{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CAJ7I43CI5EQHQJGZFCHYRJC7X","short_pith_number":"pith:CAJ7I43C","canonical_record":{"source":{"id":"1102.0904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-04T13:20:52Z","cross_cats_sorted":[],"title_canon_sha256":"06bc62712644e712a4067fa32dd67577dbaf6af99972148c02d7b80ac294428e","abstract_canon_sha256":"3a00ecb675ab68f773506bdf01d8f8c4415b7947fa9b266f6cf740e31432d16f"},"schema_version":"1.0"},"canonical_sha256":"1013f47362474903c126c9447c4522fdfe50a59caaee92664c6499f47bc8d3bf","source":{"kind":"arxiv","id":"1102.0904","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0904","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0904v1","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0904","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"CAJ7I43CI5EQ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CAJ7I43CI5EQHQJG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CAJ7I43C","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CAJ7I43CI5EQHQJGZFCHYRJC7X","target":"record","payload":{"canonical_record":{"source":{"id":"1102.0904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-04T13:20:52Z","cross_cats_sorted":[],"title_canon_sha256":"06bc62712644e712a4067fa32dd67577dbaf6af99972148c02d7b80ac294428e","abstract_canon_sha256":"3a00ecb675ab68f773506bdf01d8f8c4415b7947fa9b266f6cf740e31432d16f"},"schema_version":"1.0"},"canonical_sha256":"1013f47362474903c126c9447c4522fdfe50a59caaee92664c6499f47bc8d3bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:47.491093Z","signature_b64":"fcJMNFlEmrXTn1TdlQERPXDGmXgS5IDH+ZNVYCsYvvf5Y9EJyUhuv9Q3nD+ld81Vo6ouXQQXxZvYeorJGccvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1013f47362474903c126c9447c4522fdfe50a59caaee92664c6499f47bc8d3bf","last_reissued_at":"2026-05-18T02:54:47.490668Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:47.490668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.0904","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":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fowRfI3/B25tAVXsciTTv98PzIiizSMBVd0jkdq87+ucZuqMvQ2Sm74jMlnM+eP4AoYX5zAllgqfAXD2fEucBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:44:33.896010Z"},"content_sha256":"7decbd929c2accd8a5acfe54f916fc5765b3fc5832a8ab5cbe4767b6fb5109ea","schema_version":"1.0","event_id":"sha256:7decbd929c2accd8a5acfe54f916fc5765b3fc5832a8ab5cbe4767b6fb5109ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CAJ7I43CI5EQHQJGZFCHYRJC7X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alexei Lozinski, Claudia Negulescu, Jacek Narski, Pierre Degond","submitted_at":"2011-02-04T13:20:52Z","abstract_excerpt":"The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter $0<\\eps <<1$, the applicability (on cartesian grids) to cases of non-uniform and non-aligned anisotropy fields $b$ and the simple extension to the case of a non-constant anisotropy intensity $1/\\eps$. The mathematical approach and the numerical scheme are different from those presented in the previous work [Degond et al. (2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0904","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":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SenrQn3JGbrad/1wmsFi74b3AFGuzL4SAdRsTU2UgsTq7JH1GgL5Hcpolky97UP+7pYAgdxy4pngXgpKREC0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:44:33.896371Z"},"content_sha256":"1186f62fbde3949547d46cec0bcd89a756e14fb123c0ab90741347baa6cf4cce","schema_version":"1.0","event_id":"sha256:1186f62fbde3949547d46cec0bcd89a756e14fb123c0ab90741347baa6cf4cce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CAJ7I43CI5EQHQJGZFCHYRJC7X/bundle.json","state_url":"https://pith.science/pith/CAJ7I43CI5EQHQJGZFCHYRJC7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CAJ7I43CI5EQHQJGZFCHYRJC7X/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":"2026-06-03T18:44:33Z","links":{"resolver":"https://pith.science/pith/CAJ7I43CI5EQHQJGZFCHYRJC7X","bundle":"https://pith.science/pith/CAJ7I43CI5EQHQJGZFCHYRJC7X/bundle.json","state":"https://pith.science/pith/CAJ7I43CI5EQHQJGZFCHYRJC7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CAJ7I43CI5EQHQJGZFCHYRJC7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CAJ7I43CI5EQHQJGZFCHYRJC7X","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":"3a00ecb675ab68f773506bdf01d8f8c4415b7947fa9b266f6cf740e31432d16f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-04T13:20:52Z","title_canon_sha256":"06bc62712644e712a4067fa32dd67577dbaf6af99972148c02d7b80ac294428e"},"schema_version":"1.0","source":{"id":"1102.0904","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0904","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0904v1","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0904","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"CAJ7I43CI5EQ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CAJ7I43CI5EQHQJG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CAJ7I43C","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:1186f62fbde3949547d46cec0bcd89a756e14fb123c0ab90741347baa6cf4cce","target":"graph","created_at":"2026-05-18T02:54:47Z","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":"The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter $0<\\eps <<1$, the applicability (on cartesian grids) to cases of non-uniform and non-aligned anisotropy fields $b$ and the simple extension to the case of a non-constant anisotropy intensity $1/\\eps$. The mathematical approach and the numerical scheme are different from those presented in the previous work [Degond et al. (2","authors_text":"Alexei Lozinski, Claudia Negulescu, Jacek Narski, Pierre Degond","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-04T13:20:52Z","title":"An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0904","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":"sha256:7decbd929c2accd8a5acfe54f916fc5765b3fc5832a8ab5cbe4767b6fb5109ea","target":"record","created_at":"2026-05-18T02:54:47Z","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":"3a00ecb675ab68f773506bdf01d8f8c4415b7947fa9b266f6cf740e31432d16f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-02-04T13:20:52Z","title_canon_sha256":"06bc62712644e712a4067fa32dd67577dbaf6af99972148c02d7b80ac294428e"},"schema_version":"1.0","source":{"id":"1102.0904","kind":"arxiv","version":1}},"canonical_sha256":"1013f47362474903c126c9447c4522fdfe50a59caaee92664c6499f47bc8d3bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1013f47362474903c126c9447c4522fdfe50a59caaee92664c6499f47bc8d3bf","first_computed_at":"2026-05-18T02:54:47.490668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:47.490668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fcJMNFlEmrXTn1TdlQERPXDGmXgS5IDH+ZNVYCsYvvf5Y9EJyUhuv9Q3nD+ld81Vo6ouXQQXxZvYeorJGccvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:47.491093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0904","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7decbd929c2accd8a5acfe54f916fc5765b3fc5832a8ab5cbe4767b6fb5109ea","sha256:1186f62fbde3949547d46cec0bcd89a756e14fb123c0ab90741347baa6cf4cce"],"state_sha256":"40604dcc19193e409c3ea504d33f14a65586d13b2c87cb731267e21feae3affa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vPn8BRjcEEwaAHdZFij0gmplORMfSdh1OPy/No2PSJjpjBo3B3hSwh+ADbZDvNmtlnUh1/7f0rNGE+PEh0HpAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:44:33.898510Z","bundle_sha256":"8dd2b7825e534f4556b38086228ae27c98f73431172b56e84c7d816d638f8af3"}}