Alien-Corrected Borel Probes in Class C (Paper 20 in the Non-Holomorphic Fractal Series)

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Authors: Michael Bird
Cited by: 17
References: 4

Abstract

Paper 20 in the Non-Holomorphic Fractal Series. Papers 18 and 19 built a calibrated Borel-plane atlas for the non-holomorphic Bird map and found that natural Class C observables (orbit-multiplier, WBA, and alien-strength Watson ladder) are Feigenbaum-blind at current resolution under a gamma-family Padé–Borel skeleton with strict G1–G4 artefact filters. Here we extend that atlas by introducing explicit alien-corrected inputs derived from the Watson-side alien calculus of Papers 13–17 and feeding them back into the same Padé–Borel machinery. For each observable we construct alien-corrected coefficient sequences, re-validate G4 via synthetic Feigenbaum-pole injections, and perform full G1–G3 scans on the corresponding real data. Our computations show that the calibrated gamma-family probes detect a planted Feigenbaum-like pole with excellent stability even after first-order alien corrections, but the true Class C observables remain empirically Feigenbaum-blind on the positive axis up to N ≤ 80 and over a moderate Borel scale band. The negative Class C verdict is thus significantly strengthened: within the tested gamma-family Padé–Borel skeleton and first-order alien corrections, no Padé-stable, N-stable positive-axis Feigenbaum pole emerges in any of the orbit, WBA, or alien-strength ladders.

Fields of Study & Subjects

Morphological variations and asymmetry Mathematical Dynamics and Fractals Visual perception and processing mechanisms

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
30 March 2026
Language
EN
Document type
Preprint