{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:54FWBH2MZNP4WFQOM7TEN3KJKM","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":"a0a5b1b7498c65a587decca15690fd60476fca9c85dd7c3aba2d5613e527f7f6","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-04T08:52:35Z","title_canon_sha256":"428d6e817592cc0c405a23055666e75945cb4f982d035cec8c5be80d642d02e8"},"schema_version":"1.0","source":{"id":"2606.05879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.05879","created_at":"2026-06-05T01:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.05879v1","created_at":"2026-06-05T01:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05879","created_at":"2026-06-05T01:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"54FWBH2MZNP4","created_at":"2026-06-05T01:15:06Z"},{"alias_kind":"pith_short_16","alias_value":"54FWBH2MZNP4WFQO","created_at":"2026-06-05T01:15:06Z"},{"alias_kind":"pith_short_8","alias_value":"54FWBH2M","created_at":"2026-06-05T01:15:06Z"}],"graph_snapshots":[{"event_id":"sha256:f55ce978cd55c3023f959ec7842dec23e4963aa161612515b9e581a11236f643","target":"graph","created_at":"2026-06-05T01:15:06Z","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/2606.05879/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we consider an implicit semi-discrete approximation of a degenerate reaction-cross-diffusion system. Due to the symmetry in the parabolic part, this system is known to preserve segregation of densities -- initially non-overlapping densities belonging to different species remain segregated for all times, which leads to internal layers between different species. We show that time-discrete approximations exist and converge to a weak solution, as the timestep goes to zero.","authors_text":"Hideki Murakawa, Julia Hauser, Markus Schmidtchen","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-04T08:52:35Z","title":"Convergence of a discrete-in-time Approximation to a Degenerate Parabolic-Hyperbolic System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05879","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:a5def33f8b40e85724881371021fa8b81388ad8c91b2f2d429a4e99ea2e458bb","target":"record","created_at":"2026-06-05T01:15:06Z","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":"a0a5b1b7498c65a587decca15690fd60476fca9c85dd7c3aba2d5613e527f7f6","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-04T08:52:35Z","title_canon_sha256":"428d6e817592cc0c405a23055666e75945cb4f982d035cec8c5be80d642d02e8"},"schema_version":"1.0","source":{"id":"2606.05879","kind":"arxiv","version":1}},"canonical_sha256":"ef0b609f4ccb5fcb160e67e646ed495320d433bbfd68cd690912b615b04561ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef0b609f4ccb5fcb160e67e646ed495320d433bbfd68cd690912b615b04561ba","first_computed_at":"2026-06-05T01:15:06.624516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:06.624516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1HB+80sj35gcXU87MkGzTJ7qAHDLd4FHmltUS9Pwc7L4CHYmMLEdbE9VwNqBUioFkZgdzCAHPTZhWhh5PhyfBw==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:06.624908Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.05879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5def33f8b40e85724881371021fa8b81388ad8c91b2f2d429a4e99ea2e458bb","sha256:f55ce978cd55c3023f959ec7842dec23e4963aa161612515b9e581a11236f643"],"state_sha256":"2758087c57e0bfdd947b869f6a005dc0df7ee811e30afdd5adbf7e6911548cc3"}