Pre-Registered Confrontation of a K3 x T2 Dual-Scale Hypothesis with Data: Four Observables, Four Negative Verdicts, and a Common Cause

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-18
DOI
https://doi.org/10.5281/zenodo.22837836
Primary Topic
International Science and Diplomacy
Type
preprint
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preprint

Pre-Registered Confrontation of a K3 x T2 Dual-Scale Hypothesis with Data: Four Observables, Four Negative Verdicts, and a Common Cause

Xavier Callens, SocrateAI Scientific Agora Collaboration
Zenodo (CERN European Organization for Nuclear Research)
International Science and Diplomacy
preprint

Pre-Registered Confrontation of a K3 x T2 Dual-Scale Hypothesis with Data: Four Observables, Four Negative Verdicts, and a Common Cause

Xavier Callens, SocrateAI Scientific Agora Collaboration
preprint en

Abstract

A research programme built around a "micro/macro dual-scale" reading of string theory on $K3× T^2$ identifies the string scale with the geometric mean of the Planck length and the Hubble radius, $\alpha'=\ell_P c/H_0$, and hence a self-dual length $s=\sqrt{\ell_P c/H_0}≈47 μ$m. We report what happens when every observable this programme can derive — without passing through a compactification that has never been constructed — is written down, frozen by a git tag together with its decision rule before the verdict is computed, and then confronted with pinned data. There are exactly four such observables. (P1) $s$ as the radius of one large extra dimension is excluded by the Eöt-Wash torsion-balance bound ($<30 μ$m) and fails the neutron-star bound ($<44 μ$m); the programme's own T-duality fixes the order-one factor that could have rescued it. (C-A) Vacuum energy saturating the Cohen–Kaplan–Nelson bound with infrared length $c/H$ forces a deceleration parameter $q=+1/2$ at every epoch, for every value of its only parameter, and is excluded by the observed acceleration. (C-B) Pre-big-bang relic gravitons at the programme's string scale end at $≈6×10^{-5}$ Hz with a peak $\Omega_{\rm GW}≈10^{-65}$, more than fifty orders of magnitude below LISA's design sensitivity: not falsifiable in practice. (C-C) Cosmic F-strings have $Gμ\sim10^{-62}$: likewise out of reach. The premise shared by C-B and C-C — a meV string scale — was already excluded by LHC resonance searches. The common cause of all four negative verdicts is the identification $\alpha'=\ell_P c/H_0$ itself. Every derivation and every numerical comparison is kernel-checked in Lean 4 (DualScaleCosmology, 50 theorems; repository 621 theorems, 0 failing, release v3.16.1); the physical identifications are stated as conjectures and the experimental bounds as literature, each pinned to a source file and line range. We record the two freezes made after the relevant bounds were known as retrodictions, and the one made before its comparison document was pinned as a forward prediction. The mathematics of the programme (moonshine, dyons, lattices) is unaffected and is reported separately; the lesson is methodological: pre-registration turned an "order-one tension" into a recorded exclusion and located the single assumption responsible. Epistemic tiers. Claims are labelled Tier A (checked by the Lean 4 kernel; axioms propext, Classical.choice, Quot.sound only), Tier L (literature, cited) or Tier C (conjecture). Only Tier A statements are machine-checked; physical interpretation is not. Lean artifact: SocrateAI-Scientific-Agora-LeanMaster, tag v3.17.0 (Lean 4 v4.33.1, Mathlib). Release gates on this tag: all ten libraries build; 621 theorems pass #print axioms with standard axioms only; no sorry/admit. AI-assisted tooling (Anthropic Claude models) was used in preparing the formalization and the manuscript, under the direction of the author.

Zenodo (CERN European Organization for Nuclear Research)
Laboratoire de Mathématiques d'Orsay (FR)
Peace, Justice and strong institutions
International Science and Diplomacy
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