Phenomenology

What is Checkable in Principle

Claim What would confirm it Maturity
$\sqrt{3}$ root ratio gives $g_{SU(3)}/g_\text{short} = 1/\sqrt{3}$ within $G_2$ Established — Killing form explicit; embedding index $j=1$ means $g_3=g_2$ at GUT scale, so $1/\sqrt{3}$ does NOT appear independently in $g_3/g_2$; both $\sqrt{3}$’s (root ratio + Weinberg angle) trace to $N_c=3$ 2
$\sqrt{3}$ appears in physical scale ratio (cosmological) CMB temperature, cosmological constant, or Hubble scale stands in $\sqrt{3}$ relation to local quantum gravity scale 5
$\sin^2\theta_W = 3/8$ from 3+2 split of $u^\perp$ Derived (same number as SU(5), different mechanism — from $u$-selection) 3
Connection to measured $0.231$ via standard RG running Requires GUT scale from geometry — not yet derived 5
Golay snapping gives Born rule Specific forbidden outcome combinations in many-body entangled systems; deviations from Born rule in high-complexity experiments 5
Redshift as off-axis projection Different functional form $T(z)$ distinguishable from $T \propto 1+z$ 5–6
$Spin(2,3)$ dynamics without renormalization counterterms Reproduce Standard Model amplitudes from fixed-scale geometry 5–6
Leech tier observationally distinct At least one observable consequence differing if Leech background is absent 6

Currently Missing Entirely

  • Charge quantisation with specific ratios ($1/3$, $2/3$, $1$)
  • CKM/PMNS structure
  • Mass hierarchy
  • GUT scale from the octonionic geometry (needed to connect $\sin^2\theta_W = 3/8$ to measured $0.231$)

Full Claim Maturity Matrix

Practical reading rule

  • 1–3: safe inputs and established background — can be cited as support
  • 4: what current work must explicitly earn — pending calculations
  • 5: discussion and future work — plausible but unverified
  • 6: must be stated honestly as real weakness or missing result

Matrix

Claim Category Status Maturity
$Spin(2,3)$ has a four-component spinor representation Statics Established input 2
Choosing $u$ induces $T1/T2$ split Statics Choice + derived consequence 3
$\mathrm{Stab}(u) \cong SU(3)$ Statics Established structural fact 3
$u$ aligns with zero-mass interaction channel Statics/Epistemics Central proposal 4
Same $u$ at $G_2$, Cl(6), T1, compact/split, Gogberashvili cone map Statics Four roles explicit; compact/split identification argued via common complexification 4
Image of $\tilde{u}$ spacelike in $\mathbb{R}^{2,4}$ (Gogberashvili) Consistency Established — $u = j_n$-type (spacelike, $SU(2,1)$ stabilizer), cone map $X^n = x_n/L$, stabilizer $SO(2,3)$ ✓ 2
Off-diagonal $J_3(\mathbb{O}_\mathbb{Z})$ contains Leech sublattice Statics Established (Baez/Egan) 3
Leech embedding equivariant under $SU(3)$ Consistency Continuous equivariance is impossible; discrete equivariance is conditional on the fixed triality frame 3
$\sin^2\theta_W = 3/8$ from 3+2 split of $u^\perp$ Phenomenology Derived — same as SU(5), different mechanism 3
GUT scale at which $3/8$ applies: not yet derived from geometry Phenomenology Missing 6
$m_H/m_W$ from the $u$-framework via Todorov/Furey matching Phenomenology Imported structurally; tree-level relation established, EW threshold correction still open 3
Compact $G_2$ = internal, split $G_2$ = spacetime, same $u$ Statics/Interpretation Structural proposal 4
$\mathbb{H} \subset \mathbb{O}$ from $u$ carries $SU(2)$ doublet Statics Any quaternionic slice through $u$ carries the doublet structure; residual $SU(2)$ freedom remains 3
Cascade mechanism matches Furey & Hughes (2022) Statics Established structurally 3
Higgs as scalar component of tri$(\mathbb{H})$ triality triple Statics Established by Furey & Hughes 3
$u$ determines $u^\perp$ which determines Cl(6) which determines $qq^\dagger$ Consistency Established by matching 3
Vev scale $v \approx 246$ GeV fixed geometrically Phenomenology Dynamical gap — not yet derivable 6
$G_2 \to SO(2,4)$ encodes holographic scale Statics Established via Gogberashvili 3
Scale fixing kills RG running Dynamics Interpretation/Proposal 5
Collapse = Golay snapping Epistemics Interpretation 5
Born rule from Golay quadratic form Consistency Missing theorem 6
$SU(3)$ as physical QCD color Consistency Gap — may be permanent 6
Redshift as off-axis projection Phenomenology Speculative interpretation 5–6
CKM/PMNS structure Phenomenology Missing 6
First hard numerical prediction: $\sin^2\theta_W = 3/8$ (tree level) Phenomenology Derived 3