{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:O7WP5AKVA66WMZ6TRSIRQDLA43","short_pith_number":"pith:O7WP5AKV","canonical_record":{"source":{"id":"1212.4132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-17T20:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"5ef732a1ff1cff45b3dc168d336c7a5b43aedb4a57df0c95340e51bba25a1522","abstract_canon_sha256":"172809aee6e32f5e15a99aac3b94ce6f993552be4be97322855795c3701fa559"},"schema_version":"1.0"},"canonical_sha256":"77ecfe815507bd6667d38c91180d60e6e2a1790f25e46d27396678ff14fe7e85","source":{"kind":"arxiv","id":"1212.4132","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4132","created_at":"2026-05-18T01:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4132v1","created_at":"2026-05-18T01:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4132","created_at":"2026-05-18T01:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"O7WP5AKVA66W","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O7WP5AKVA66WMZ6T","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O7WP5AKV","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:O7WP5AKVA66WMZ6TRSIRQDLA43","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-17T20:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"5ef732a1ff1cff45b3dc168d336c7a5b43aedb4a57df0c95340e51bba25a1522","abstract_canon_sha256":"172809aee6e32f5e15a99aac3b94ce6f993552be4be97322855795c3701fa559"},"schema_version":"1.0"},"canonical_sha256":"77ecfe815507bd6667d38c91180d60e6e2a1790f25e46d27396678ff14fe7e85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:31.376820Z","signature_b64":"0sTRS3f7grJkTX/vHQf0LjC0uczPKoHmKhI3N4z49cfvWSD5rcm6Rkfli1SUg5/zyhf7209S+h2DGIly14/vDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77ecfe815507bd6667d38c91180d60e6e2a1790f25e46d27396678ff14fe7e85","last_reissued_at":"2026-05-18T01:52:31.376112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:31.376112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4132","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":"2026-05-18T01:52:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yv5Wiz/7k46dueqYJIlr+8nS8CnTaFE5wxmdmD0fr9d+jT6E4s2QAeEBIOtVDq/2syvs6TOfXG9NuIdnnevGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:13:24.114650Z"},"content_sha256":"0fded35f671f695e5fe3fabe93acf1a277d828809853271df638883e4c631a2c","schema_version":"1.0","event_id":"sha256:0fded35f671f695e5fe3fabe93acf1a277d828809853271df638883e4c631a2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:O7WP5AKVA66WMZ6TRSIRQDLA43","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Dynamics for Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Cory Hauck, Hayden Schaeffer, Russel Caflisch, Stanley Osher","submitted_at":"2012-12-17T20:41:35Z","abstract_excerpt":"We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4132","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":"2026-05-18T01:52:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ACC3LUt1WGVQv5whYme9MtqxmmeaGtNTBtzMMvvnWpofr368e9+pz9MuPoCMMqKigd3BszJnES8hi98TjvC5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:13:24.115005Z"},"content_sha256":"d9d0ffe3995936110ece0ec0382fa2d75d610e707a141e8cc1b16dd4ccc6420e","schema_version":"1.0","event_id":"sha256:d9d0ffe3995936110ece0ec0382fa2d75d610e707a141e8cc1b16dd4ccc6420e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7WP5AKVA66WMZ6TRSIRQDLA43/bundle.json","state_url":"https://pith.science/pith/O7WP5AKVA66WMZ6TRSIRQDLA43/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7WP5AKVA66WMZ6TRSIRQDLA43/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":"2026-05-31T20:13:24Z","links":{"resolver":"https://pith.science/pith/O7WP5AKVA66WMZ6TRSIRQDLA43","bundle":"https://pith.science/pith/O7WP5AKVA66WMZ6TRSIRQDLA43/bundle.json","state":"https://pith.science/pith/O7WP5AKVA66WMZ6TRSIRQDLA43/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7WP5AKVA66WMZ6TRSIRQDLA43/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:O7WP5AKVA66WMZ6TRSIRQDLA43","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":"172809aee6e32f5e15a99aac3b94ce6f993552be4be97322855795c3701fa559","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-17T20:41:35Z","title_canon_sha256":"5ef732a1ff1cff45b3dc168d336c7a5b43aedb4a57df0c95340e51bba25a1522"},"schema_version":"1.0","source":{"id":"1212.4132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4132","created_at":"2026-05-18T01:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4132v1","created_at":"2026-05-18T01:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4132","created_at":"2026-05-18T01:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"O7WP5AKVA66W","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O7WP5AKVA66WMZ6T","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O7WP5AKV","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:d9d0ffe3995936110ece0ec0382fa2d75d610e707a141e8cc1b16dd4ccc6420e","target":"graph","created_at":"2026-05-18T01:52:31Z","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 investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, d","authors_text":"Cory Hauck, Hayden Schaeffer, Russel Caflisch, Stanley Osher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-17T20:41:35Z","title":"Sparse Dynamics for Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4132","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":"sha256:0fded35f671f695e5fe3fabe93acf1a277d828809853271df638883e4c631a2c","target":"record","created_at":"2026-05-18T01:52:31Z","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":"172809aee6e32f5e15a99aac3b94ce6f993552be4be97322855795c3701fa559","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-12-17T20:41:35Z","title_canon_sha256":"5ef732a1ff1cff45b3dc168d336c7a5b43aedb4a57df0c95340e51bba25a1522"},"schema_version":"1.0","source":{"id":"1212.4132","kind":"arxiv","version":1}},"canonical_sha256":"77ecfe815507bd6667d38c91180d60e6e2a1790f25e46d27396678ff14fe7e85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77ecfe815507bd6667d38c91180d60e6e2a1790f25e46d27396678ff14fe7e85","first_computed_at":"2026-05-18T01:52:31.376112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:31.376112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0sTRS3f7grJkTX/vHQf0LjC0uczPKoHmKhI3N4z49cfvWSD5rcm6Rkfli1SUg5/zyhf7209S+h2DGIly14/vDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:31.376820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fded35f671f695e5fe3fabe93acf1a277d828809853271df638883e4c631a2c","sha256:d9d0ffe3995936110ece0ec0382fa2d75d610e707a141e8cc1b16dd4ccc6420e"],"state_sha256":"3f293cb7f07b157bd6cfc1dfdbd12478fcd2c829c55fd789ee186f39b621cc48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HLDqMouFoX5FwKVWz4Y5RXhXTS+fHZCnVMbb653ZMxIyVwqnGSIL/KicMPn+zsisO6u4VVwkEZ6vIBPDEkqTDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:13:24.117118Z","bundle_sha256":"c7bd2ae50e5f350428682e7bccd021bc4f1d15b35b5bea5126b40b1d3becb88f"}}