{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:DZF2P7NQJVA4EPMUTSRZ4TJ33Q","short_pith_number":"pith:DZF2P7NQ","canonical_record":{"source":{"id":"2007.07418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-15T00:51:57Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2a0911c1e9a4d300833a1c7be0ae8178892ae109de5540a4885f766309109d10","abstract_canon_sha256":"a43ea1a2b18ae4821b32f0774bf8ad12786375bb21673a28b72e9d8f228bc075"},"schema_version":"1.0"},"canonical_sha256":"1e4ba7fdb04d41c23d949ca39e4d3bdc110b16632bff516a4cd94f9647823475","source":{"kind":"arxiv","id":"2007.07418","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.07418","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"2007.07418v2","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.07418","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"DZF2P7NQJVA4","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"pith_short_16","alias_value":"DZF2P7NQJVA4EPMU","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"pith_short_8","alias_value":"DZF2P7NQ","created_at":"2026-07-05T03:06:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:DZF2P7NQJVA4EPMUTSRZ4TJ33Q","target":"record","payload":{"canonical_record":{"source":{"id":"2007.07418","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-15T00:51:57Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2a0911c1e9a4d300833a1c7be0ae8178892ae109de5540a4885f766309109d10","abstract_canon_sha256":"a43ea1a2b18ae4821b32f0774bf8ad12786375bb21673a28b72e9d8f228bc075"},"schema_version":"1.0"},"canonical_sha256":"1e4ba7fdb04d41c23d949ca39e4d3bdc110b16632bff516a4cd94f9647823475","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:06:43.964973Z","signature_b64":"xTt9YOG9fcvPq8IXeziAE0dl94eyfvttcXzhI1dEAMcBk9CmTbZiQEiPhYpTwiDPm/p14azBzVyzTRcku+tqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e4ba7fdb04d41c23d949ca39e4d3bdc110b16632bff516a4cd94f9647823475","last_reissued_at":"2026-07-05T03:06:43.964599Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:06:43.964599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.07418","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:06:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hoXtjvfY1MR4cGxCrhzPDnkpQjt/WVHxACM3vwzP3jbMefUmVuLIZbgg27II8zlT2Rgd5MtIsFtMCmvCAmQADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T02:57:47.629396Z"},"content_sha256":"4fa36f61be95cbb86804044e8929c890e40b2d2ee1aff30014c7b5273713a806","schema_version":"1.0","event_id":"sha256:4fa36f61be95cbb86804044e8929c890e40b2d2ee1aff30014c7b5273713a806"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:DZF2P7NQJVA4EPMUTSRZ4TJ33Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Thomas Y. Hou, Yifan Chen, Yixuan Wang","submitted_at":"2020-07-15T00:51:57Z","abstract_excerpt":"In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove the proposed multiscale method achieves nearly exponential convergence in the approximation error with respect to the computational degrees of freedom. Our strategy is to perform an energy orthogonal decomposition of the solution space into a coarse scale component comprising $a$-harmonic functions in each element of the mesh, and a fine scale component named the bubble part that can be computed lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.07418","kind":"arxiv","version":2},"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/2007.07418/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":"2026-07-05T03:06:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vosb/teE0wuTwy8VLp6XoQzozcGoudbRGndk3d5fr0NpkZ020G3/DROxfnJpOTJDlRTrF1bJFuXz1aHVtQyICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T02:57:47.630432Z"},"content_sha256":"2c435bd8eac5ca03e3900da49ba37206fcf0e764a6152664e30e900e274dad7b","schema_version":"1.0","event_id":"sha256:2c435bd8eac5ca03e3900da49ba37206fcf0e764a6152664e30e900e274dad7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DZF2P7NQJVA4EPMUTSRZ4TJ33Q/bundle.json","state_url":"https://pith.science/pith/DZF2P7NQJVA4EPMUTSRZ4TJ33Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DZF2P7NQJVA4EPMUTSRZ4TJ33Q/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":"2026-08-11T02:57:47Z","links":{"resolver":"https://pith.science/pith/DZF2P7NQJVA4EPMUTSRZ4TJ33Q","bundle":"https://pith.science/pith/DZF2P7NQJVA4EPMUTSRZ4TJ33Q/bundle.json","state":"https://pith.science/pith/DZF2P7NQJVA4EPMUTSRZ4TJ33Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DZF2P7NQJVA4EPMUTSRZ4TJ33Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:DZF2P7NQJVA4EPMUTSRZ4TJ33Q","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":"a43ea1a2b18ae4821b32f0774bf8ad12786375bb21673a28b72e9d8f228bc075","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-15T00:51:57Z","title_canon_sha256":"2a0911c1e9a4d300833a1c7be0ae8178892ae109de5540a4885f766309109d10"},"schema_version":"1.0","source":{"id":"2007.07418","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.07418","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"2007.07418v2","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.07418","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"DZF2P7NQJVA4","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"pith_short_16","alias_value":"DZF2P7NQJVA4EPMU","created_at":"2026-07-05T03:06:43Z"},{"alias_kind":"pith_short_8","alias_value":"DZF2P7NQ","created_at":"2026-07-05T03:06:43Z"}],"graph_snapshots":[{"event_id":"sha256:2c435bd8eac5ca03e3900da49ba37206fcf0e764a6152664e30e900e274dad7b","target":"graph","created_at":"2026-07-05T03:06:43Z","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/2007.07418/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove the proposed multiscale method achieves nearly exponential convergence in the approximation error with respect to the computational degrees of freedom. Our strategy is to perform an energy orthogonal decomposition of the solution space into a coarse scale component comprising $a$-harmonic functions in each element of the mesh, and a fine scale component named the bubble part that can be computed lo","authors_text":"Thomas Y. Hou, Yifan Chen, Yixuan Wang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-15T00:51:57Z","title":"Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.07418","kind":"arxiv","version":2},"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":"sha256:4fa36f61be95cbb86804044e8929c890e40b2d2ee1aff30014c7b5273713a806","target":"record","created_at":"2026-07-05T03:06:43Z","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":"a43ea1a2b18ae4821b32f0774bf8ad12786375bb21673a28b72e9d8f228bc075","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-15T00:51:57Z","title_canon_sha256":"2a0911c1e9a4d300833a1c7be0ae8178892ae109de5540a4885f766309109d10"},"schema_version":"1.0","source":{"id":"2007.07418","kind":"arxiv","version":2}},"canonical_sha256":"1e4ba7fdb04d41c23d949ca39e4d3bdc110b16632bff516a4cd94f9647823475","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e4ba7fdb04d41c23d949ca39e4d3bdc110b16632bff516a4cd94f9647823475","first_computed_at":"2026-07-05T03:06:43.964599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:06:43.964599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xTt9YOG9fcvPq8IXeziAE0dl94eyfvttcXzhI1dEAMcBk9CmTbZiQEiPhYpTwiDPm/p14azBzVyzTRcku+tqDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:06:43.964973Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.07418","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fa36f61be95cbb86804044e8929c890e40b2d2ee1aff30014c7b5273713a806","sha256:2c435bd8eac5ca03e3900da49ba37206fcf0e764a6152664e30e900e274dad7b"],"state_sha256":"e0dd522ce16cb02ddef6fbb2e110547e67730267da21bedc61f16038c65748ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bn/ShgycerKgOfjkvEoNxn/g/Tngx6b8RnTdv7+26LCQVkemIlL1FKp5mRgtPX+Z/jJqK223HR87Hyxmg2FjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T02:57:47.635430Z","bundle_sha256":"39a77430d3803f5c83ddc22c0b90f17c4b64bf748796c5225f690dcbf19c3733"}}