{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DTR5S4HX3EAM6EFE25PBESTIAI","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":"e963550a37731bdf2141737fa4e3bafe389760dddb2c7faf60670649fa0ece14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-01T21:26:37Z","title_canon_sha256":"5e4a12d061712e8fc78b60ac44cc63ac2a603aa0f57c7950df51537a615f22fe"},"schema_version":"1.0","source":{"id":"1406.0208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0208","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0208v1","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0208","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"DTR5S4HX3EAM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DTR5S4HX3EAM6EFE","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DTR5S4HX","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:cf05677b694009b80e2b56013048406ad28fb8d26d76ef87f28763a2f9925bb2","target":"graph","created_at":"2026-05-18T02:50:41Z","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":"The purpose of the present paper is to study the limit cycles of one-parameter perturbed plane Hamiltonian vector field $X_\\varepsilon$ $$ X_\\varepsilon : \\left\\{ \\begin{array}{llr} \\dot{x}=\\;\\; H_y+\\varepsilon f(x,y)\\\\ \\dot{y}=-H_x+\\varepsilon g(x,y), \\end{array} \\;\\;\\;\\;\\; H~=\\frac{1}{2} y^2~+U(x)\n  \\right. $$ which bifurcate from the period annuli of $X_0$ for sufficiently small $\\varepsilon$. Here $U$ is a univariate polynomial of degree four without symmetry, and $f, g$ are arbitrary cubic polynomials in two variables.\n  We take a period annulus and parameterize the related displacement m","authors_text":"Iliya D. Iliev, Lubomir Gavrilov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-01T21:26:37Z","title":"Cubic perturbations of elliptic Hamiltonian vector fields of degree three"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0208","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":"sha256:7e270374c4c2ad967f89c2a1d03cddd481b7ec351c65b882886a8b630714b8e4","target":"record","created_at":"2026-05-18T02:50:41Z","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":"e963550a37731bdf2141737fa4e3bafe389760dddb2c7faf60670649fa0ece14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-01T21:26:37Z","title_canon_sha256":"5e4a12d061712e8fc78b60ac44cc63ac2a603aa0f57c7950df51537a615f22fe"},"schema_version":"1.0","source":{"id":"1406.0208","kind":"arxiv","version":1}},"canonical_sha256":"1ce3d970f7d900cf10a4d75e124a68022f7d5f802044a04610f7d26f745e00ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ce3d970f7d900cf10a4d75e124a68022f7d5f802044a04610f7d26f745e00ed","first_computed_at":"2026-05-18T02:50:41.528237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:41.528237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h0GkG52wC6jSo64DObfru3GcOSLAt9Qn3LP62HkXOWLAGwAoac3khw5bWXnrgE1isQQjNTIvJNEWNi1Ue+abCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:41.528772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e270374c4c2ad967f89c2a1d03cddd481b7ec351c65b882886a8b630714b8e4","sha256:cf05677b694009b80e2b56013048406ad28fb8d26d76ef87f28763a2f9925bb2"],"state_sha256":"818a617efb8f60a93f13613516a6cd23ef0a1d20a8e55c9bd2bfab14efc89970"}