{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AJXSPMP5JZGXYSAATAYSH3ZXQT","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":"dfcec04f042496b0f487211e37cc67ddaf53732b50dbd2fea831c0dcd93fe05e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-18T20:33:15Z","title_canon_sha256":"40891c267e167a8ca10331051c9c0810bc9a9e1d7eb5e71225ba6669486181d9"},"schema_version":"1.0","source":{"id":"1509.05792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05792","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05792v1","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05792","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"pith_short_12","alias_value":"AJXSPMP5JZGX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AJXSPMP5JZGXYSAA","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AJXSPMP5","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:2d4c891cbe4ea741035f925a912aaf04f4a391239dced14cba5cdd8bbd2ab7e9","target":"graph","created_at":"2026-05-18T01:32:42Z","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":"Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems does not generalize to infinite-dimensions. In this paper a unified approach to Lyapunov's indirect method for infinite-dimensional system is described. It is shown how existing sufficient conditions fit this framework and a new sufficient condition is presented.","authors_text":"Amenda Chow, Kirsten Morris, Rasha Al Jamal","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-18T20:33:15Z","title":"Linearized stability analysis of nonlinear partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05792","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:d3c484d45d3facfe3f79f0a5b54c0c4998df02e6e4a5a6545bda3fdb1313d062","target":"record","created_at":"2026-05-18T01:32:42Z","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":"dfcec04f042496b0f487211e37cc67ddaf53732b50dbd2fea831c0dcd93fe05e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-18T20:33:15Z","title_canon_sha256":"40891c267e167a8ca10331051c9c0810bc9a9e1d7eb5e71225ba6669486181d9"},"schema_version":"1.0","source":{"id":"1509.05792","kind":"arxiv","version":1}},"canonical_sha256":"026f27b1fd4e4d7c4800983123ef3784e51c5f48b18ae90133e3f5b4399b0689","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"026f27b1fd4e4d7c4800983123ef3784e51c5f48b18ae90133e3f5b4399b0689","first_computed_at":"2026-05-18T01:32:42.311402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:42.311402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LFBLZ/ircm3+YeC1iF7H+RmrVR65DN/ajkrZ1/oMpY74E4//nu+cCSGZ7CcGy8CHotuKZR7XEYM3TfWMH4MzAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:42.311881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3c484d45d3facfe3f79f0a5b54c0c4998df02e6e4a5a6545bda3fdb1313d062","sha256:2d4c891cbe4ea741035f925a912aaf04f4a391239dced14cba5cdd8bbd2ab7e9"],"state_sha256":"af89a783bc724b705ac7afd16eae3f91981acf8d8423ce857077460dae13fd53"}