{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EDE6LRSUGX5DOJB2CKVICEVA44","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":"ed5810160d31648e59b40c404c416eecba5e8fd05e7a08a5f8c169a8d20f515a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-02T15:27:44Z","title_canon_sha256":"e3599d3123b7bec707dc8c8b689b52e7ff63493f6be0b3eaa2762308d5413a42"},"schema_version":"1.0","source":{"id":"1411.0269","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0269","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0269v1","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0269","created_at":"2026-05-18T02:38:52Z"},{"alias_kind":"pith_short_12","alias_value":"EDE6LRSUGX5D","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EDE6LRSUGX5DOJB2","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EDE6LRSU","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:e29fa8571a8c03575bda1b49b5e130414c65644cd9ad030fdab1bd3b85ceb9bf","target":"graph","created_at":"2026-05-18T02:38:52Z","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 consider a reaction-diffusion system with discontinuous reaction terms modeled by non-ideal relays. The system is motivated by an epigenetic population model of evolution of two-phenotype bacteria which switch phenotype in response to variations of environment. We prove the formation of patterns in the phenotype space. The mechanism responsible for pattern formation is based on memory (hysteresis) of the non-ideal relays.","authors_text":"Dmitrii Rachinskii, Pavel Gurevich","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-02T15:27:44Z","title":"Pattern formation in parabolic equations containing hysteresis with diffusive thresholds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0269","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":"sha256:50e161d721c773aa5f1fb054ea9a6f75ed3e0ac75d97e9ad958a509c473eced6","target":"record","created_at":"2026-05-18T02:38:52Z","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":"ed5810160d31648e59b40c404c416eecba5e8fd05e7a08a5f8c169a8d20f515a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-02T15:27:44Z","title_canon_sha256":"e3599d3123b7bec707dc8c8b689b52e7ff63493f6be0b3eaa2762308d5413a42"},"schema_version":"1.0","source":{"id":"1411.0269","kind":"arxiv","version":1}},"canonical_sha256":"20c9e5c65435fa37243a12aa8112a0e72868adbd7b77067ba631137bb0a6400b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20c9e5c65435fa37243a12aa8112a0e72868adbd7b77067ba631137bb0a6400b","first_computed_at":"2026-05-18T02:38:52.102251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:52.102251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ECPqzKNz1UnTtID1s2eaACLVJwYxUlO9bRn6cayuO5JFa9LcdpckQErgh2yxT+xpZJ9cRWllKyTbNAOVzA+4Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:52.102846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0269","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50e161d721c773aa5f1fb054ea9a6f75ed3e0ac75d97e9ad958a509c473eced6","sha256:e29fa8571a8c03575bda1b49b5e130414c65644cd9ad030fdab1bd3b85ceb9bf"],"state_sha256":"180433cb6523483d0278eaacf985439443a085e1d54dd98feba513c240785a59"}