{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:443X3OAOYE6MOJC6M5SGYKO7IQ","short_pith_number":"pith:443X3OAO","canonical_record":{"source":{"id":"1003.4160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-22T13:51:58Z","cross_cats_sorted":[],"title_canon_sha256":"619006c9551c287196b63246d55e5f52b8881038fa8a6a67320b54f8a081fdd8","abstract_canon_sha256":"a2820eed42a16428b4a2a5c9c6045d205e28f6b06ec4f867d5267fd1f2643516"},"schema_version":"1.0"},"canonical_sha256":"e7377db80ec13cc7245e67646c29df4415899f6b361dc726843e00e3c9191db1","source":{"kind":"arxiv","id":"1003.4160","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4160","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4160v1","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4160","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"pith_short_12","alias_value":"443X3OAOYE6M","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"443X3OAOYE6MOJC6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"443X3OAO","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:443X3OAOYE6MOJC6M5SGYKO7IQ","target":"record","payload":{"canonical_record":{"source":{"id":"1003.4160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-22T13:51:58Z","cross_cats_sorted":[],"title_canon_sha256":"619006c9551c287196b63246d55e5f52b8881038fa8a6a67320b54f8a081fdd8","abstract_canon_sha256":"a2820eed42a16428b4a2a5c9c6045d205e28f6b06ec4f867d5267fd1f2643516"},"schema_version":"1.0"},"canonical_sha256":"e7377db80ec13cc7245e67646c29df4415899f6b361dc726843e00e3c9191db1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:45.722500Z","signature_b64":"CzJqb7WjrizNracIjI6msVi96gUrZkhdAHTzkYLeEtoptVhzo76p8Ta1JG/IG3L/HJnkXUd+SKUGltolgeC3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7377db80ec13cc7245e67646c29df4415899f6b361dc726843e00e3c9191db1","last_reissued_at":"2026-05-18T04:28:45.721999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:45.721999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.4160","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":"2026-05-18T04:28:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PnxC2ke3NZ7YTUHaYo4h9Xj9V58gBXmdgi5y0d1xUF+Pzide09xxkZHnnoDBYEYyzOeh1emu+wKhgXbO5ElnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:42:15.329308Z"},"content_sha256":"db8633a61aa05352a8a995afddffd9cebec773a89dc8a2fc1f988767208bda20","schema_version":"1.0","event_id":"sha256:db8633a61aa05352a8a995afddffd9cebec773a89dc8a2fc1f988767208bda20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:443X3OAOYE6MOJC6M5SGYKO7IQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogenization and enhancement for the G-equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"James Nolen, Panagiotis E. Souganidis, Pierre Cardaliaguet (LM)","submitted_at":"2010-03-22T13:51:58Z","abstract_excerpt":"We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4160","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":"2026-05-18T04:28:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jq9O3nMuf4rVyP59crch//3LvdXEBNiyiwYm9l3pNY031PpmFWv+hH1/Q7FUx5wbLZWuwC0b3qcPiKPYwFmIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:42:15.329669Z"},"content_sha256":"114610ae1f027149f1bc54d591d1329611cf2139756818ef2552da2e5e8c943c","schema_version":"1.0","event_id":"sha256:114610ae1f027149f1bc54d591d1329611cf2139756818ef2552da2e5e8c943c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/443X3OAOYE6MOJC6M5SGYKO7IQ/bundle.json","state_url":"https://pith.science/pith/443X3OAOYE6MOJC6M5SGYKO7IQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/443X3OAOYE6MOJC6M5SGYKO7IQ/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":"2026-06-09T09:42:15Z","links":{"resolver":"https://pith.science/pith/443X3OAOYE6MOJC6M5SGYKO7IQ","bundle":"https://pith.science/pith/443X3OAOYE6MOJC6M5SGYKO7IQ/bundle.json","state":"https://pith.science/pith/443X3OAOYE6MOJC6M5SGYKO7IQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/443X3OAOYE6MOJC6M5SGYKO7IQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:443X3OAOYE6MOJC6M5SGYKO7IQ","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":"a2820eed42a16428b4a2a5c9c6045d205e28f6b06ec4f867d5267fd1f2643516","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-22T13:51:58Z","title_canon_sha256":"619006c9551c287196b63246d55e5f52b8881038fa8a6a67320b54f8a081fdd8"},"schema_version":"1.0","source":{"id":"1003.4160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4160","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4160v1","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4160","created_at":"2026-05-18T04:28:45Z"},{"alias_kind":"pith_short_12","alias_value":"443X3OAOYE6M","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"443X3OAOYE6MOJC6","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"443X3OAO","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:114610ae1f027149f1bc54d591d1329611cf2139756818ef2552da2e5e8c943c","target":"graph","created_at":"2026-05-18T04:28:45Z","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 consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances","authors_text":"James Nolen, Panagiotis E. Souganidis, Pierre Cardaliaguet (LM)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-22T13:51:58Z","title":"Homogenization and enhancement for the G-equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4160","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:db8633a61aa05352a8a995afddffd9cebec773a89dc8a2fc1f988767208bda20","target":"record","created_at":"2026-05-18T04:28:45Z","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":"a2820eed42a16428b4a2a5c9c6045d205e28f6b06ec4f867d5267fd1f2643516","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-22T13:51:58Z","title_canon_sha256":"619006c9551c287196b63246d55e5f52b8881038fa8a6a67320b54f8a081fdd8"},"schema_version":"1.0","source":{"id":"1003.4160","kind":"arxiv","version":1}},"canonical_sha256":"e7377db80ec13cc7245e67646c29df4415899f6b361dc726843e00e3c9191db1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7377db80ec13cc7245e67646c29df4415899f6b361dc726843e00e3c9191db1","first_computed_at":"2026-05-18T04:28:45.721999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:45.721999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CzJqb7WjrizNracIjI6msVi96gUrZkhdAHTzkYLeEtoptVhzo76p8Ta1JG/IG3L/HJnkXUd+SKUGltolgeC3BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:45.722500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db8633a61aa05352a8a995afddffd9cebec773a89dc8a2fc1f988767208bda20","sha256:114610ae1f027149f1bc54d591d1329611cf2139756818ef2552da2e5e8c943c"],"state_sha256":"712cf73db72bb06ccd32f0787076a2bebe9ffd4bcd70aa72f8a08f7fe817fca0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bs2QAEicZuzFbeJYaWmirisZbbDalKONo3SFRlPsskdU3YFZDimJuYUs73gDjno42q0iqprXqqrsfIhYF0LFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:42:15.331613Z","bundle_sha256":"91e3bc6b5003ba2a8d1a8be7b848da6b06b52902e61d1604ded4a5c4956bf31f"}}