{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JT2A7WEOK3TI3LXLYQO5INKSLJ","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":"fef29366b534f3c04f9f8bc3f03772971109494bcd34c9307cfe02cb80093ebe","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-24T18:13:43Z","title_canon_sha256":"98ef7185433a95161592f182088235c60d1f30749e92cb92aab5abd741713ff2"},"schema_version":"1.0","source":{"id":"1507.06939","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06939","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06939v2","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06939","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"pith_short_12","alias_value":"JT2A7WEOK3TI","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JT2A7WEOK3TI3LXL","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JT2A7WEO","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:3d54123b7dc4aef823fbf5fe093c1a3d6e9a7fdf73afdbaf95fa4d0983574f18","target":"graph","created_at":"2026-05-18T00:35:51Z","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":"A combinatorial interpretation is given of Devlin's word problem underlying the classical center-focus problem of Poincare for non-autonomous differential equations. It turns out that the canonical polynomials of Devlin are from the point of view of connected graded Hopf algebras intimately related to the graded components of a Hopf algebra antipode applied to the formal power series of Ferfera. The link is made by passing through control theory since the Abel equation, which describes a center, is equivalent to an output feedback equation, and the Hopf algebra of output feedback is derived fr","authors_text":"Kurusch Ebrahimi-Fard, W. Steven Gray","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-24T18:13:43Z","title":"Center problem, Abel equation and the Faa di Bruno Hopf algebra for output feedback"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06939","kind":"arxiv","version":2},"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:ffe5b0b15168e3968cfb446ea20ada42c1dffc945d4ed8219b59d5a902e3e79b","target":"record","created_at":"2026-05-18T00:35:51Z","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":"fef29366b534f3c04f9f8bc3f03772971109494bcd34c9307cfe02cb80093ebe","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-24T18:13:43Z","title_canon_sha256":"98ef7185433a95161592f182088235c60d1f30749e92cb92aab5abd741713ff2"},"schema_version":"1.0","source":{"id":"1507.06939","kind":"arxiv","version":2}},"canonical_sha256":"4cf40fd88e56e68daeebc41dd435525a6e71ecf854f287e747b4e618c6dbcab3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cf40fd88e56e68daeebc41dd435525a6e71ecf854f287e747b4e618c6dbcab3","first_computed_at":"2026-05-18T00:35:51.962734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:51.962734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rssaRdcwoDEuZ10MFz9F2dCOuNsRgoJY7MgP7tbDxprbFXtfdn9mT9V5G//j7Sa7cxfSU5qJYXvWp4jWhERPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:51.963093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06939","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffe5b0b15168e3968cfb446ea20ada42c1dffc945d4ed8219b59d5a902e3e79b","sha256:3d54123b7dc4aef823fbf5fe093c1a3d6e9a7fdf73afdbaf95fa4d0983574f18"],"state_sha256":"260453011138bef8139396818aeec9e16e4b837e23c1bd487ef062f362ef8051"}