{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OPLD6CT5AC4KNTVYGO4Y5VJ5XP","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":"08ef141020a2dec7fa2994e3878fc9bc8f69ad34037546d496784b634936b94b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-10T14:16:25Z","title_canon_sha256":"9e809eeb0e7da86107167c67e87acb72dc19fb2027bba5d78bc31caa6fb3ed65"},"schema_version":"1.0","source":{"id":"1310.2827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2827","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2827v1","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2827","created_at":"2026-05-18T03:10:46Z"},{"alias_kind":"pith_short_12","alias_value":"OPLD6CT5AC4K","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OPLD6CT5AC4KNTVY","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OPLD6CT5","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:e4b0018132045b3cc7069c906c28ef4cba8351394b0987a3becc1f328f4b6665","target":"graph","created_at":"2026-05-18T03:10:46Z","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 introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition and the hybrid discontinuous Galerkin methods. The method utilizes three different scales: (1) the scale of the partition of the domain of the problem, (2) the sale of partition of the boundaries of the subdomains (related to the corresponding space of Lagrange multipliers), and (3) the fine grid scale that is assumed to resolve the scale of the heterogeneous","authors_text":"Ke Shi, Raytcho Lazarov, Yalchin Efendiev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-10T14:16:25Z","title":"A multiscale HDG method for second order elliptic equations. Part I. Polynomial and homogenization-based multiscale spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2827","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":"sha256:3e6643e076f6000eb58fe3e2bbd6806b5bf55cff0fc36b627bd5d80bde609160","target":"record","created_at":"2026-05-18T03:10:46Z","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":"08ef141020a2dec7fa2994e3878fc9bc8f69ad34037546d496784b634936b94b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-10T14:16:25Z","title_canon_sha256":"9e809eeb0e7da86107167c67e87acb72dc19fb2027bba5d78bc31caa6fb3ed65"},"schema_version":"1.0","source":{"id":"1310.2827","kind":"arxiv","version":1}},"canonical_sha256":"73d63f0a7d00b8a6ceb833b98ed53dbbfdf5b7c07d2282861426765b5c08b693","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73d63f0a7d00b8a6ceb833b98ed53dbbfdf5b7c07d2282861426765b5c08b693","first_computed_at":"2026-05-18T03:10:46.587669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:46.587669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gEn2aOqlPZU3AI+OQvRvZoarDsZocz9ioBBs+9fYd23haIjmjdsfBccpjZf+zafJSS6StfJ/CbivcKU0IZiyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:46.588423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e6643e076f6000eb58fe3e2bbd6806b5bf55cff0fc36b627bd5d80bde609160","sha256:e4b0018132045b3cc7069c906c28ef4cba8351394b0987a3becc1f328f4b6665"],"state_sha256":"4d272214af5be157f3532eddaf6402155aad678b2770d76351e9e8e7feeead64"}