Mirny's Cosmodynamics: Notes. Note No. 4 Phase function g(ψ): three candidates and a narrow anapausta
Abstract
In Note 1, the Mirny threshold was written as HPM(ψ)=φ2−110−ΔH g(ψ), where g(ψ) is the phase function of breathing and the slope at the saddle point D0=−7.77 is a measurable quantity. Here we show: (i) from the definition of D0D0 as local steepness follows a rigid relation ∣D0∣=ΔH⋅max∣g′(ψ)∣, independent of the candidate's functional form; (ii) for ΔH=0.03–0.07, the required steepness is 155–259 per unit phase, and the 10→90% transition occupies 0.004–0.010 of the phase — the anapause is narrow for any reasonable candidate; (iii) the three canonical candidates (logistic, smoothed step, and narrow step) differ only in their shape inside the narrow transition; (iv) the test distinguishes not form but sharpness: a step between adjacent DESI bins confirms the narrow anapause, while a smooth slope across the whole zone is the way to die.
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BibTeX
@misc{borodin2026mirnys,
title = {{Mirny's Cosmodynamics: Notes. Note No. 4 Phase function g(ψ): three candidates and a narrow anapausta}},
author = {Oleg Borodin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23659811},
url = {https://zenodo.org/records/23659811},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mirny's Cosmodynamics: Notes. Note No. 4 Phase function g(ψ): three candidates and a narrow anapausta
AU - Oleg Borodin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23659811
UR - https://zenodo.org/records/23659811
AB - In Note 1, the Mirny threshold was written as HPM(ψ)=φ2−110−ΔH g(ψ), where g(ψ) is the phase function of breathing and the slope at the saddle point D0=−7.77 is a measurable quantity. Here we show: (i) from the definition of D0D0 as local steepness follows a rigid relation ∣D0∣=ΔH⋅max∣g′(ψ)∣, independent of the candidate's functional form; (ii) for ΔH=0.03–0.07, the required steepness is 155–259 per unit phase, and the 10→90% transition occupies 0.004–0.010 of the phase — the anapause is narrow for any reasonable candidate; (iii) the three canonical candidates (logistic, smoothed step, and narrow step) differ only in their shape inside the narrow transition; (iv) the test distinguishes not form but sharpness: a step between adjacent DESI bins confirms the narrow anapause, while a smooth slope across the whole zone is the way to die.
ER -