Monomials Beyond the Far Standard: The Quartic Arrives at φ_i = 2.0761 — and It Is Not Alone

The monomial rolling-field class is computed beyond the far standard and below the standard: gated digit-for-digit on the far-standard packet's rows, the parent's standard-condition maxima (0.1815 / 0.0620 / 0.0319 / 0.0190 / 0.0128), and the interval packet's own exhibits (quartic maxima 0.2283 / 0.4442, the quadratic row at phi_i = 1.25, and both ends of its threshold bracket [1.20349, 1.20361]), the quartic's surface begins at phi_i* = 2.0761 (bisected), the sextic's at 2.8831 and the octic's at 3.6804, while the decic is still short at the stated scan end phi_i = 4.00 (0.5935). Below the standard every maximum falls monotonically and nothing conditions in phi_i in [0.10, 0.50). The class now reads as a staircase of four located thresholds. Odd n excluded on the parent's printed ground. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-03
DOI
https://doi.org/10.5281/zenodo.23936685
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

Monomials Beyond the Far Standard: The Quartic Arrives at φ_i = 2.0761 — and It Is Not Alone

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

Monomials Beyond the Far Standard: The Quartic Arrives at φ_i = 2.0761 — and It Is Not Alone

William Alexander Aldred
preprint en

Abstract

The monomial rolling-field class is computed beyond the far standard and below the standard: gated digit-for-digit on the far-standard packet's rows, the parent's standard-condition maxima (0.1815 / 0.0620 / 0.0319 / 0.0190 / 0.0128), and the interval packet's own exhibits (quartic maxima 0.2283 / 0.4442, the quadratic row at phi_i = 1.25, and both ends of its threshold bracket [1.20349, 1.20361]), the quartic's surface begins at phi_i* = 2.0761 (bisected), the sextic's at 2.8831 and the octic's at 3.6804, while the decic is still short at the stated scan end phi_i = 4.00 (0.5935). Below the standard every maximum falls monotonically and nothing conditions in phi_i in [0.10, 0.50). The class now reads as a staircase of four located thresholds. Odd n excluded on the parent's printed ground. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
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