Retracted work
Everything on this page is wrong. It is kept because deleting it would be worse.
What survived, for contrast
One claim: the acceleration scale of the mass-discrepancy–acceleration relation is set by the dark-energy density, a₀ = κ c √(G ρ_Λ) = c H_Λ / Z = 9.36 × 10⁻¹¹ m s⁻², realised as modified gravity. It reproduces the radial acceleration relation on 175 SPARC galaxies at 0.108 dex.
Even that is narrower than it looks. The law and its de Sitter–Unruh derivation are Milgrom’s (1999), and his derivation fixes a coefficient 11.58× larger than the one used here. The contribution is a re-normalisation of that coefficient to fit data, plus the relativistic (Aether–Scalar–Tensor-embedded) completion. It is also currently in conflict with the inner-planet ephemerides at the level of ~10³ unless the relation is read as an infrared statement rather than an exact one.
The numerology
Claims that fundamental constants follow from Z². This is the core of what was retracted.
Claimed: Claimed derivations of the fine-structure constant, the proton-to-electron mass ratio, the Weinberg angle, CKM elements and cosmological density parameters, all from Z² = 32π/3.
Why it is retracted: Numerology. It failed a look-elsewhere / false-discovery test: a randomly chosen constant of similar size reproduces the same retrodictions equally well. Chance alone hits roughly ten of nineteen targets.
Claimed: The cube×sphere construction: Z² = 8 × (4π/3), presented as the origin of all coupling constants and mass hierarchies.
Why it is retracted: The "8" (fixed points of a T³/Z₂ orbifold) and the "4π/3" (spherical measure) do not combine into a physical coupling. In the one place 32π/3 legitimately appears — the coefficient Z in a₀ = cH_Λ/Z — every π and both integers cancel, and what is left (κ = ½) is a free posit.
Claimed: An argument that Z² = 32π/3 is a fundamental constant of nature.
Why it is retracted: It is not. It appears only as a coefficient in the acceleration scale, and the de Sitter–Unruh argument that produces it actually predicts a coefficient 11.58× larger (Milgrom 1999). The value in use is fitted to data, not derived.
Claimed: A tool that computed "predicted" values of fundamental constants from Z.
Why it is retracted: It reproduces the retracted derivations. Its outputs are numerical coincidences.
Claimed: sin²θ_W = 3/13, Ω_Λ = 13/19, specific particle masses.
Why it is retracted: Retracted numerology. The surviving falsifiable predictions are gravity-side and pre-registered: the wide-binary γ, the Lorentz-violation dipole sign, and the shape of a₀(z).
Claimed: Comparisons of this framework against ΛCDM on particle-physics constants.
Why it is retracted: The particle-physics side of the comparison uses retracted numerology. Only the gravity-side comparison — the radial acceleration relation — is meaningful.
Claimed: Pairings of Z² with cultural, historical and biological patterns.
Why it is retracted: Numerical coincidences. Included at the time as play; kept now as an illustration of how the pattern-matching went wrong.
The cosmic topology
Claims about the global shape of the universe, and the visualisations built to render it.
Claimed: A claim that the universe is a 20.6 Gpc orbifold, with the DESI four-point correlation function as confirmation.
Why it is retracted: Tested against CMB matched-circle statistics and rejected. The claimed 4PCF "confirmation" does not survive as evidence for a topology.
Claimed: An interactive render of the claimed orbifold topology.
Why it is retracted: Renders a rejected topology. Kept because the visualisation itself is the artefact worth showing.
Claimed: A second rendering of the same rejected topology.
Why it is retracted: Same rejection.
Claimed: A lattice underlying the orbifold claim.
Why it is retracted: Part of the retracted numerology.
Applications and extensions
Places the number was extended into domains it had no business in.
Claimed: A claim that Z² = 32π/3 appears in protein-backbone geometry and bears on the origin of life.
Why it is retracted: Failed a false-discovery test — proteins show no significant Z² signal beyond chance. The framework makes no prediction about the origin of life, and never should have.
Claimed: A Z²-derived particle candidate with a specific keV mass.
Why it is retracted: The framework has no dark-matter particle (its operative arm is modified gravity). The quoted mass was fabricated.
Claimed: Claims that Z² sets primordial structure formation.
Why it is retracted: Numerology. The surviving claim concerns the present-day galactic acceleration scale, not primordial structure.
Claimed: A claimed cluster confirmation.
Why it is retracted: Relies on the retracted cluster numerology. Galaxy clusters are in fact a standing difficulty for MOND-type theories — including this one — not a confirmation of any of them.
Claimed: A Z²-based account of anomalous quasar observations.
Why it is retracted: Part of the retracted numerology.
Claimed: A narrative of the universe’s long-term future built on Z².
Why it is retracted: Built on the retracted numerology.
Claimed: The full visualisation gallery, including the constant "derivations" and the rejected topology.
Why it is retracted: Mixed. Some panels depict retracted material; the empirically grounded ones — the radial acceleration and Tully–Fisher relations — are on the Simulations page instead.