FQxI Forum Post — Alternative Models of Reality Thread
Ready to copy-paste directly into the forum
March 14, 2026
Title: Regulated Tolerance as a Universal Structural Principle (Δ > 0)
I'd like to share a framework I've been developing independently and get feedback from this community.
The core idea is simple: exact zero tolerance is not physically realizable in any real system. This isn't a new observation — Heisenberg uncertainty, supercooling in phase transitions, CP violation, transcendental π, and gravitational wave propagation all demonstrate that nature operates within a regulated tolerance band rather than at exact closure. What I'm proposing is that this pattern constitutes a universal structural principle, not a collection of unrelated anomalies.
I call this Δ > 0: the tolerance band is not noise, not error, not an approximation waiting to be refined away. It is the operating condition.
That much I'd argue is already visible in existing data and requires no new equations. The more ambitious claim is that the framework derives a specific candidate for the universal fraction that must exist in the tolerance band at any phase transition. The erfc fixed-point equation erfc(φL³ × η) = η, where φL is the golden ratio, has a unique positive solution η* ≈ 0.20949. No free parameters. No fitting.
The first external test: Moore and Molinero's 2011 Nature simulation of water-ice nucleation (Nature 479, 506–508) found approximately 20% of molecules in an intermediate state — not liquid, not solid — at the transition point. The framework predicts 20.949% from pure algebra with no water-specific inputs. The match falls within the reported precision. I've contacted Prof. Molinero requesting higher-precision data.
A second prediction — that CP violation in beauty baryon decays will continue strengthening, with Λb⁰ → ΛK⁺K⁻ as the next channel to cross threshold — is timestamped on Zenodo (DOI: 10.5281/zenodo.15894519) ahead of LHCb Run 3 results expected late 2026.
My background is in precision machining and aerospace tooling (patents for kinematic tooling with 25 millionths of an inch repeatability, Gage R&R confirmed). The Δ > 0 principle was first observed in physical reality — every tolerance band I ever held a part to, every kinematic mount that required controlled clearance to function — before the mathematics existed to describe it. I don't have an institutional affiliation or arXiv access.
The full archive (58 papers) is freely available at leveille.substack.com. Paper 58 ("The Operating System and the Constant") is designed as the entry point and cleanly separates the qualitative principle (Δ > 0, which I'd argue is already settled by existing data) from the quantitative claim (η* = 0.20949, which is falsifiable and currently under test).
I'd welcome critical feedback — particularly on whether the erfc fixed-point equation has precedent in renormalization group literature, whether the Molinero match is as significant as I believe it is, and whether the two-tier framing (operating system vs. engineering constant) is a useful way to present the work.
Thank you for reading.
Anderson Leveille
Independent Research
exactlyinfinite.substack.com
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