{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DFJQTI64RTIWYOOO6VX3RTGGAK","short_pith_number":"pith:DFJQTI64","canonical_record":{"source":{"id":"1504.02385","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-09T16:54:20Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a0d1d291d90a431a8f362f0a0acc1d40d54cb2a57f5937c510abfbec4ef99653","abstract_canon_sha256":"11f06bb866bb40e2a6429e749ac62e569a25b15c431fcdcd239fbeb64e3f04cf"},"schema_version":"1.0"},"canonical_sha256":"195309a3dc8cd16c39cef56fb8ccc602bf891d864de0bf34cd92bbde9a592d80","source":{"kind":"arxiv","id":"1504.02385","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02385","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02385v5","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02385","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"DFJQTI64RTIW","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DFJQTI64RTIWYOOO","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DFJQTI64","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DFJQTI64RTIWYOOO6VX3RTGGAK","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02385","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-09T16:54:20Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a0d1d291d90a431a8f362f0a0acc1d40d54cb2a57f5937c510abfbec4ef99653","abstract_canon_sha256":"11f06bb866bb40e2a6429e749ac62e569a25b15c431fcdcd239fbeb64e3f04cf"},"schema_version":"1.0"},"canonical_sha256":"195309a3dc8cd16c39cef56fb8ccc602bf891d864de0bf34cd92bbde9a592d80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:39.810309Z","signature_b64":"2cajDNo641ys0rknsCvxFGCb25SDzEA7Pu+xeYT1jXJMRlP33DlW6JAm/v/mbvMzN9NsdmDMy3O7Pz00ptnmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"195309a3dc8cd16c39cef56fb8ccc602bf891d864de0bf34cd92bbde9a592d80","last_reissued_at":"2026-05-18T00:29:39.809673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:39.809673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02385","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xfuLudPu+i72qPwU1nb4Fr5Gx6D/V/g4A4jlNf4E/jO5PLiRq7/cxhd+RY2vUMWIvXW+LZ2ZeeiLUOkE56g/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:09:30.232452Z"},"content_sha256":"c044bce54c78299bded7bb83d83a40ae7fda5842dc6d12af2adec1cbd47b69d4","schema_version":"1.0","event_id":"sha256:c044bce54c78299bded7bb83d83a40ae7fda5842dc6d12af2adec1cbd47b69d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DFJQTI64RTIWYOOO6VX3RTGGAK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatially discrete reaction-diffusion equations with discontinuous hysteresis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Pavel Gurevich, Sergey Tikhomirov","submitted_at":"2015-04-09T16:54:20Z","abstract_excerpt":"We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic nonlinearity. We analyze a new mechanism that leads to appearance of a spatio-temporal pattern called {\\it rattling}: the solution exhibits a propagation phenomenon different from the classical traveling wave, while the hysteretic nonlinearity, loosely speaking, takes a different value at every second spatial point, independently of the grid size. Such a dynamics "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02385","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ScANLl5RfQ5xU+RQ77y+xZw7/Qr4h0QC0g6ZT7ptmpQOk/RC0+xY0VoifLIQj2AkUp0fO0nGK/ZXoSlJAyB+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:09:30.233119Z"},"content_sha256":"e823f972f0dea1b96857a8bda399a31b6c07c2c8166d16fa646f0d8d517d0f83","schema_version":"1.0","event_id":"sha256:e823f972f0dea1b96857a8bda399a31b6c07c2c8166d16fa646f0d8d517d0f83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFJQTI64RTIWYOOO6VX3RTGGAK/bundle.json","state_url":"https://pith.science/pith/DFJQTI64RTIWYOOO6VX3RTGGAK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFJQTI64RTIWYOOO6VX3RTGGAK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T20:09:30Z","links":{"resolver":"https://pith.science/pith/DFJQTI64RTIWYOOO6VX3RTGGAK","bundle":"https://pith.science/pith/DFJQTI64RTIWYOOO6VX3RTGGAK/bundle.json","state":"https://pith.science/pith/DFJQTI64RTIWYOOO6VX3RTGGAK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFJQTI64RTIWYOOO6VX3RTGGAK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DFJQTI64RTIWYOOO6VX3RTGGAK","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":"11f06bb866bb40e2a6429e749ac62e569a25b15c431fcdcd239fbeb64e3f04cf","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-09T16:54:20Z","title_canon_sha256":"a0d1d291d90a431a8f362f0a0acc1d40d54cb2a57f5937c510abfbec4ef99653"},"schema_version":"1.0","source":{"id":"1504.02385","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02385","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02385v5","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02385","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"DFJQTI64RTIW","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DFJQTI64RTIWYOOO","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DFJQTI64","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:e823f972f0dea1b96857a8bda399a31b6c07c2c8166d16fa646f0d8d517d0f83","target":"graph","created_at":"2026-05-18T00:29:39Z","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 address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic nonlinearity. We analyze a new mechanism that leads to appearance of a spatio-temporal pattern called {\\it rattling}: the solution exhibits a propagation phenomenon different from the classical traveling wave, while the hysteretic nonlinearity, loosely speaking, takes a different value at every second spatial point, independently of the grid size. Such a dynamics ","authors_text":"Pavel Gurevich, Sergey Tikhomirov","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-09T16:54:20Z","title":"Spatially discrete reaction-diffusion equations with discontinuous hysteresis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02385","kind":"arxiv","version":5},"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:c044bce54c78299bded7bb83d83a40ae7fda5842dc6d12af2adec1cbd47b69d4","target":"record","created_at":"2026-05-18T00:29:39Z","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":"11f06bb866bb40e2a6429e749ac62e569a25b15c431fcdcd239fbeb64e3f04cf","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-09T16:54:20Z","title_canon_sha256":"a0d1d291d90a431a8f362f0a0acc1d40d54cb2a57f5937c510abfbec4ef99653"},"schema_version":"1.0","source":{"id":"1504.02385","kind":"arxiv","version":5}},"canonical_sha256":"195309a3dc8cd16c39cef56fb8ccc602bf891d864de0bf34cd92bbde9a592d80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"195309a3dc8cd16c39cef56fb8ccc602bf891d864de0bf34cd92bbde9a592d80","first_computed_at":"2026-05-18T00:29:39.809673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:39.809673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2cajDNo641ys0rknsCvxFGCb25SDzEA7Pu+xeYT1jXJMRlP33DlW6JAm/v/mbvMzN9NsdmDMy3O7Pz00ptnmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:39.810309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02385","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c044bce54c78299bded7bb83d83a40ae7fda5842dc6d12af2adec1cbd47b69d4","sha256:e823f972f0dea1b96857a8bda399a31b6c07c2c8166d16fa646f0d8d517d0f83"],"state_sha256":"205a158d4fd4492a9fbb8127665a1a9a0076e4a2272168f176c2d20e081f4dff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vtbWoMhsHyR9E0qO+Tzwoi7itEzxKdByA6IIBSR98zBZwu827eKmRpUfH9mf3ilbdXeTLi0BC+Q001iQo+txAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:09:30.236743Z","bundle_sha256":"10a8e24da4354a04ce0b4ccb651eeab6ef52fdc1cb23241834469dbbd2c688fd"}}