{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6FES6WDHYNK4IPFGQQ4UYYQXTZ","short_pith_number":"pith:6FES6WDH","schema_version":"1.0","canonical_sha256":"f1492f5867c355c43ca684394c62179e5e7a625fcbfd98b36ca18291366d7011","source":{"kind":"arxiv","id":"1510.03736","version":2},"attestation_state":"computed","paper":{"title":"Computing the Maslov index from singularities of a matrix Riccati equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Thomas McCauley","submitted_at":"2015-10-13T15:17:47Z","abstract_excerpt":"We study the Maslov index as a tool to analyze stability of steady state solutions to a reaction-diffusion equation in one spatial dimension. We show that the path of unstable subspaces associated to this equation is governed by a matrix Riccati equation whose solution $S$ develops singularities when changes in the Maslov index occur. Our main result proves that at these singularities the change in Maslov index equals the number of eigenvalues of $S$ that increase to $+\\infty$ minus the number of eigenvalues that decrease to $-\\infty$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.03736","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-13T15:17:47Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"e26e7d81e663214565a2650bb5c53d1bf1f4af0360c5a7750e2776fcc7c558e5","abstract_canon_sha256":"5ddb6fb83c568ee901ae5ad5f89b56dbac688f8e1bb1ea932188d8c1cbb43813"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:45.268311Z","signature_b64":"fccnK1ut1BTE2FmZ8K+bipES+1V80T8kjtA5iH33nm/RHe+06MiFcqDnmUIdMtKj12v20haOvGxTc08zVvJTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1492f5867c355c43ca684394c62179e5e7a625fcbfd98b36ca18291366d7011","last_reissued_at":"2026-05-18T01:28:45.267948Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:45.267948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing the Maslov index from singularities of a matrix Riccati equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Thomas McCauley","submitted_at":"2015-10-13T15:17:47Z","abstract_excerpt":"We study the Maslov index as a tool to analyze stability of steady state solutions to a reaction-diffusion equation in one spatial dimension. We show that the path of unstable subspaces associated to this equation is governed by a matrix Riccati equation whose solution $S$ develops singularities when changes in the Maslov index occur. Our main result proves that at these singularities the change in Maslov index equals the number of eigenvalues of $S$ that increase to $+\\infty$ minus the number of eigenvalues that decrease to $-\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03736","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.03736","created_at":"2026-05-18T01:28:45.267997+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.03736v2","created_at":"2026-05-18T01:28:45.267997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03736","created_at":"2026-05-18T01:28:45.267997+00:00"},{"alias_kind":"pith_short_12","alias_value":"6FES6WDHYNK4","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6FES6WDHYNK4IPFG","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6FES6WDH","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6FES6WDHYNK4IPFGQQ4UYYQXTZ","json":"https://pith.science/pith/6FES6WDHYNK4IPFGQQ4UYYQXTZ.json","graph_json":"https://pith.science/api/pith-number/6FES6WDHYNK4IPFGQQ4UYYQXTZ/graph.json","events_json":"https://pith.science/api/pith-number/6FES6WDHYNK4IPFGQQ4UYYQXTZ/events.json","paper":"https://pith.science/paper/6FES6WDH"},"agent_actions":{"view_html":"https://pith.science/pith/6FES6WDHYNK4IPFGQQ4UYYQXTZ","download_json":"https://pith.science/pith/6FES6WDHYNK4IPFGQQ4UYYQXTZ.json","view_paper":"https://pith.science/paper/6FES6WDH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.03736&json=true","fetch_graph":"https://pith.science/api/pith-number/6FES6WDHYNK4IPFGQQ4UYYQXTZ/graph.json","fetch_events":"https://pith.science/api/pith-number/6FES6WDHYNK4IPFGQQ4UYYQXTZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6FES6WDHYNK4IPFGQQ4UYYQXTZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6FES6WDHYNK4IPFGQQ4UYYQXTZ/action/storage_attestation","attest_author":"https://pith.science/pith/6FES6WDHYNK4IPFGQQ4UYYQXTZ/action/author_attestation","sign_citation":"https://pith.science/pith/6FES6WDHYNK4IPFGQQ4UYYQXTZ/action/citation_signature","submit_replication":"https://pith.science/pith/6FES6WDHYNK4IPFGQQ4UYYQXTZ/action/replication_record"}},"created_at":"2026-05-18T01:28:45.267997+00:00","updated_at":"2026-05-18T01:28:45.267997+00:00"}