Local Uniform Finite Cyclicity of the $H_{14}^{3}$ Semihyperbolic Hemicycle

We prove local uniform finite cyclicity for the labelled $H_{14}^{3}$ semihyperbolic hemicycle of a quadratic vector field. More precisely, in one fixed annular neighborhood of the compactified graphic, the number of isolated limit cycles is uniformly bounded for all sufficiently small values of the full five-parameter source-normalized quotient unfolding. This is the case left open in the corresponding quadratic-hemicycle analysis because a noncompact source, two semihyperbolic endpoints, and an upper-equatorial degeneration occur simultaneously. The proof constructs a finite atlas of stopped first hits before forming any full-lap return. An intersection argument represents each counted cycle by exactly one retained itinerary. The resulting analytic equations are treated by a matched source estimate, a direct Liénard--Dulac argument on the exact mixed face, and hyperbolic, central, strict-lips, middle, and root-scale zero theorems on the remaining regimes. A finite specialization argument includes coefficient, boundary, collapse, and identity values. The distinctive point is that all estimates remain uniform in the five original parameters. The resulting bound is existential.
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Ancillary files (details):
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- h14_3_reproducibility/README.md
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- h14_3_reproducibility/certificates/verify_endpoint_joint_uniformity.py
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- h14_3_reproducibility/certificates/verify_source_six_jet_owner_dag.py
- h14_3_reproducibility/certificates/verify_ultra_mixed_dulac.py
- h14_3_reproducibility/data/source_six_jet_owner_dag_summary.json
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- h14_3_reproducibility/reproduce/environment.lock
- h14_3_reproducibility/reproduce/expected_outputs.json
- h14_3_reproducibility/reproduce/reproduce_all.sh
- h14_3_reproducibility/specifications/bautin.md
- h14_3_reproducibility/specifications/chart_checks.md
- h14_3_reproducibility/specifications/endpoint.md
- h14_3_reproducibility/specifications/middle_qhh.md
- h14_3_reproducibility/specifications/mixed_dulac.md
- h14_3_reproducibility/specifications/open_aff.md
- h14_3_reproducibility/specifications/root_scale.md
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