The 0.1 Hz Heart-Coherence Peak Sits at Baroreflex Resonance, Not at 1/φ² = 0.381966 Hz: withdrawal of the golden-ratio readings of that peak, and the free-exponent control that retires the ladder forms with them
Year: 2026
Type: preprint
Abstract: This erratum withdraws the identity 0.1 Hz = 1/φ², in all four entries that print it, and with it every golden-ratio reading of the heart-coherence peak, including the two ladder forms that divide a Schumann frequency by φ⁸ and by φ⁹. The arithmetic does not hold: 1/φ² = 2 - φ = 0.381966011 Hz exactly, a deviation of 282%. Nor is 0.1 Hz reached by a ladder with a free exponent. No integer power of φ lands on it from any anchor; the nearest rungs miss by 9.83% at 1 Hz, 3.01% at the Schumann 7.83 Hz anchor and 4.06% at 7.91 Hz. The 3.01% miss looked survivable, and the reason it is not generalizes. A ladder with a free integer exponent has rungs spaced by a factor of φ, so every target on the line lies within [-21.384862%, +27.201965%] of some rung. With the exponent chosen freely to fit each target, the fraction of targets a relative tolerance τ admits is exact in closed form, Pr(|miss| ≤ τ) = ln[(1+τ)/(1-τ)] / ln b, for a ladder of ratio b. At b = φ the median miss is 11.9726%, which closes to (φ^½ - 1)/(φ^½ + 1); 9.1451% of targets land within 2.2% of a rung, about one in eleven, and 12.5139% within 3.01%, about one in eight. Every figure is an exact value of the closed form and carries no simulation error. A reported 3.01% agreement is what about one random number in eight achieves, so it carries no information. The same control retires the φ¹⁹ descent used elsewhere in this project, where a 2.2% agreement is one random target in eleven. The 0.1 Hz finding itself is not withdrawn. It is measured, well replicated, and has a mechanism: 0.1 Hz is the baroreflex resonance frequency, set by the roughly five-second delay of the cardiovascular baroreflex loop, which is why paced breathing at six breaths a minute, 0.1 Hz exactly, entrains it. Nothing downstream was derived from the withdrawn identity, and the measurement stays as a measured input. What is gained is a control computed before the agreement is read: absent a mechanism fixing anchor and exponent independently, the figure to beat is 12.5139%. A script recomputes every number, 32 checks, 32 pass.
Author: Almasy, Jason
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224422850