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We prove that if $\\Sigma$ is $(r,R)$-pinched with $\\frac{R}{r}<\\sqrt{\\frac{5}{3}}$, then $\\Sigma$ carries at least two geometrically distinct P-symmetric closed characteristics which possess at least $2n-4\\kappa$ Floquet multipliers on the unit circle of the complex plane."},"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":"1504.08060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-30T02:41:41Z","cross_cats_sorted":[],"title_canon_sha256":"0aac36a9ec137490d25a0631b32011eef95b01469b0b34ba30dcda27fb0f20ef","abstract_canon_sha256":"dda7a8623d30fe92016c02647454615204e3db4ef3f673b6ff4b9c09c5994293"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:23.434989Z","signature_b64":"KvmnK6kGF07B9hzTRSAiTBST/u776vmn1PwDM+K6D06N+UYMEmoDqZNlvOidBBkpklHq3m1K8P7qELg4ewmiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08923233cb494d88cc5e0bac4017a37f2d31e44ac5ae3f2695a63ccd4efe4e69","last_reissued_at":"2026-05-18T02:17:23.434361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:23.434361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable P-symmetric closed characteristics on partially symmetric compact convex hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Duanzhi Zhang, Hui Liu","submitted_at":"2015-04-30T02:41:41Z","abstract_excerpt":"In this paper, let $n\\geq2$ be an integer, $P=diag(-I_{n-\\kappa},I_\\kappa,-I_{n-\\kappa},I_\\kappa)$ for some integer $\\kappa\\in[0, n-1)$, and $\\Sigma \\subset {\\bf R}^{2n}$ be a partially symmetric compact convex hypersurface, i.e., $x\\in \\Sigma$ implies $Px\\in\\Sigma$. We prove that if $\\Sigma$ is $(r,R)$-pinched with $\\frac{R}{r}<\\sqrt{\\frac{5}{3}}$, then $\\Sigma$ carries at least two geometrically distinct P-symmetric closed characteristics which possess at least $2n-4\\kappa$ Floquet multipliers on the unit circle of the complex plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08060","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":"1504.08060","created_at":"2026-05-18T02:17:23.434467+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.08060v1","created_at":"2026-05-18T02:17:23.434467+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08060","created_at":"2026-05-18T02:17:23.434467+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCJDEM6LJFGY","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCJDEM6LJFGYRTC6","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCJDEM6L","created_at":"2026-05-18T12:29:14.074870+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/BCJDEM6LJFGYRTC6BOWEAF5DP4","json":"https://pith.science/pith/BCJDEM6LJFGYRTC6BOWEAF5DP4.json","graph_json":"https://pith.science/api/pith-number/BCJDEM6LJFGYRTC6BOWEAF5DP4/graph.json","events_json":"https://pith.science/api/pith-number/BCJDEM6LJFGYRTC6BOWEAF5DP4/events.json","paper":"https://pith.science/paper/BCJDEM6L"},"agent_actions":{"view_html":"https://pith.science/pith/BCJDEM6LJFGYRTC6BOWEAF5DP4","download_json":"https://pith.science/pith/BCJDEM6LJFGYRTC6BOWEAF5DP4.json","view_paper":"https://pith.science/paper/BCJDEM6L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.08060&json=true","fetch_graph":"https://pith.science/api/pith-number/BCJDEM6LJFGYRTC6BOWEAF5DP4/graph.json","fetch_events":"https://pith.science/api/pith-number/BCJDEM6LJFGYRTC6BOWEAF5DP4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCJDEM6LJFGYRTC6BOWEAF5DP4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCJDEM6LJFGYRTC6BOWEAF5DP4/action/storage_attestation","attest_author":"https://pith.science/pith/BCJDEM6LJFGYRTC6BOWEAF5DP4/action/author_attestation","sign_citation":"https://pith.science/pith/BCJDEM6LJFGYRTC6BOWEAF5DP4/action/citation_signature","submit_replication":"https://pith.science/pith/BCJDEM6LJFGYRTC6BOWEAF5DP4/action/replication_record"}},"created_at":"2026-05-18T02:17:23.434467+00:00","updated_at":"2026-05-18T02:17:23.434467+00:00"}