{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JT2A7WEOK3TI3LXLYQO5INKSLJ","short_pith_number":"pith:JT2A7WEO","canonical_record":{"source":{"id":"1507.06939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-24T18:13:43Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"98ef7185433a95161592f182088235c60d1f30749e92cb92aab5abd741713ff2","abstract_canon_sha256":"fef29366b534f3c04f9f8bc3f03772971109494bcd34c9307cfe02cb80093ebe"},"schema_version":"1.0"},"canonical_sha256":"4cf40fd88e56e68daeebc41dd435525a6e71ecf854f287e747b4e618c6dbcab3","source":{"kind":"arxiv","id":"1507.06939","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JT2A7WEOK3TI3LXLYQO5INKSLJ","target":"record","payload":{"canonical_record":{"source":{"id":"1507.06939","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-24T18:13:43Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"98ef7185433a95161592f182088235c60d1f30749e92cb92aab5abd741713ff2","abstract_canon_sha256":"fef29366b534f3c04f9f8bc3f03772971109494bcd34c9307cfe02cb80093ebe"},"schema_version":"1.0"},"canonical_sha256":"4cf40fd88e56e68daeebc41dd435525a6e71ecf854f287e747b4e618c6dbcab3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:51.963093Z","signature_b64":"rssaRdcwoDEuZ10MFz9F2dCOuNsRgoJY7MgP7tbDxprbFXtfdn9mT9V5G//j7Sa7cxfSU5qJYXvWp4jWhERPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cf40fd88e56e68daeebc41dd435525a6e71ecf854f287e747b4e618c6dbcab3","last_reissued_at":"2026-05-18T00:35:51.962734Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:51.962734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.06939","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zMC+e6w661/TINJeW4fQuGYZIJGl3hjZl4Ik+HLZmnnR08NUwRdl1pFjzimZ54XyOk5wov16gOIHJg+mcwp4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:30:28.496502Z"},"content_sha256":"ffe5b0b15168e3968cfb446ea20ada42c1dffc945d4ed8219b59d5a902e3e79b","schema_version":"1.0","event_id":"sha256:ffe5b0b15168e3968cfb446ea20ada42c1dffc945d4ed8219b59d5a902e3e79b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JT2A7WEOK3TI3LXLYQO5INKSLJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Center problem, Abel equation and the Faa di Bruno Hopf algebra for output feedback","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RA","authors_text":"Kurusch Ebrahimi-Fard, W. Steven Gray","submitted_at":"2015-07-24T18:13:43Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06939","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gw+nYoJv6uwZqmnXteJPC0wWgoSSv3KT4O/hFas/O4CZifAFVGb/JVGbEoGq2W+3szMwOworGGkR5ezDOxNTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:30:28.496848Z"},"content_sha256":"3d54123b7dc4aef823fbf5fe093c1a3d6e9a7fdf73afdbaf95fa4d0983574f18","schema_version":"1.0","event_id":"sha256:3d54123b7dc4aef823fbf5fe093c1a3d6e9a7fdf73afdbaf95fa4d0983574f18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JT2A7WEOK3TI3LXLYQO5INKSLJ/bundle.json","state_url":"https://pith.science/pith/JT2A7WEOK3TI3LXLYQO5INKSLJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JT2A7WEOK3TI3LXLYQO5INKSLJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T22:30:28Z","links":{"resolver":"https://pith.science/pith/JT2A7WEOK3TI3LXLYQO5INKSLJ","bundle":"https://pith.science/pith/JT2A7WEOK3TI3LXLYQO5INKSLJ/bundle.json","state":"https://pith.science/pith/JT2A7WEOK3TI3LXLYQO5INKSLJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JT2A7WEOK3TI3LXLYQO5INKSLJ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"41rQAI1vDatCGGPUTc7A5wowiJkvND3ERrYS0oj9JmIdGHcbqn9tLOAEm41ENyd5uLRGtBTa2nR+vhYgmXaHDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:30:28.498809Z","bundle_sha256":"c527022b5951bf9c0535eaad35c8d89a98bebd317fb5a64459b81749e8951f6a"}}