Conformal Padé–Borel Probes across the Full Atlas: A New Borel Family for the Non-Holomorphic Bird Map Negative Atlas (Paper 23 in the Non-Holomorphic Fractal Series)

Paper 23 in the Non-Holomorphic Fractal Series. Papers 19–22 established a resolution-calibrated negative Feigenbaum atlas for the non-holomorphic Bird map at both finite C = 0.3605 (Class C) and in the Aether limit (α → ∞), using the same γ-family Padé–Borel engine throughout. Paper 23 asks whether this Feigenbaum-window blindness persists when the Borel family itself is changed: specifically, whether a conformal-Borel map φ(s) = s/(1 + s/s_c) can reveal any Padé-stable, N-stable pole in the Feigenbaum window [0.85, 1.15] that the γ engine has consistently missed. We construct the conformal Padé–Borel variant as a minimal patch to the Paper 22 drivers, calibrate it via an independent G4 synthetic protocol, and deploy it across the full atlas: Class C and Aether, all three ladder types, through N ≤ 80. For every calibrated ladder the conformal engine passes G4 at machine-precision accuracy and the corresponding real-data scans show no Padé-stable poles in [0.85, 1.15]. The conformal engine therefore provides an independent, chart-change robustness audit of the γ-family result: the null verdict is not an artefact of the particular Borel family used in Papers 19–22.