The Factor of Two, Priced: Press and Schechter's Gaussian Count, the Threshold It Imports, and the Doubling It Inserts by Hand
Year: 2026
Type: preprint
Abstract: Census pricing (row CC-111, Scout Batch 7) of the founding step of Press & Schechter's 'Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation,' ApJ 187, 425-438 (1974), against a fixed bench (postulated / derived / numeric return / reach). The step is two-layered: a collapse criterion imported whole from spherical top-hat collapse (delta_c = 1.686, labelled imported) applied to an assumed Gaussian field, and a factor of two inserted by hand because the raw Gaussian count integrates to half the mass in the universe. Verified in the notebook (14 checks, exit 0, math.erfc only) from the imported threshold plus declared sigma bench points (not measured cosmology): F_raw(sigma=1) = 0.045898, doubled F_PS = 0.091796, the doubling exactly 2.000000 at every sigma; F_raw tends to 0.500000 as sigma grows (0.493274 at sigma=100), never to 1 -- the cloud-in-cloud deficit the factor hides, whose excursion-set derivation (Bond et al. 1991) is credited at its own address and not spent for 1974. Threshold audit: at sigma=1 the doubled fraction swings from 0.133614 (delta_c=1.5) to 0.057433 (delta_c=1.9), a factor 2.326 -- larger than the famous inserted factor. Multiplicity f(sigma) peaks at sigma = delta_c (0.483941). Scout-grade verification disclosed on the manuscript's face (CC-91 form); one author is living -- the work is priced, the man is not addressed, no contact was made. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.
Author: Aldred, William Alexander
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225239978
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