Difference between revisions of "Paper Symbols"

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<!--no latex--><span class="tex">k<sub>𝓲</sub> = k<sub>𝓲</sub><sup>intr</sup> + k<sub>𝓲</sub><sup>dyn</sup></span><!--/no latex--><!--latex:\[k_{\mathcal{i}} = k_{\mathcal{i}}^{\mathrm{intr}} + k_{\mathcal{i}}^{\mathrm{dyn}}\]-->
 
<!--no latex--><span class="tex">k<sub>𝓲</sub> = k<sub>𝓲</sub><sup>intr</sup> + k<sub>𝓲</sub><sup>dyn</sup></span><!--/no latex--><!--latex:\[k_{\mathcal{i}} = k_{\mathcal{i}}^{\mathrm{intr}} + k_{\mathcal{i}}^{\mathrm{dyn}}\]-->
 +
 +
==== Resistance parameters ====
 +
 +
<!--no latex--><span class="tex">k<sub>A</sub>, k<sub>n</sub> — proto‑stress resistances</span><br/>
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<span class="tex">k<sub>χ</sub>, k<sub>u</sub> — proto‑vorticity resistances</span><!--/no latex--><!--latex:
 +
 +
 +
\[
 +
k_{A},\,k_{n}\ \text{— proto‑stress resistances}
 +
\]
 +
 +
 +
 +
 +
\[
 +
k_{\chi},\,k_{u}\ \text{— proto‑vorticity resistances}
 +
\]
 +
 +
 +
-->
 +
 +
==== Structure of resistances ====
 +
 +
<!--no latex--><span class="tex">k<sub>x</sub> = k<sub>x</sub><sup>(intr)</sup> + k<sub>x</sub><sup>(dyn)</sup>,\; x ∈ {A,n,χ,u}</span><!--/no latex--><!--latex:
 +
 +
 +
\[
 +
k_{x} = k_{x}^{(\mathrm{intr})} + k_{x}^{(\mathrm{dyn})},
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\qquad
 +
x \in \{A,\,n,\,\chi,\,u\}
 +
\]
 +
 +
 +
-->
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 +
==== Operational hypotheses (to be refined) ====
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 +
<!--no latex--><span class="tex">k<sub>χ</sub> ≈ ε<sub>0</sub></span><br/>
 +
<span class="tex">k<sub>u</sub> ≈ μ<sub>0</sub></span><!--/no latex--><!--latex:
 +
 +
 +
\[
 +
k_{\chi} \approx \varepsilon_{0}
 +
\]
 +
 +
 +
 +
 +
\[
 +
k_{u} \approx \mu_{0}
 +
\]
 +
 +
 +
-->
  
 
== Event-point(s) (EP) ==
 
== Event-point(s) (EP) ==

Revision as of 19:30, 13 July 2026

The Primary Source of Reality

Fundamental Force (FF)

F₀

Elementary Field (EF)

𝓕 = F₀(A, n, χ, u; kA, kn, kχ, ku)

Total resistances

k𝓲 = k𝓲intr + k𝓲dyn

Resistance parameters

kA, kn — proto‑stress resistances
kχ, ku — proto‑vorticity resistances

Structure of resistances

kx = kx(intr) + kx(dyn),\; x ∈ {A,n,χ,u}

Operational hypotheses (to be refined)

kχ ≈ ε0
ku ≈ μ0

Event-point(s) (EP)

nn

Elementary Events (EE)

EE(𝑥,τ)= δ𝓕(𝑥,τ)

Response of the Field

EE(𝑥,τ)= δ𝓕(𝑥,τ) = Resp𝓕(𝑥,τ; F₀, kA, kn, kχ, ku)

Decomposition

EE = {A, n, χ, u}

Instantaneous configuration

σ = (A, n, χ, u)ist

Statistical configuration

(A(τ), n(τ), χ(τ), u(τ))

Elementary Action

EA = (ΔPA, ΔPn, ΔPχ, ΔPu)

ΔP𝓲 = τ𝓲actual − τ𝓲stochastically\ symmetric

Modes / Components

  • Perturbation: ΔPA = τAactual − τAstochastically symmetric
  • Translation: ΔPn = τnactual − τnstochastically symmetric
  • Rotation:Chirality: ΔPχ = τχactual − τχstochastically symmetric
  • Rotation:AxisOrientation: ΔPu = τuactual − τustochastically symmetric

Information / Energy (Potentials Φ)

Equilibrium conditions

𝓒M = 𝓒(ΔPA) = 0

𝓒A = 𝓒(ΔPn) = 0

𝓒E = 𝓒(ΔPχ) = 0

𝓒B = 𝓒(ΔPu) = 0

Diffuse solutions

ΦM, ΦA, ΦE, ΦB ∈ Sol(𝓒)

InfoStructures

Wave‑like InfoStructures

Derived from

ΔPn, ΔPu

Equilibrium condition

𝓒wave(ΔPn, ΔPu) = 0

Proto‑wave equation

𝓦[Ψ; ΔPn, ΔPu] = 0

Vortex‑like InfoStructures

Derived from

ΔPA, ΔPn, ΔPχ, ΔPu

Equilibrium condition

𝓒vortex(ΔPA, ΔPn, ΔPχ, ΔPu) = 0

Proto‑vortex equation

𝓥[Ξ; ΔPA, ΔPn, ΔPχ, ΔPu] = 0

Interaction‑mediating InfoStructures

Relational equilibrium

𝓒int(Ψ, Ξ) = 0

Proto‑interaction equation

𝓘[Ψ, Ξ] = 0

Geometric Projection

Wave projection

Proj(𝓦) → QM wave equations

Vortex projection

Proj(𝓥) → spinor equations

Interaction projection

Proj(𝓘) → gauge equations

Forms

No new fundamental equation