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We obtain second order asymptotics for the eigenvalues bifurcated from non-real Krein indefinite eigenvalues with multiplicity two."},"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":"1903.12403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-29T09:01:29Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"b18346e625e477e45dae9dd660ac0aaa1d0446dd291b1d422f98b41e170c20ed","abstract_canon_sha256":"d96aae7c28e2b1ad5044cc9d2b7cd5efc47b5cb760eb86b60705ee0ae1e876b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:54.141749Z","signature_b64":"8+srnmE1+hPdWVl7bvt9sb9JBwqtHQkz4kPod8WzncwhF8oJT8Nq3VIpyIprFlZ2Gu/YFP8tcOa632PEMr8kCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb1ccaf4cb9796539937af50c912ece7c18b777e1593ad21797aed7608763237","last_reissued_at":"2026-05-17T23:49:54.141244Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:54.141244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second order asymptotics for Krein indefinite multipliers with multiplicity two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Jingzhi Yan, Yinshan Chang","submitted_at":"2019-03-29T09:01:29Z","abstract_excerpt":"We consider linear Hamiltonian equations in $\\mathbb{R}^{4}$ of the following type \\begin{equation}\n  \\frac{\\mathrm{d}\\gamma}{\\mathrm{d}t}(t)=J_{4}A(t)\\gamma(t), \\gamma(0)\\in\\operatorname{Sp}(4,\\mathbb{R}), \\end{equation} where $J=J_{4}\\overset{\\text{def}}{=}\\begin{bmatrix}0 & \\operatorname{Id}_2\\\\-\\operatorname{Id}_2 & 0\\end{bmatrix}$ and $A:t\\mapsto A(t)$ is a $C^1$-continuous curve in the space of $4\\times 4$ real matrices which are symmetric. We obtain second order asymptotics for the eigenvalues bifurcated from non-real Krein indefinite eigenvalues with multiplicity two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12403","kind":"arxiv","version":1},"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":"1903.12403","created_at":"2026-05-17T23:49:54.141351+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.12403v1","created_at":"2026-05-17T23:49:54.141351+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12403","created_at":"2026-05-17T23:49:54.141351+00:00"},{"alias_kind":"pith_short_12","alias_value":"7MOMV5GLS6LF","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7MOMV5GLS6LFHGJX","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7MOMV5GL","created_at":"2026-05-18T12:33:12.712433+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/7MOMV5GLS6LFHGJXV5IMSEXM47","json":"https://pith.science/pith/7MOMV5GLS6LFHGJXV5IMSEXM47.json","graph_json":"https://pith.science/api/pith-number/7MOMV5GLS6LFHGJXV5IMSEXM47/graph.json","events_json":"https://pith.science/api/pith-number/7MOMV5GLS6LFHGJXV5IMSEXM47/events.json","paper":"https://pith.science/paper/7MOMV5GL"},"agent_actions":{"view_html":"https://pith.science/pith/7MOMV5GLS6LFHGJXV5IMSEXM47","download_json":"https://pith.science/pith/7MOMV5GLS6LFHGJXV5IMSEXM47.json","view_paper":"https://pith.science/paper/7MOMV5GL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.12403&json=true","fetch_graph":"https://pith.science/api/pith-number/7MOMV5GLS6LFHGJXV5IMSEXM47/graph.json","fetch_events":"https://pith.science/api/pith-number/7MOMV5GLS6LFHGJXV5IMSEXM47/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7MOMV5GLS6LFHGJXV5IMSEXM47/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7MOMV5GLS6LFHGJXV5IMSEXM47/action/storage_attestation","attest_author":"https://pith.science/pith/7MOMV5GLS6LFHGJXV5IMSEXM47/action/author_attestation","sign_citation":"https://pith.science/pith/7MOMV5GLS6LFHGJXV5IMSEXM47/action/citation_signature","submit_replication":"https://pith.science/pith/7MOMV5GLS6LFHGJXV5IMSEXM47/action/replication_record"}},"created_at":"2026-05-17T23:49:54.141351+00:00","updated_at":"2026-05-17T23:49:54.141351+00:00"}