Alien-Corrected Borel Probes in Class C (Paper 20 in the Non-Holomorphic Fractal Series)
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2026
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| _version_ | 1866901078638854144 |
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| author | Bird, Michael |
| author_facet | Bird, Michael |
| contents | 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. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19338894 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Alien-Corrected Borel Probes in Class C (Paper 20 in the Non-Holomorphic Fractal Series) Bird, Michael non-holomorphic fractals resurgence alien calculus Borel singularity Padé-Borel Feigenbaum constant alien-corrected probes Watson-Borel-alien Bird classification 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. |
| title | Alien-Corrected Borel Probes in Class C (Paper 20 in the Non-Holomorphic Fractal Series) |
| topic | non-holomorphic fractals resurgence alien calculus Borel singularity Padé-Borel Feigenbaum constant alien-corrected probes Watson-Borel-alien Bird classification |
| url | https://doi.org/10.5281/zenodo.19338894 |