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April 3, 20260 citationsOpen Access

Borel-Plane Probes at the Aether Limit: Extended Negative Atlas for the Non-Holomorphic Bird Map (Paper 21 in the Non-Holomorphic Fractal Series)

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MBMichael Bird

Key Points

  • This work aims to extend the negative atlas established for the non-holomorphic Bird map to the Aether limit.
  • Utilized the Aether-limit orbit-multiplier slope ladder with 500 terms.
  • Feeding data into a direct clone of the Paper 20 gamma-family driver.
  • Reproduced results closely matching established fingerprints from previous papers.
  • Analyzed data against real Aether data for singularities.
  • No Padé-stable, N-stable singularity identified in the Feigenbaum window.
  • Confirmed stability across various numerical slices with 8/8 hits.
  • Extended negative atlas from finite-C Class C to infinite-α regime.
  • Planted pole mapping shows stable results at s₀ = 0.19013.

Abstract

Paper 21 in the Non-Holomorphic Fractal Series. Papers 18–20 established a calibrated negative atlas for the non-holomorphic Bird map at finite C = 0. 3605: the orbit-multiplier, Watson–Borel (WBA), and alien-strength ladders all show no Padé-stable, N-stable real-axis singularity in the Feigenbaum window 0. 85, 1. 15 under the calibrated gamma-family Padé–Borel skeleton, even after first-order alien correction. We now extend this atlas to the Aether limit (α → ∞) of the Bird map, feeding the Aether-limit orbit-multiplier slope ladder (500 terms) into a direct clone of the Paper 20 gamma-family driver. The G4 synthetic calibration reproduces the Paper 19/20 fingerprint exactly: a planted pole at s₀ = 0. 19013 maps to s̃ ≈ 0. 9995 (stable across all N ∈ 40, 60, 80 and Padé slices, 8/8 hits). Against real Aether data, no Padé-stable, N-stable singularity is found in the Feigenbaum window for any σ ∈ 1, 2, 5. 263, 10, either with or without first-order global-scale alien correction. At the Aether limit the Feigenbaum pole remains invisible to the calibrated gamma-family Padé–Borel probe at N ≤ 80, extending the negative atlas from finite-C Class C to the infinite-α regime.

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Cite This Study

Michael Bird (2026) studied this question.

synapsesocial.com/papers/69cf5ede5a333a821460d8fchttps://doi.org/10.5281/zenodo.19343659
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Phase transitions, cusp cascades, and a Feigenbaum-type universality in the Aether fractal family2026 · 14 citations
  2. 2Orbit-multiplier resurgence and the Borel geometry of the Feigenbaum cascade in Aether fractals2026 · 20 citations
  3. 3Structural Impossibility of Watson–Boundary-Layer Anchor Reproduction and the Picard–Lefschetz Redefinition of the Class A Stokes Constant (Paper 15 in the Non-Holomorphic Fractal Series)2026 · 8 citations
  4. 4The Near-Boundary Picard–Lefschetz Stokes Law and the Alien Jump at s = 1 (Paper 17 in the Non-Holomorphic Fractal Series)2026 · 7 citations
  5. 5The α-Dependence of the Class-A Stokes Constant: Exact Exponent from Half-Thimble Geometry2026 · 9 citations