What question did this study set out to answer?

The aim is to explore integer relations among 82 constants using exact arithmetic and the PSLQ algorithm.

April 23, 2026Open Access

The 82/82 Independence Record: 82 tests, zero relations, derivation beats search.

Puntos clave

The aim is to explore integer relations among 82 constants using exact arithmetic and the PSLQ algorithm.
Applied the PSLQ integer relation algorithm to 82 constants from three categories: physical, dynamical, and analytical.
Conducted tests at high precision (up to 100 digits) and documented both successes and failures against standard measurements.
Implemented sanity checks to confirm operational status of the PSLQ algorithm.
Found zero compact relations among the tested constants against a 20-constant transcendental basis.
Demonstrated the highest precision PSLQ result with new tests on Bessel zeros.
Confirmed that derivation, rather than search, yields meaningful results, as all tested relations from derivation passed validation.

Resumen

The 82/82 Independence Record: 82 tests, zero relations, derivation beats search. This paper is part of the HOWL research archive—a collection of physics papers exploring integer fraction derivations across multiple domains using exact arithmetic and automated comparison. Abstract The PSLQ integer relation algorithm, applied to 82 constants from three categories — physical (SM parameters, clock ratios, mass ratios), dynamical (Feigenbaum constants, BCS gap), and analytical (Bessel zeros) — finds zero compact relations against a 20-constant standard transcendental basis at precisions from 4 to 100 digits with maxcoeff 10, 000. The 10 new Bessel zero tests from this session operate at 100-digit precision — 70 orders of magnitude more discriminating than the SM parameter tests and the highest-precision PSLQ in the series. The sanity check confirms the algorithm is operational: PSLQ finds the known relation π² = 6ζ (2) as the integer vector 1, 0, −6. The methodological conclusion across the full series: every parameter reduction came from physical derivation (θQCD = 0 from energy minimization in PHYS-7, α ↔ aₑ at 4. 3 ppb from QED perturbation theory in PHYS-9, Koide K = 2/3 conditional from a trigonometric identity in PHYS-8), while every PSLQ search returned noise indistinguishable from control irrationals. Derivation beats search. The 82/82 null establishes that the standard transcendental basis is genuinely minimal — no tested constant collapses to a formula involving the others — and redirects future effort toward derivation rather than numerical pattern hunting. Falsification Criteria All papers in this archive are subject to falsification through direct comparison to published experimental measurements. Each derived value is tested against independent data with explicit PASS/FAIL criteria. Any derived value that fails its comparison is documented and published alongside the successes. Research Context This archive documents an ongoing research program in integer fraction physics. The methodology is: derive values from gauge group integers using exact fraction arithmetic, compare to published measurements, and document all results including failures. The archive spans multiple physics domains connected through the soliton boundary framework described in the constituent papers. Package Contents manuscript. md: The complete derivation and supporting analysis. README. md: Navigation, dependencies, and citation (Registry: HOWL-MATH-6-2026). Dependencies: HOWL-MATH-1-2026, HOWL-MATH-4-2026, HOWL-MATH-5-2026, HOWL-PHYS-10-2026 Motto: Derive. Compare. Publish. Status: Complete

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Cite This Study

Geoffrey Howland (Wed,) studied this question.

synapsesocial.com/papers/69e9b85585696592c86eba08 https://doi.org/https://doi.org/10.5281/zenodo.19665709

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