{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GJMZZQJHMR5H57IMDGXRPRIEJQ","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":"e873294e4dad58ad1ff0dfe55821987f438ea4c2cb9de1c26f91fdb27f4d088b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2021-06-10T01:45:13Z","title_canon_sha256":"0e97369f69455831560d300cd68c58d4ab46524b2e77730e598d2ae2c454ba30"},"schema_version":"1.0","source":{"id":"2106.05452","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.05452","created_at":"2026-07-05T03:33:44Z"},{"alias_kind":"arxiv_version","alias_value":"2106.05452v2","created_at":"2026-07-05T03:33:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.05452","created_at":"2026-07-05T03:33:44Z"},{"alias_kind":"pith_short_12","alias_value":"GJMZZQJHMR5H","created_at":"2026-07-05T03:33:44Z"},{"alias_kind":"pith_short_16","alias_value":"GJMZZQJHMR5H57IM","created_at":"2026-07-05T03:33:44Z"},{"alias_kind":"pith_short_8","alias_value":"GJMZZQJH","created_at":"2026-07-05T03:33:44Z"}],"graph_snapshots":[{"event_id":"sha256:baca7f5fcb11e91d8aa19479e27a42d3e4d5c9109ac7f343159474f0c3b9cbb9","target":"graph","created_at":"2026-07-05T03:33:44Z","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/2106.05452/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a numerical scheme for the solution of nonlinear mixed-dimensional PDEs describing coupled processes in embedded tubular network system in exchange with a bulk domain. Such problems arise in various biological and technical applications such as in the modeling of root-water uptake, heat exchangers, or geothermal wells. The nonlinearity appears in form of solution-dependent parameters such as pressure-dependent permeability or temperature-dependent thermal conductivity. We derive and analyse a numerical scheme based on distributing the bulk-network coupling source term by a smoothing","authors_text":"Hanchuan Wu, Martin Schneider, Timo Koch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2021-06-10T01:45:13Z","title":"Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.05452","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":"sha256:05247c2bb75c4d9768e72a7277f1b63a860f1a630bf34960170830aa46951362","target":"record","created_at":"2026-07-05T03:33:44Z","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":"e873294e4dad58ad1ff0dfe55821987f438ea4c2cb9de1c26f91fdb27f4d088b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CE","submitted_at":"2021-06-10T01:45:13Z","title_canon_sha256":"0e97369f69455831560d300cd68c58d4ab46524b2e77730e598d2ae2c454ba30"},"schema_version":"1.0","source":{"id":"2106.05452","kind":"arxiv","version":2}},"canonical_sha256":"32599cc127647a7efd0c19af17c5044c3dc763d6a0ebffc402c30984015ddf0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32599cc127647a7efd0c19af17c5044c3dc763d6a0ebffc402c30984015ddf0c","first_computed_at":"2026-07-05T03:33:44.352293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:33:44.352293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"68T0ovnj2oq99eQ5NJKpsH+eK84jVApAkgBr3ovOuwdCqiaSsechkfgId+eKHRgXV6kKc+9WbnMVFGncoOh9CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:33:44.352769Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.05452","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05247c2bb75c4d9768e72a7277f1b63a860f1a630bf34960170830aa46951362","sha256:baca7f5fcb11e91d8aa19479e27a42d3e4d5c9109ac7f343159474f0c3b9cbb9"],"state_sha256":"c3fd1e7b08d6ac91398b553e8709591d6c91a1e0c52260e109f790a1d011075c"}