{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:56MGQFKBU5DQ73ZVFYE2XZXOVT","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":"5c77cb8689c39e05498d7401f1570a23a90282996bb653f822a75c2b356b832d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-02-18T01:13:52Z","title_canon_sha256":"b4968de0d8a1a76818262978851ed6acb5fa7c41afb0428afbf576e0109a87d3"},"schema_version":"1.0","source":{"id":"2302.09203","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.09203","created_at":"2026-07-05T05:56:41Z"},{"alias_kind":"arxiv_version","alias_value":"2302.09203v2","created_at":"2026-07-05T05:56:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.09203","created_at":"2026-07-05T05:56:41Z"},{"alias_kind":"pith_short_12","alias_value":"56MGQFKBU5DQ","created_at":"2026-07-05T05:56:41Z"},{"alias_kind":"pith_short_16","alias_value":"56MGQFKBU5DQ73ZV","created_at":"2026-07-05T05:56:41Z"},{"alias_kind":"pith_short_8","alias_value":"56MGQFKB","created_at":"2026-07-05T05:56:41Z"}],"graph_snapshots":[{"event_id":"sha256:f5ed32b962ff8a857558f6d68952ca22bf5bf12fabdbae2f58b21041f0d764db","target":"graph","created_at":"2026-07-05T05:56:41Z","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/2302.09203/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the linear stability analysis of a pathway-based diffusion model (PBDM), which characterizes the dynamics of the engineered Escherichia coli populations [X. Xue and C. Xue and M. Tang, P LoS Computational Biology, 14 (2018), pp. e1006178]. This stability analysis considers small perturbations of the density and chemical concentration around two non-trivial steady states, and the linearized equations are transformed into a generalized eigenvalue problem. By formal analysis, when the internal variable responds to the outside signal fast enough, the PBDM converges to an anisotropic","authors_text":"Jiangyan Liang, Min Tang, Ning Jiang, Yaming Zhang, Yi-Long Luo","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-02-18T01:13:52Z","title":"Pattern formation of a pathway-based diffusion model: linear stability analysis and an asymptotic preserving method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.09203","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":"sha256:7edd1352d237ed945a9185839c083676c9c46ef1f80ec3e9e6bb1409f24c9217","target":"record","created_at":"2026-07-05T05:56:41Z","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":"5c77cb8689c39e05498d7401f1570a23a90282996bb653f822a75c2b356b832d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-02-18T01:13:52Z","title_canon_sha256":"b4968de0d8a1a76818262978851ed6acb5fa7c41afb0428afbf576e0109a87d3"},"schema_version":"1.0","source":{"id":"2302.09203","kind":"arxiv","version":2}},"canonical_sha256":"ef98681541a7470fef352e09abe6eeacdd062dfcaba9807155a7ac58097a9ab3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef98681541a7470fef352e09abe6eeacdd062dfcaba9807155a7ac58097a9ab3","first_computed_at":"2026-07-05T05:56:41.500812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:56:41.500812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qqIltr4fGOHKmuc7Bls7jKSOmI1xSWPG8ytKdMb8klDIwo/jIEhcG5QSRWyLyCCdiqLGAgSZQRvCkDo4aLcNDw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:56:41.501165Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.09203","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7edd1352d237ed945a9185839c083676c9c46ef1f80ec3e9e6bb1409f24c9217","sha256:f5ed32b962ff8a857558f6d68952ca22bf5bf12fabdbae2f58b21041f0d764db"],"state_sha256":"85a9c34aae452693d456bdbe4c52d4696f93f4b22b3e8bf0703fa3054804a51d"}