{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X7VGRGR2WMYMFS53QHXIYCS66V","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":"b2195c30b00e2f512bf022bd7256cb1c1c800d6d383a511f415f65ce0ae8a93d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-08T17:35:17Z","title_canon_sha256":"fbbfc2886d87d0ebff07411f71832dfe118ffb14d74464fded7724e0c87369a2"},"schema_version":"1.0","source":{"id":"1606.02648","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02648","created_at":"2026-05-18T00:53:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02648v2","created_at":"2026-05-18T00:53:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02648","created_at":"2026-05-18T00:53:59Z"},{"alias_kind":"pith_short_12","alias_value":"X7VGRGR2WMYM","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X7VGRGR2WMYMFS53","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X7VGRGR2","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:26eeb235b7f8fd93346a68efaacc1bf64bfe5c769a97e4d1f1eea76e7ae02236","target":"graph","created_at":"2026-05-18T00:53:59Z","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 study the approximation of a multiscale reaction-diffusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done via micro-macro flux conditions. Our target system has a typical structure for reaction-diffusion-flow problems in media with distributed microstructures (also called, double porosity materials). Besides ensuring basic estimates for the convergence of two-scale semi-discrete Galerkin approximations, we provide a set of {\\em a priori} feedback estimates and a local feedback error estimator that help in designing a distributed-high-e","authors_text":"Adrian Muntean, Martin Lind","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-08T17:35:17Z","title":"A priori feedback estimates for multiscale reaction-diffusion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02648","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:eb8fd4cf44c30f7c2487b0b8b7314e4c8ce17efd05e714dcd9667aafe7445475","target":"record","created_at":"2026-05-18T00:53:59Z","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":"b2195c30b00e2f512bf022bd7256cb1c1c800d6d383a511f415f65ce0ae8a93d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-08T17:35:17Z","title_canon_sha256":"fbbfc2886d87d0ebff07411f71832dfe118ffb14d74464fded7724e0c87369a2"},"schema_version":"1.0","source":{"id":"1606.02648","kind":"arxiv","version":2}},"canonical_sha256":"bfea689a3ab330c2cbbb81ee8c0a5ef57b1966a7ae11dae7f2afe58061f98c2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfea689a3ab330c2cbbb81ee8c0a5ef57b1966a7ae11dae7f2afe58061f98c2f","first_computed_at":"2026-05-18T00:53:59.994077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:59.994077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SSAncIPZD/4Pka2sKBKS5Vg8BRa6fPcS9B+qzTA2aHVnVFP0RKFor+M4VGPRNd7FmMjJeBsJcY2nfFaMyekCBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:59.994485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02648","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb8fd4cf44c30f7c2487b0b8b7314e4c8ce17efd05e714dcd9667aafe7445475","sha256:26eeb235b7f8fd93346a68efaacc1bf64bfe5c769a97e4d1f1eea76e7ae02236"],"state_sha256":"1c609b3504e7c2cc58e6fabbcdc134af06373ed3965bd32f05721556e38ce92e"}