{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:V6HDT3JUFONEU7VZMG7H5C7AAB","short_pith_number":"pith:V6HDT3JU","canonical_record":{"source":{"id":"1111.6903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-29T17:08:27Z","cross_cats_sorted":[],"title_canon_sha256":"4cf57a81b2bac7f785bca3dc2a3f29375b8f82be504252b79f91e6862d9c86ce","abstract_canon_sha256":"6309c82b4e7a47b8e6a3129f7e84c53eae6be27149c369157f6e66d57b3db6bb"},"schema_version":"1.0"},"canonical_sha256":"af8e39ed342b9a4a7eb961be7e8be000448a7566cda0cebe2d4b6013859e0c38","source":{"kind":"arxiv","id":"1111.6903","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6903","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6903v1","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6903","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"pith_short_12","alias_value":"V6HDT3JUFONE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V6HDT3JUFONEU7VZ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V6HDT3JU","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:V6HDT3JUFONEU7VZMG7H5C7AAB","target":"record","payload":{"canonical_record":{"source":{"id":"1111.6903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-29T17:08:27Z","cross_cats_sorted":[],"title_canon_sha256":"4cf57a81b2bac7f785bca3dc2a3f29375b8f82be504252b79f91e6862d9c86ce","abstract_canon_sha256":"6309c82b4e7a47b8e6a3129f7e84c53eae6be27149c369157f6e66d57b3db6bb"},"schema_version":"1.0"},"canonical_sha256":"af8e39ed342b9a4a7eb961be7e8be000448a7566cda0cebe2d4b6013859e0c38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:28.284910Z","signature_b64":"i0Z7zMD33rEsMy5y32+hPIfLgUQXHcMMUqdRODoRh/6dDDo+1LGBceEGkXAMXCCaub0EgN89eUu5rDC1/04CCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af8e39ed342b9a4a7eb961be7e8be000448a7566cda0cebe2d4b6013859e0c38","last_reissued_at":"2026-05-18T04:07:28.284404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:28.284404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.6903","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":"2026-05-18T04:07:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WimFIRp+Qj71CqUU/35HzbszN+tn/uwTrNlsWwC/DIEcPFxBmNSbd0H0/Pe4ZNf/HB8VIFag8F4yOawj5GuGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:26:41.474279Z"},"content_sha256":"02121ceb1469a4d677f9d6c8daeb1e62053b2cd820b17af0990d6716647a36dd","schema_version":"1.0","event_id":"sha256:02121ceb1469a4d677f9d6c8daeb1e62053b2cd820b17af0990d6716647a36dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:V6HDT3JUFONEU7VZMG7H5C7AAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Augmented Fast Marching Method for Level Set Reinitialization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"David Salac","submitted_at":"2011-11-29T17:08:27Z","abstract_excerpt":"Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the fast marching method is presented. This augmented fast marching method will calculate the signed distance function and up to the second-order derivatives of the signed distance function for arbitrary interfaces. In addition to enforcing the condition $|\\nabla\\phi|^2=1$, where $\\phi$ is the level set function, the method ensures that $\\nabla(|\\nabla\\phi|)^2=0$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6903","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":"2026-05-18T04:07:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BxFEnhe9k+ZELQf6Ddv5AxxUxUN5fl0fuKlcqMvu6mTgnpcvTLWJJoPRKXDo1rcbwkhymq4uqjxs5s1y7MLFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:26:41.474633Z"},"content_sha256":"bbe342a66310e8fc77272e7f7fbefff49a830944aa4bf63a1dbc8156f332cb72","schema_version":"1.0","event_id":"sha256:bbe342a66310e8fc77272e7f7fbefff49a830944aa4bf63a1dbc8156f332cb72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6HDT3JUFONEU7VZMG7H5C7AAB/bundle.json","state_url":"https://pith.science/pith/V6HDT3JUFONEU7VZMG7H5C7AAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6HDT3JUFONEU7VZMG7H5C7AAB/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":"2026-06-27T11:26:41Z","links":{"resolver":"https://pith.science/pith/V6HDT3JUFONEU7VZMG7H5C7AAB","bundle":"https://pith.science/pith/V6HDT3JUFONEU7VZMG7H5C7AAB/bundle.json","state":"https://pith.science/pith/V6HDT3JUFONEU7VZMG7H5C7AAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6HDT3JUFONEU7VZMG7H5C7AAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V6HDT3JUFONEU7VZMG7H5C7AAB","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":"6309c82b4e7a47b8e6a3129f7e84c53eae6be27149c369157f6e66d57b3db6bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-29T17:08:27Z","title_canon_sha256":"4cf57a81b2bac7f785bca3dc2a3f29375b8f82be504252b79f91e6862d9c86ce"},"schema_version":"1.0","source":{"id":"1111.6903","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6903","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6903v1","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6903","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"pith_short_12","alias_value":"V6HDT3JUFONE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V6HDT3JUFONEU7VZ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V6HDT3JU","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:bbe342a66310e8fc77272e7f7fbefff49a830944aa4bf63a1dbc8156f332cb72","target":"graph","created_at":"2026-05-18T04:07:28Z","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":"Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the fast marching method is presented. This augmented fast marching method will calculate the signed distance function and up to the second-order derivatives of the signed distance function for arbitrary interfaces. In addition to enforcing the condition $|\\nabla\\phi|^2=1$, where $\\phi$ is the level set function, the method ensures that $\\nabla(|\\nabla\\phi|)^2=0$ a","authors_text":"David Salac","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-29T17:08:27Z","title":"The Augmented Fast Marching Method for Level Set Reinitialization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6903","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":"sha256:02121ceb1469a4d677f9d6c8daeb1e62053b2cd820b17af0990d6716647a36dd","target":"record","created_at":"2026-05-18T04:07:28Z","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":"6309c82b4e7a47b8e6a3129f7e84c53eae6be27149c369157f6e66d57b3db6bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-11-29T17:08:27Z","title_canon_sha256":"4cf57a81b2bac7f785bca3dc2a3f29375b8f82be504252b79f91e6862d9c86ce"},"schema_version":"1.0","source":{"id":"1111.6903","kind":"arxiv","version":1}},"canonical_sha256":"af8e39ed342b9a4a7eb961be7e8be000448a7566cda0cebe2d4b6013859e0c38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af8e39ed342b9a4a7eb961be7e8be000448a7566cda0cebe2d4b6013859e0c38","first_computed_at":"2026-05-18T04:07:28.284404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:28.284404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i0Z7zMD33rEsMy5y32+hPIfLgUQXHcMMUqdRODoRh/6dDDo+1LGBceEGkXAMXCCaub0EgN89eUu5rDC1/04CCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:28.284910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6903","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02121ceb1469a4d677f9d6c8daeb1e62053b2cd820b17af0990d6716647a36dd","sha256:bbe342a66310e8fc77272e7f7fbefff49a830944aa4bf63a1dbc8156f332cb72"],"state_sha256":"b90417dd7192cebbf79d2dd53d404735485fee70c0d2873c035b7c66d1f08c70"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SItFWWQ4mO+WRDnfzPislKg0uO0Gw21iYB0wA5Drorc798oXoSCpTCFMupuN5tiKMkgzva6t6Xwo4dD8mR+NCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T11:26:41.476674Z","bundle_sha256":"af1a554ac917071773658daf04e4eb9063f38e7a079be96ff9dbd070311e77cb"}}