{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V5EADEC6NLTKERO77Y2XRCS7KG","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":"7f29ecfff72b7775f1a18f15b57fdc0730d9d9ed1af18d20484f35941e5e20dc","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-21T17:18:52Z","title_canon_sha256":"40b601f66f6dcb243ce43ba85868dae51a394e6e0d6cfdc8ac07fc10d4a8ffef"},"schema_version":"1.0","source":{"id":"1802.07676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07676","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07676v1","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07676","created_at":"2026-05-18T00:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"V5EADEC6NLTK","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"V5EADEC6NLTKERO7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"V5EADEC6","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:3e3b47026fc2da8c5bfc07cbdb50e8cab3c941b3e36283ec6916bf18649f9cbd","target":"graph","created_at":"2026-05-18T00:22:49Z","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":"In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects are important as organizing centers of more complicated flows. Our analysis uses spatial dynamics combined with an instantaneous phase-tracking technique to obtain detailed pointwise estimates describing perturbations to lowest order as a phase-shift radiating outward at a linear rate plus a pair of localized approximately Gaussian excitations along the pha","authors_text":"Bj\\\"orn Sandstede, Kevin Zumbrun, Margaret Beck, Toan T. Nguyen","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-21T17:18:52Z","title":"Nonlinear stability of source defects in oscillatory media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07676","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:e0c264627b5c4c8e6d6f2544a043073991c81144cd88d033440b15b3b7f10373","target":"record","created_at":"2026-05-18T00:22:49Z","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":"7f29ecfff72b7775f1a18f15b57fdc0730d9d9ed1af18d20484f35941e5e20dc","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-21T17:18:52Z","title_canon_sha256":"40b601f66f6dcb243ce43ba85868dae51a394e6e0d6cfdc8ac07fc10d4a8ffef"},"schema_version":"1.0","source":{"id":"1802.07676","kind":"arxiv","version":1}},"canonical_sha256":"af4801905e6ae6a245dffe35788a5f5182afc1a77ca412198ef6ab9e3763c126","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af4801905e6ae6a245dffe35788a5f5182afc1a77ca412198ef6ab9e3763c126","first_computed_at":"2026-05-18T00:22:49.645489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:49.645489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87nMCJ7v3NXWKYUDHKAH9q+lPT6rUGZ5ibOQTFvR8EABf92+PBYfe80JPZ01b49YTWl7v5u/zR9V3RNZA107AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:49.645877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0c264627b5c4c8e6d6f2544a043073991c81144cd88d033440b15b3b7f10373","sha256:3e3b47026fc2da8c5bfc07cbdb50e8cab3c941b3e36283ec6916bf18649f9cbd"],"state_sha256":"f0c792f7e5c25691703efd617c3ce34904f987dd7f33a6388c289042393a9113"}