{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RZOVSP5R57BXZGIOY32NUVDIVO","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":"9fc1258cd12f10d0cf9ef4e1b33e958de6f132c2e0017ed3c7bed90189395e0a","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-19T15:57:09Z","title_canon_sha256":"32d1c0f675f50092e0c865a014ac6652252ecd3bc4555f1fa28143d35ec052c4"},"schema_version":"1.0","source":{"id":"2606.21560","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.21560","created_at":"2026-06-23T01:13:14Z"},{"alias_kind":"arxiv_version","alias_value":"2606.21560v1","created_at":"2026-06-23T01:13:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21560","created_at":"2026-06-23T01:13:14Z"},{"alias_kind":"pith_short_12","alias_value":"RZOVSP5R57BX","created_at":"2026-06-23T01:13:14Z"},{"alias_kind":"pith_short_16","alias_value":"RZOVSP5R57BXZGIO","created_at":"2026-06-23T01:13:14Z"},{"alias_kind":"pith_short_8","alias_value":"RZOVSP5R","created_at":"2026-06-23T01:13:14Z"}],"graph_snapshots":[{"event_id":"sha256:fc357f3e947759486dc5829c5214ded98fe99dc74ceab04cd54f6dfadbc319a7","target":"graph","created_at":"2026-06-23T01:13:14Z","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/2606.21560/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we prove an Aubin-Nitsche Lemma for a positivity-preserving discretisation of an elliptic\n  problem. Due to the nonlinearity of the discretisation, the result requires as a first step\n  the proposal of a linearised adjoint problem that can be linked to the method of\n  choice by appropriately selecting weights. This linearised adjoint problem, together\n  with a regularity result, allow the proof of an optimal-order error estimate in the $L^2$-norm of\n  the error.","authors_text":"Gabriel R. Barrenechea, Theophile Chaumont-Frelet","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-19T15:57:09Z","title":"An Aubin-Nitsche Lemma for a positivity-preserving finite element method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21560","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":"sha256:187e60fa3b9d232168609a794b8035ecade4ee22fc90a53b48ecbd145d13e040","target":"record","created_at":"2026-06-23T01:13:14Z","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":"9fc1258cd12f10d0cf9ef4e1b33e958de6f132c2e0017ed3c7bed90189395e0a","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-19T15:57:09Z","title_canon_sha256":"32d1c0f675f50092e0c865a014ac6652252ecd3bc4555f1fa28143d35ec052c4"},"schema_version":"1.0","source":{"id":"2606.21560","kind":"arxiv","version":1}},"canonical_sha256":"8e5d593fb1efc37c990ec6f4da5468ab8b0d37c48f974bc4916d74d117f54360","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e5d593fb1efc37c990ec6f4da5468ab8b0d37c48f974bc4916d74d117f54360","first_computed_at":"2026-06-23T01:13:14.643431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:13:14.643431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ps77leUpUdV8CIDhGRM7L8FBkPbsgoyQujqNjUqumgsvBWnAXtjxLPdBWDh8nsojU5J9GgAVrUG76BeFi4QHCQ==","signature_status":"signed_v1","signed_at":"2026-06-23T01:13:14.643879Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.21560","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:187e60fa3b9d232168609a794b8035ecade4ee22fc90a53b48ecbd145d13e040","sha256:fc357f3e947759486dc5829c5214ded98fe99dc74ceab04cd54f6dfadbc319a7"],"state_sha256":"1b534092ad4815869a52531f9a8a1b9fb6e709c990fb32dac16ed30118aea86a"}