Research
The Golden Physics Project pursues a unified mathematical framework for fundamental physics derived from a single algebraic identity: the self-duality of Haar measure on the multiplicative group (ℝ⁺, ×). The map dμ(ω⁻¹) = dμ(ω) — the order-two involution on the simplest non-compact abelian group — is the origin of the entire structure.
Three Cayley–Dickson doublings ℝ→ℂ→ℍ→𝕆 elevate this to the Grassmannian Gr(2,4), which is the canopy of the framework and the natural home of four-dimensional quantum gravity via celestial holography. The Standard Model gauge factors SU(3)×SU(2)×U(1), exactly three fermion generations, sin²θW = 3/8, and the Yang–Mills mass gap M = 2N/(k+N)·ΛQCD are proposed to follow from the algebraic structure, with physical inputs entered as explicit hypotheses.
The central identification Δ = 2s — between the celestial conformal dimension and the Riemann zeta variable — places the unitarity locus of the celestial CFT on the same line as the critical line of the zeta function, so that the Riemann Hypothesis becomes a question inside the framework. Both are fixed-point conditions of the same involution at the conformal boundary (verified in Lean). The shadow symmetry Δ ↔ 2−Δ is time reversal T, not CPT.
Work is conducted independently in Cardinal, Ontario. All preprints are open access in the Golden Physics Project community on Zenodo.
Selected Work
Twistor Theory and the Resolution of the Googly Problem
Shadow = T from first principles and a Yang–Mills twistor datum: a resolution of Penrose's googly obstruction. Shadow = T is machine-verified. Zenodo ↗
On the Nature of Nature — v19
979-page monograph presenting the full framework: celestial holography, the three Millennium Prize problem programmes, the Standard Model, cosmology. The Lean formalization tracks which parts are machine-verified. Zenodo ↗
Yang–Mills Mass Gap via Celestial Holography
Proposes a constructive route to a mass gap M = 2N/(k+N)·ΛQCD for compact simple gauge groups. Conjectural; not a solution of the Clay problem. Zenodo ↗
The Haar–Measure Constraint and the Riemann Hypothesis
Presents the Haar-measure argument for Re(s) = 1/2. Unrefereed; its central step is recorded as open in the formalization. Zenodo ↗
The Fixed-Point Paradox
A Lawvere-style argument that Counterfactual Freedom is incoherent under stated definitions, bearing on both libertarian free will and hard determinism. Zenodo ↗
Approach
The programme aims to derive its constants from the algebra rather than fit them: the Standard Model gauge factors, three fermion generations, sin²θW = 3/8 and the mass gap are proposed to follow. Where physical inputs are needed they enter as explicit hypotheses, and each claim is tagged verified, argued or open.
Every claim is placed in one tier: machine-verified in Lean 4, argued in a manuscript but not machine-checked, or open. The Lean tree has zero sorry and zero custom axioms, and unproved results are kept as named, counted placeholders. Analogies are labelled as analogies.
The framework ascends from the simplest possible object — Haar measure on (ℝ⁺, ×) — through three algebraic doublings to spacetime. Gr(2,4) is the canopy, not the origin.
Where a gap exists, it is named precisely. The Riemann Hypothesis is reduced to a single positivity statement but not proved; the Yang–Mills mass gap is a conjectural programme; BSD is an open conjecture with a structural reading only. None is claimed solved in the Clay sense.