QFunity & Epinomis: The Modern Desmos | Relational Unification

QFunity as the Modern Desmos Epinomique

Bridging Ethic Article (Nov 2025) with Emergent Pre-Temporal in QFunity

1. The Ethic Article Context – November 2025

Key Concepts from « Ampliar lo posible: Epinomis y la metafísica de la complejidad cuántica »

The article revives the Epinomic Desmos as a relational link accepting fundamental incommensurability between quantum and gravitational domains. It emphasizes asymmetry as constitutive principle, active geometry/information (holographic), and the participating observer dissolving subject/object boundary.

External Reference:

Ethic Article (2025)

The article calls for a modern Desmos: QFunity provides it via EPT relational non-commutativity.

2. The Core of QFunity: Emergent Pre-Temporal State (EPT)

EPT Definition & Mathematical Foundation

EPT is the acausal, pre-geometric, fractal substrate: EPT = {B^ϵ, V^ϵ} with initial commutativity.

\[\boxed{\text{EPT} = \{ \hat{B}^\epsilon, \hat{V}^\epsilon \} \quad \text{with} \quad [\hat{B}^\epsilon, \hat{V}^\epsilon] = 0 \quad (t < 0)}\]

Operators

\(\hat{B}^\epsilon\): Torsion-Rotation operator (Pillar 1)
\(\hat{V}^\epsilon\): Vibrational potential (Pillar 2)
Observer scale \(\epsilon\) (Pillar 3): \(\epsilon \in [\ell_P, 10^{20}\,\text{m}]\)

Links: EPT Page • Rotation

EPT as the concrete Desmos: relational core unifying domains without reduction.

3. Symmetry Breaking & Emergence of Time – The Relational Desmos

Non-Commutativity as the Epinomic Link

Critical symmetry breaking triggers time and causality via non-commutativity.

\[\boxed{i\hbar \frac{\partial}{\partial t} \equiv [\hat{B}^\epsilon, \hat{V}^\epsilon]}\]

\[\boxed{\lim_{\epsilon \to 0^+} [\hat{B}^\epsilon \hat{V}^\epsilon – \hat{V}^\epsilon \hat{B}^\epsilon] \Psi_{\text{EPT}} = \Lambda \cdot \frac{\Psi_{\text{EPT}}}{\sqrt{\|\Psi_{\text{EPT}}\|^2 + \epsilon^2}}}\]

This commutator defines the Desmos: quantum & gravity emerge as different projections of the same relation.

Perfect mathematical embodiment of relational unity accepting incommensurability.

4. Asymmetry as Constitutive Principle

« Zero Does Not Exist » Pillar

Asymmetry is fundamental; no exact zero → no singularities, no perfect symmetry.

\[\boxed{\Lambda_{\text{eff}} = \Lambda_{\text{EPT}} \frac{\|\Psi\|^2 + \epsilon^2}{\|\Psi\|^2 + \epsilon^2}}\]

Dark matter as torsional shadows; matter/antimatter asymmetry inherited from EPT.

Asymmetry is structural → aligns precisely with Ethic’s constitutive view.

5. Active Geometry & Information – Holographic Emergence

Scale-Dependent Emergent Metric

\[\boxed{g_{\mu\nu}(\epsilon) = g_{\mu\nu}^{\text{GR}} + \frac{\ell_P^2}{\epsilon^2} g_{\mu\nu}^{\text{LQG}} + \alpha’ \cdot g_{\mu\nu}^{\text{strings}}}\]

EPT fractal dimension \(D_f \approx 2.718\) encodes information → natural holographic principle.

Geometry actively organizes information from fractal EPT substrate.

6. The Participating Observer in QFunity

Scale ϵ as Dynamic Parameter

\[\boxed{P_{\text{collapse}} = \frac{|\langle \phi | \psi \rangle|^2}{\|\Psi\|^2 + \epsilon^2}}\]

Observer scale ϵ regulates measurement & causality perception (acausal at Planck → causal at macro).

Observer is integral participant → dissolves subject/object boundary mathematically.

7. Synthesis: Ethic Concepts vs QFunity Formalization

Ethic Concept	Metaphysical Description	QFunity Formalization
Desmos Epinomique	Relational link accepting incommensurability	[B^ϵ, V^ϵ] ≠ 0 → time & reality emergence
Asymmetry Constitutive	Source of order & complexity	« Zero does not exist » + Λ_eff relic
Active Geometry/Info	Holographic encoding	Fractal EPT D_f ≈ 2.718 + g_μν(ϵ)
Participating Observer	Dissolves subject/object	ϵ in all equations + regularized collapse

8. Predictions & Testable Implications

Fractal signatures in CMB: C(θ) ∝ θ^{-0.718}
Torsional GW spectrum: Ω_GW(f) ∝ f^{1.436}
Extended emergence time for JWST galaxies.

Testable with future CMB precision, GW detectors, high-energy experiments.

Link: Grok Validation 2025

QFunity operationalizes Ethic’s metaphysical vision into falsifiable physics.

References & Links

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