{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:VY3CVX6JJ4CYSJEUTRYWQYXL4R","short_pith_number":"pith:VY3CVX6J","canonical_record":{"source":{"id":"math/0612238","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2006-12-09T16:35:46Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0c70b67d1682cc8e4c328eb1709d4a01bdac1b94b9b6f5a23eedb1c1d08f70d5","abstract_canon_sha256":"57020de0313bfd2101877f75461a6332ce25d9a0ce676490c7d909c086a1b1a7"},"schema_version":"1.0"},"canonical_sha256":"ae362adfc94f058924949c716862ebe46e51003a28b2906089426f12c0ae4ee7","source":{"kind":"arxiv","id":"math/0612238","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612238","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612238v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612238","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"VY3CVX6JJ4CY","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"VY3CVX6JJ4CYSJEU","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"VY3CVX6J","created_at":"2026-06-03T22:06:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:VY3CVX6JJ4CYSJEUTRYWQYXL4R","target":"record","payload":{"canonical_record":{"source":{"id":"math/0612238","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2006-12-09T16:35:46Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0c70b67d1682cc8e4c328eb1709d4a01bdac1b94b9b6f5a23eedb1c1d08f70d5","abstract_canon_sha256":"57020de0313bfd2101877f75461a6332ce25d9a0ce676490c7d909c086a1b1a7"},"schema_version":"1.0"},"canonical_sha256":"ae362adfc94f058924949c716862ebe46e51003a28b2906089426f12c0ae4ee7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:21.511592Z","signature_b64":"jhxxsLlYCl/IVkuYHlhzsFl/OQ3zea/qq7hCMbOaIAxHfUDWxpslyELrQkEVrLZJf18CX+DK0DGP0uMPx3gGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae362adfc94f058924949c716862ebe46e51003a28b2906089426f12c0ae4ee7","last_reissued_at":"2026-06-03T22:06:21.511208Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:21.511208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0612238","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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+tWNQ7MWl4kJMBJnpVVz4gJNoIeww8vq8tKFgd1q9T2Xv4SaazO2hx4e2TqOaPPWot5yJOyYGlRm5U9NJNhBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:40:58.199822Z"},"content_sha256":"5cb8ba2570cc92e7736b720c05bc69dde89e11582e6f670b70ecada1a30e64f8","schema_version":"1.0","event_id":"sha256:5cb8ba2570cc92e7736b720c05bc69dde89e11582e6f670b70ecada1a30e64f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:VY3CVX6JJ4CYSJEUTRYWQYXL4R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High order relaxed schemes for nonlinear reaction diffusion problems","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Fausto Cavalli, Matteo Semplice","submitted_at":"2006-12-09T16:35:46Z","abstract_excerpt":"Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto diffusive relaxed schemes for the numerical approximation of nonlinear reaction diffusion equations. High order methods are obtained by coupling ENO and WENO schemes for space discretization with IMEX schemes for time integration, where the implicit part can be explicitly solved at a linear cost. To illustrate the high accuracy and good properties of the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612238","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0612238/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YzAzCF5bGPMATjt9EB4uxDUGAshTwe9zPGmaXxLSHsimS/wbb+V2FiE7+nqH17ytzk2K+XZo0lkjtlj1p56EAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:40:58.200236Z"},"content_sha256":"ef03085b9d766b4b42ea1d7d2eadeef9bc659f8eef8b335e51803d2e88d23020","schema_version":"1.0","event_id":"sha256:ef03085b9d766b4b42ea1d7d2eadeef9bc659f8eef8b335e51803d2e88d23020"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VY3CVX6JJ4CYSJEUTRYWQYXL4R/bundle.json","state_url":"https://pith.science/pith/VY3CVX6JJ4CYSJEUTRYWQYXL4R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VY3CVX6JJ4CYSJEUTRYWQYXL4R/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":"2026-06-09T12:40:58Z","links":{"resolver":"https://pith.science/pith/VY3CVX6JJ4CYSJEUTRYWQYXL4R","bundle":"https://pith.science/pith/VY3CVX6JJ4CYSJEUTRYWQYXL4R/bundle.json","state":"https://pith.science/pith/VY3CVX6JJ4CYSJEUTRYWQYXL4R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VY3CVX6JJ4CYSJEUTRYWQYXL4R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:VY3CVX6JJ4CYSJEUTRYWQYXL4R","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":"57020de0313bfd2101877f75461a6332ce25d9a0ce676490c7d909c086a1b1a7","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2006-12-09T16:35:46Z","title_canon_sha256":"0c70b67d1682cc8e4c328eb1709d4a01bdac1b94b9b6f5a23eedb1c1d08f70d5"},"schema_version":"1.0","source":{"id":"math/0612238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612238","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612238v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612238","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"VY3CVX6JJ4CY","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"VY3CVX6JJ4CYSJEU","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"VY3CVX6J","created_at":"2026-06-03T22:06:21Z"}],"graph_snapshots":[{"event_id":"sha256:ef03085b9d766b4b42ea1d7d2eadeef9bc659f8eef8b335e51803d2e88d23020","target":"graph","created_at":"2026-06-03T22:06:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0612238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto diffusive relaxed schemes for the numerical approximation of nonlinear reaction diffusion equations. High order methods are obtained by coupling ENO and WENO schemes for space discretization with IMEX schemes for time integration, where the implicit part can be explicitly solved at a linear cost. To illustrate the high accuracy and good properties of the pr","authors_text":"Fausto Cavalli, Matteo Semplice","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2006-12-09T16:35:46Z","title":"High order relaxed schemes for nonlinear reaction diffusion problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612238","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":"sha256:5cb8ba2570cc92e7736b720c05bc69dde89e11582e6f670b70ecada1a30e64f8","target":"record","created_at":"2026-06-03T22:06:21Z","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":"57020de0313bfd2101877f75461a6332ce25d9a0ce676490c7d909c086a1b1a7","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2006-12-09T16:35:46Z","title_canon_sha256":"0c70b67d1682cc8e4c328eb1709d4a01bdac1b94b9b6f5a23eedb1c1d08f70d5"},"schema_version":"1.0","source":{"id":"math/0612238","kind":"arxiv","version":1}},"canonical_sha256":"ae362adfc94f058924949c716862ebe46e51003a28b2906089426f12c0ae4ee7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae362adfc94f058924949c716862ebe46e51003a28b2906089426f12c0ae4ee7","first_computed_at":"2026-06-03T22:06:21.511208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:21.511208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jhxxsLlYCl/IVkuYHlhzsFl/OQ3zea/qq7hCMbOaIAxHfUDWxpslyELrQkEVrLZJf18CX+DK0DGP0uMPx3gGAQ==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:21.511592Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cb8ba2570cc92e7736b720c05bc69dde89e11582e6f670b70ecada1a30e64f8","sha256:ef03085b9d766b4b42ea1d7d2eadeef9bc659f8eef8b335e51803d2e88d23020"],"state_sha256":"adadb677cade269a0580dc6ae835b21e5090c88880e550145281cbb4bc0d04ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uWi90yEbEzOta3OByA4sLRjRX722h7oiQO2ks8um4GLX6dr6cIzFdTNJRYrWF/jD8PVq65duN60RqMiIjEdlAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:40:58.202103Z","bundle_sha256":"f9f1c675b7a4945be701d495dfc37a867c42c16bc7a16ed4d4b17fa4873ede29"}}