The Unequal Multiplicities
Year: 2026
Type: preprint
Abstract: All-Fields programme paper (All-Fields Run, Batch 19 (AF)), November 2026. Written November 2026; publicly deposited 9 November 2026. The compositions of the two bounded readings at unequal multiplicity — the symmetric reading taken once, twice or three times against the one-sided reading taken a different number of times, six compositions in all — are graded at their own fronts, at the two grains the readings' ladders share. No unequal composition's kernel has a front-exact zero: the smallest front share among the twelve rows graded is 5.184×10⁻¹, eleven orders and more above the line at which a zero would be declared, and the largest is 9.859×10⁻¹. The shares are set first by the assignment of the multiplicities: at each grain the six order strictly by the one-sided reading's fraction of the total multiplicity, from 5.184×10⁻¹ where the symmetric reading carries three of the four factors to 9.859×10⁻¹ where the one-sided reading carries three of the four, and at fixed total depth four the equal fourfold's share stands strictly between its two unequal neighbours' at both grains. With this grading the composition family stands complete — the readings singly, their composition, its powers at equal multiplicity, and
Author: Aldred, William Alexander
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225621738
Cites:
Cited by:
Related to: