{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:CJUCVA7NFXKMOWXRJ2YDSVEWP6","short_pith_number":"pith:CJUCVA7N","canonical_record":{"source":{"id":"2401.12799","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-01-23T14:31:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"15de0598965bc91a37ee83132d1ce20d8f88bc3329a81e2dab473e85dce71123","abstract_canon_sha256":"1300119ae381d680abb97612141fef2100e6924fc0c13a0ba514a0624b864cb0"},"schema_version":"1.0"},"canonical_sha256":"12682a83ed2dd4c75af14eb03954967f9354d0be1a20edcf4cf25e3d3f21e17d","source":{"kind":"arxiv","id":"2401.12799","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.12799","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"arxiv_version","alias_value":"2401.12799v5","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12799","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"pith_short_12","alias_value":"CJUCVA7NFXKM","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"pith_short_16","alias_value":"CJUCVA7NFXKMOWXR","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"pith_short_8","alias_value":"CJUCVA7N","created_at":"2026-07-05T10:52:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:CJUCVA7NFXKMOWXRJ2YDSVEWP6","target":"record","payload":{"canonical_record":{"source":{"id":"2401.12799","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-01-23T14:31:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"15de0598965bc91a37ee83132d1ce20d8f88bc3329a81e2dab473e85dce71123","abstract_canon_sha256":"1300119ae381d680abb97612141fef2100e6924fc0c13a0ba514a0624b864cb0"},"schema_version":"1.0"},"canonical_sha256":"12682a83ed2dd4c75af14eb03954967f9354d0be1a20edcf4cf25e3d3f21e17d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:52:10.385844Z","signature_b64":"zJ60Xiql7yZRcEP1LZGibdwp4UwoiEKncjZKV7KY368OkWUC+bpnFpPCBAIjE34MBQCcqKBU6ztR/nGC6bA0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12682a83ed2dd4c75af14eb03954967f9354d0be1a20edcf4cf25e3d3f21e17d","last_reissued_at":"2026-07-05T10:52:10.385447Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:52:10.385447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.12799","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:52:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tuv8xNDm/WwPVBLoaWPfzzxaVGkO8D1/nEkRUvUcGLQWqrQQ8qXgOPvJ0yuRVm+vSxjBpnZaPu3Vg4lAnIU2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:42:39.850662Z"},"content_sha256":"05f9ff81b182869dd79fe8b3ad0309f922299ecbb34f569d8632d4543b525183","schema_version":"1.0","event_id":"sha256:05f9ff81b182869dd79fe8b3ad0309f922299ecbb34f569d8632d4543b525183"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:CJUCVA7NFXKMOWXRJ2YDSVEWP6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some convergence analysis for multicontinuum homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Wing Tat Leung","submitted_at":"2024-01-23T14:31:29Z","abstract_excerpt":"In this paper, we provide an analysis of a recently proposed multicontinuum homogenization technique. The analysis differs from those used in classical homogenization methods for several reasons. First, the cell problems in multicontinuum homogenization use constraint problems and can not be directly substituted into the differential operator. Secondly, the problem contains high contrast that remains in the homogenized problem. The homogenized problem averages the microstructure while containing the small parameter. In this analysis, we first based on our previous techniques, CEM-GMsFEM, to de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12799","kind":"arxiv","version":5},"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/2401.12799/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":"2026-07-05T10:52:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U3CPtWceS16ZnHm1i4RdQ6ROz6InEcwosljmu67ZTl+EKLnYcPo8BoNCD6hOa5Zh9SR14YDpbIhnTwBRGBMxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:42:39.851751Z"},"content_sha256":"58fa66645dd20ab8b90c0391174f0023f3be674c2cdace7def728303ea96aebc","schema_version":"1.0","event_id":"sha256:58fa66645dd20ab8b90c0391174f0023f3be674c2cdace7def728303ea96aebc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJUCVA7NFXKMOWXRJ2YDSVEWP6/bundle.json","state_url":"https://pith.science/pith/CJUCVA7NFXKMOWXRJ2YDSVEWP6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJUCVA7NFXKMOWXRJ2YDSVEWP6/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":"2026-08-09T15:42:39Z","links":{"resolver":"https://pith.science/pith/CJUCVA7NFXKMOWXRJ2YDSVEWP6","bundle":"https://pith.science/pith/CJUCVA7NFXKMOWXRJ2YDSVEWP6/bundle.json","state":"https://pith.science/pith/CJUCVA7NFXKMOWXRJ2YDSVEWP6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJUCVA7NFXKMOWXRJ2YDSVEWP6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CJUCVA7NFXKMOWXRJ2YDSVEWP6","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":"1300119ae381d680abb97612141fef2100e6924fc0c13a0ba514a0624b864cb0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-01-23T14:31:29Z","title_canon_sha256":"15de0598965bc91a37ee83132d1ce20d8f88bc3329a81e2dab473e85dce71123"},"schema_version":"1.0","source":{"id":"2401.12799","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.12799","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"arxiv_version","alias_value":"2401.12799v5","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12799","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"pith_short_12","alias_value":"CJUCVA7NFXKM","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"pith_short_16","alias_value":"CJUCVA7NFXKMOWXR","created_at":"2026-07-05T10:52:10Z"},{"alias_kind":"pith_short_8","alias_value":"CJUCVA7N","created_at":"2026-07-05T10:52:10Z"}],"graph_snapshots":[{"event_id":"sha256:58fa66645dd20ab8b90c0391174f0023f3be674c2cdace7def728303ea96aebc","target":"graph","created_at":"2026-07-05T10:52:10Z","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/2401.12799/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we provide an analysis of a recently proposed multicontinuum homogenization technique. The analysis differs from those used in classical homogenization methods for several reasons. First, the cell problems in multicontinuum homogenization use constraint problems and can not be directly substituted into the differential operator. Secondly, the problem contains high contrast that remains in the homogenized problem. The homogenized problem averages the microstructure while containing the small parameter. In this analysis, we first based on our previous techniques, CEM-GMsFEM, to de","authors_text":"Wing Tat Leung","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-01-23T14:31:29Z","title":"Some convergence analysis for multicontinuum homogenization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12799","kind":"arxiv","version":5},"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":"sha256:05f9ff81b182869dd79fe8b3ad0309f922299ecbb34f569d8632d4543b525183","target":"record","created_at":"2026-07-05T10:52:10Z","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":"1300119ae381d680abb97612141fef2100e6924fc0c13a0ba514a0624b864cb0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-01-23T14:31:29Z","title_canon_sha256":"15de0598965bc91a37ee83132d1ce20d8f88bc3329a81e2dab473e85dce71123"},"schema_version":"1.0","source":{"id":"2401.12799","kind":"arxiv","version":5}},"canonical_sha256":"12682a83ed2dd4c75af14eb03954967f9354d0be1a20edcf4cf25e3d3f21e17d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12682a83ed2dd4c75af14eb03954967f9354d0be1a20edcf4cf25e3d3f21e17d","first_computed_at":"2026-07-05T10:52:10.385447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:52:10.385447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zJ60Xiql7yZRcEP1LZGibdwp4UwoiEKncjZKV7KY368OkWUC+bpnFpPCBAIjE34MBQCcqKBU6ztR/nGC6bA0Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:52:10.385844Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.12799","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05f9ff81b182869dd79fe8b3ad0309f922299ecbb34f569d8632d4543b525183","sha256:58fa66645dd20ab8b90c0391174f0023f3be674c2cdace7def728303ea96aebc"],"state_sha256":"66565343c65fdb50f762b78b3e4cead2d7cd8a48eb920e0f16e456855ec073f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uptdB3KVAX01Le6hgIV+lO0mZqvMZ77Pj0+O0i2IPQ5j1IQDBqRBKYd2O7GNlgy0wdflK7QU2N7iqYI3+PKvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T15:42:39.859901Z","bundle_sha256":"d38c206578a0a6c3e9e69f71484805e16f60f7011c3fd9990d5cee7e9a21942a"}}