ICT · PrincipiaInstitute for Constructivist Theory
CONCEPT PAGE · DRAFT DEV
QCD Central

QCD must be fully reconstructed to actually be a Lie-algebraic solution.

The standard 8-λ (Gell-Mann matrix) method obeys the same mathematical rules as a Lie algebra, but QCD as practiced is not one — it has no geometric representation. The Hermitian-adjoint shortcut for anti-particles is excluded a-priori by the Harari–Seiberg causality criterion, so experimental-math extensions of the current 8-λ methods are doomed from the start. The ICT reconstruction proceeds in three stages, arrayed left to right below.

1QCD

the single corner cubie

One corner cubie replaces one λ-matrix. Each cubie carries three states ( + / 0 / − ), which handles particle, neutral, and anti-particle configurations geometrically — no Hermitian adjoint required.

λa  ⟶  ca ∈ { +, 0, − }

Illustrates

  • Tri-state cubie as the fundamental construction unit
  • Causality-safe anti-particle representation
  • The basic vocabulary of the constructivist picture

2QCD

paired-cubie interactions

Two cubies in interaction: state exchanges along shared edges model gluon-like couplings. This is where the communication problem with the standard picture becomes visible — the algebra of exchanges is constructive, not matrix-multiplicative.

ca ⊗ cb ⟶ exchange(edgeab)

Illustrates

  • Edge-exchange as the interaction mechanism
  • Why matrix commutators mis-count physical states
  • The bridge from 1-cubie vocabulary to full geometry

3QCD

the full 8-corner reconstruction

All eight corner cubies assembled: the complete geometric replacement of the 8-λ method. A genuine geometric representation — hence a genuine Lie-algebraic solution — with the proton as its first physical target.

{ λ₁ … λ₈ }  ⟶  { c₁ … c₈ }³

Illustrates

  • The reconstructed algebra, corners labeled c1–c8
  • 3⁸ state space vs. the 8-λ adjoint shortcut
  • Foundation for the Proton Video (below)
Window / New Work at Various Scales

Where this program applies — and where it deliberately does not

ICT constructions apply at the QCD and QWD levels only. Nuclei belong to the QED scale; the Proton Video (below) is the flagship illustration at the QCD scale. Planck-scale geometries are strictly a-priori gedanken exercises and remain outside the working program. Each scale's draft dev page carries its governing equations and a rough current-problems list — select them from the Fundamental-Formula slider on the landing page.

[ PROTON VIDEO — placeholder slot · QCD scale · VV important ]

<video controls width="720" src="proton.mp4"></video> — drop the file in and replace this box