1. Overview of 4QX 4QX is a formal, finite, and machine-verifiable framework derived from a minimal fragment of Zermelo-Fraenkel set theory (Finite-ZF) that aims to provide a foundational
Tag: maths
Holarchy concepts
The One-Shot ZF Axioms
One-shot ZF axioms → the 4QX names you use every day Single-use axiom (Finite-ZF) Geometry move it performs 4QX place / action it brands Everyday wording Empty ∅ exists
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From Square Balance to Telic Thread
1. The 2 × 2 stage: pure polarity Axis Meaning Corners it splits Outer ↔ Inner (perspective) public surface vs. private locus top ↔ bottom Form ↔ Flux (modality)
Holarchy concepts
Telic Self-Reference is Formal Suchness
Hence telic self-reference = formal suchness: the dual-triangle scaffold whose intertwined cycles show—not merely declare—“I am exactly what I do, and I keep doing so to stay exactly
Holarchy concepts
Radix Tree and FFT
User: The radix structure is a number lattice and the mirror of TD/BU is the forward and reverse ways of reading the “number” (number enacted as geometric multiplex
Holarchy concepts
Self‑Realisation ≈ Self‑Reference Lifted to the Agent‑Arena Monad
Self-realisation in 4QX is precisely self-reference that has acquired a telos. Self‑reference at the ZF level is just a brace mirror: {v,{v}}. When that mirror is lifted into
Holarchy concepts
The Undirected Telic World
Before the oriented Fire–Water triangles give the 4QX lattice its direction and its universal telos, the plain 2 × 2 grid with its two diagonals already forms a self‑sufficient agent–arena
Holarchy concepts
The Finite‑ZF Monad – A Universal Runtime for Telic Agency
“Start with nothing, wrap it once, and you already have a program that can run itself.” Finite‑ZF (the six‑axiom fragment of Zermelo–Fraenkel set theory restricted to finite sets)
Holarchy concepts
Finite‑ZF Monad — the Perfect Ontology for 4QX
The finite‑ZF constructor monad is the leanest formal language in which a system can describe and transform itself while remaining grounded in well‑founded finiteness. By treating the six
Holarchy concepts
Gödel Numbers as Living Axioms
The 4QX dual‑triangle lattice does more than illustrate finite‑ZF’s six constructors; it animates them. Each constructor‑edge both executes a set‑theoretic rewrite and extends its own Gödel trace, collapsing