{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R4Q4222NS7H5M3FGW32VQ42HBF","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":"cb2582eca5adac75665210fd560476ae979c3de02b7a328d2b831967a62c8c0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-27T16:22:22Z","title_canon_sha256":"b7688dbec11cadd017a16df6884b444b578a3bc80cf04954e767089992ad9992"},"schema_version":"1.0","source":{"id":"1708.08101","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08101","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08101v2","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08101","created_at":"2026-05-18T00:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"R4Q4222NS7H5","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R4Q4222NS7H5M3FG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R4Q4222N","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:4597c66f4e0fa72bb3155aed7c40b81041d087c32968f5240339d4ed8e6b7ac2","target":"graph","created_at":"2026-05-18T00:23:08Z","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 study scalar delay equations $$\\dot{x} (t) = \\lambda f(x(t-1)) + b^{-1} (x(t) + x(t -p/2))$$ with odd nonlinearity $f$, real nonzero parameters $\\lambda, \\, b$, and two positive time delays $1,\\ p/2$. We assume supercritical Hopf~bifurcation from $x \\equiv 0$ in the well-understood single-delay case $b = \\infty$. Normalizing $f' (0)=1$, branches of constant minimal period $p_k = 2\\pi/\\omega_k$ are known to bifurcate from eigenvalues $i\\omega_k = i(k+\\tfrac{1}{2})\\pi$ at $\\lambda_k = (-1)^{k+1}\\omega_k$, for any nonnegative integer $k$. The unstable dimension of these rapidly oscillating per","authors_text":"Bernold Fiedler, Isabelle Schneider","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-27T16:22:22Z","title":"Stabilized rapid oscillations in a delay equation: Feedback control by a small resonant delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08101","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":"sha256:83645153566e81fc09ac21dd525572af1a9fdac7d1807a844db4792d8c4a475f","target":"record","created_at":"2026-05-18T00:23:08Z","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":"cb2582eca5adac75665210fd560476ae979c3de02b7a328d2b831967a62c8c0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-27T16:22:22Z","title_canon_sha256":"b7688dbec11cadd017a16df6884b444b578a3bc80cf04954e767089992ad9992"},"schema_version":"1.0","source":{"id":"1708.08101","kind":"arxiv","version":2}},"canonical_sha256":"8f21cd6b4d97cfd66ca6b6f55873470949e8e3811b58b6d9face999c5edc54c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f21cd6b4d97cfd66ca6b6f55873470949e8e3811b58b6d9face999c5edc54c1","first_computed_at":"2026-05-18T00:23:08.543919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:08.543919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+44zi41ysbyHifPeJaXC66iyvd1KuWNYc6KQJTlyzjV+VmL8rrWKtqze/5fwAsZhPtSAjPeGyEEr0cL9Dz70Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:08.544625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08101","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83645153566e81fc09ac21dd525572af1a9fdac7d1807a844db4792d8c4a475f","sha256:4597c66f4e0fa72bb3155aed7c40b81041d087c32968f5240339d4ed8e6b7ac2"],"state_sha256":"98147ca0f161d83c5ba9279b404071411d91f21cbe5df32aa0c6ab25fa1f6eae"}