331a57770d367f51aaad61724fed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-30T21:43:28Z","title_canon_sha256":"1da663e75666ef7055825f0b4cfc3ca1e27b39d2f99905786152b731fcf37ade"},"schema_version":"1.0","source":{"id":"1605.00168","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00168","created_at":"2026-05-18T00:38:09Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00168v4","created_at":"2026-05-18T00:38:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00168","created_at":"2026-05-18T00:38:09Z"},{"alias_kind":"pith_short_12","alias_value":"PYOFTJGPNNVH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYOFTJGPNNVH243K","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYOFTJGP","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:f5e5dca89f4ef4478657df02d31b31822a929659bc04ec4112b9c5ac44aea0c9","target":"graph","created_at":"2026-05-18T00:38:09Z","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 present qualitative and quantitative homogenization results for pathwise Hamilton-Jacobi equations with \"rough\" multiplicative driving signals. When there is only one such signal and the Hamiltonian is convex, we show that the equation, as well as equations with smooth approximating paths, homogenize. In the multi-signal setting, we demonstrate that blow-up or homogenization may take place. The paper also includes a new well-posedness result, which gives explicit estimates for the continuity of the solution map and the equicontinuity of solutions in the spatial variable.","authors_text":"Benjamin Seeger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-30T21:43:28Z","title":"Homogenization of pathwise Hamilton-Jacobi equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00168","kind":"arxiv","version":4},"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":"sha256:53b69bf8e772d26e4f8eab843fd0840826f0b86640283ec2960c8a9af9569c7c","target":"record","created_at":"2026-05-18T00:38:09Z","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":"6076d97f90c3aeb76d4c50b82eade3cceb78331a57770d367f51aaad61724fed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-30T21:43:28Z","title_canon_sha256":"1da663e75666ef7055825f0b4cfc3ca1e27b39d2f99905786152b731fcf37ade"},"schema_version":"1.0","source":{"id":"1605.00168","kind":"arxiv","version":4}},"canonical_sha256":"7e1c59a4cf6b6a7d736aca7feddcf7d59b1d3717ec2e08d38072334ca56ddaa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e1c59a4cf6b6a7d736aca7feddcf7d59b1d3717ec2e08d38072334ca56ddaa6","first_computed_at":"2026-05-18T00:38:09.447551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:09.447551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S+za/u3NJC9hyD3oxBdcKVEfwuIfW7WGgi4j0rnzMrxL14s2mUIEXQwEJ4fHEXyLYJ+SSnahSEE4HqVbnSVDDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:09.448201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00168","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53b69bf8e772d26e4f8eab843fd0840826f0b86640283ec2960c8a9af9569c7c","sha256:f5e5dca89f4ef4478657df02d31b31822a929659bc04ec4112b9c5ac44aea0c9"],"state_sha256":"077ccef97f15fe7f78da4a86f8852d1a0dc1582ec36c185c0888c3f0f3774b28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hhgnn7+YXffRP4uqC9t7aSz1EaBx+mu/qu4XEEt4ZNgWeK9jMr3HBNi5yKtcHHXGWfHhjB1rLzGB7wlUMxyoCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T11:00:03.967493Z","bundle_sha256":"111c113a2564d0c2401bc05a4eec1cc99fc4730e814f1f2318191a8548ccb2f5"}}