{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QQIIAMY2LWX7SBOODWPMVFHELQ","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":"9883ea191281620c0f7c6b8f4684f6b2886c5a73a37c54c7bcb5c740b88ea0b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-15T18:44:20Z","title_canon_sha256":"8e61d7b05b75a27f909f479876b2623dc304c0e4f4b99bbe640cab2f8a667d90"},"schema_version":"1.0","source":{"id":"1705.05408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05408","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05408v1","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05408","created_at":"2026-05-18T00:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"QQIIAMY2LWX7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QQIIAMY2LWX7SBOO","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QQIIAMY2","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:52e0dfb98224760c385d0d2d764ceaf141a4f9705cbe12ca73403924ec470537","target":"graph","created_at":"2026-05-18T00:44:22Z","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":"We consider the family of dehomogenized Loud's centers $X_{\\mu}=y(x-1)\\partial_x+(x+Dx^2+Fy^2)\\partial_y,$ where $\\mu=(D,F)\\in\\mathbb{R}^2,$ and we study the number of critical periodic orbits that emerge or dissapear from the polycycle at the boundary of the period annulus. This number is defined exactly the same way as the well-known notion of cyclicity of a limit periodic set and we call it criticality. The previous results on the issue for the family $\\{X_{\\mu},\\mu\\in\\mathbb{R}^2\\}$ distinguish between parameters with criticality equal to zero (regular parameters) and those with criticalit","authors_text":"David Rojas, Jordi Villadelprat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-15T18:44:20Z","title":"A criticality result for polycycles in a family of quadratic reversible centers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05408","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:e7931fa6656ce12946929259d191333532918817fe68e3a60091fc4ef330a1df","target":"record","created_at":"2026-05-18T00:44:22Z","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":"9883ea191281620c0f7c6b8f4684f6b2886c5a73a37c54c7bcb5c740b88ea0b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-15T18:44:20Z","title_canon_sha256":"8e61d7b05b75a27f909f479876b2623dc304c0e4f4b99bbe640cab2f8a667d90"},"schema_version":"1.0","source":{"id":"1705.05408","kind":"arxiv","version":1}},"canonical_sha256":"841080331a5daff905ce1d9eca94e45c17d758efd3f3779a2cad8a2a6a351cf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"841080331a5daff905ce1d9eca94e45c17d758efd3f3779a2cad8a2a6a351cf6","first_computed_at":"2026-05-18T00:44:22.794094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:22.794094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KWY5Z/VKcqnXdOLq7ARGcPkE5Qvr3h5DlWYtQv+XhybRNrGuZ+4wGg0S/CRsUsMDCrMWYx5ZzSqAH1DqoY0CAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:22.794502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7931fa6656ce12946929259d191333532918817fe68e3a60091fc4ef330a1df","sha256:52e0dfb98224760c385d0d2d764ceaf141a4f9705cbe12ca73403924ec470537"],"state_sha256":"de53067f6cb5486eb78e92addb834be2eac2838a8118464ec49f1c2559f73ef1"}