{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ISKZ4AVKSDF6HTUF5ST464KHZD","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":"f0377f7dc54227825a86fd3309f32cad4de7bebe0d796592e40144f2a449e9bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-31T10:06:28Z","title_canon_sha256":"03c1ec0bc58a6f647ca7876e9f1d80d663e971d67c55a10e969c6f7881eb21e8"},"schema_version":"1.0","source":{"id":"1807.11736","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11736","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11736v2","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11736","created_at":"2026-05-17T23:44:02Z"},{"alias_kind":"pith_short_12","alias_value":"ISKZ4AVKSDF6","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"ISKZ4AVKSDF6HTUF","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"ISKZ4AVK","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:323e3497c8b66c0fcb08dabebfd150b40c828087e7bfdbee7f1bcc31dcf79c76","target":"graph","created_at":"2026-05-17T23:44:02Z","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 establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum limit. For the verification of the spectral properties, we need to study a functional differential equation of mixed type (MFDE) with unbounded shifts. We avoid the use of exponential dichotomies and phase spaces, by building on a technique developed by Bates, Chen and Chmaj for the discrete Nagumo equation. This allows us to transfer several crucial Fredholm properties from the PDE setting to our discrete setting.","authors_text":"H.J. Hupkes, W.M. Schouten","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-31T10:06:28Z","title":"Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11736","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":"sha256:67b0f5d5469a0e434e955c9c7e3f8dbc66a62f0d93f812c214c0ab1485d6f5f2","target":"record","created_at":"2026-05-17T23:44:02Z","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":"f0377f7dc54227825a86fd3309f32cad4de7bebe0d796592e40144f2a449e9bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-31T10:06:28Z","title_canon_sha256":"03c1ec0bc58a6f647ca7876e9f1d80d663e971d67c55a10e969c6f7881eb21e8"},"schema_version":"1.0","source":{"id":"1807.11736","kind":"arxiv","version":2}},"canonical_sha256":"44959e02aa90cbe3ce85eca7cf7147c8f65cf551827ee6b21159b352a315eccb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44959e02aa90cbe3ce85eca7cf7147c8f65cf551827ee6b21159b352a315eccb","first_computed_at":"2026-05-17T23:44:02.885179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:02.885179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9z5op9jvupJTTjjMOQTQSxHZX+WbzHTQscBbc5/icGyC4mqZ0P9QICBmTv2ItRE0jlAOOJMD4UKTnl++GDEFBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:02.885737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11736","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67b0f5d5469a0e434e955c9c7e3f8dbc66a62f0d93f812c214c0ab1485d6f5f2","sha256:323e3497c8b66c0fcb08dabebfd150b40c828087e7bfdbee7f1bcc31dcf79c76"],"state_sha256":"3cd20501da25a21d07a626d549ecf0abdd938c449677b96c94986858b37b7b5b"}