Difference between revisions of "Paper Symbols"
From Evolutionary Knowledge Base
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== Elementary Events (EE) == | == Elementary Events (EE) == | ||
| − | <!--no latex--><span class="tex">EE(𝑥,τ)= δ𝓕(𝑥,τ)</span><!--/no latex--><!--latex: | + | <!--no latex--><span class="tex">EE(𝑥,τ)= δ𝓕(𝑥,τ)</span><!--/no latex--><!--latex:\[EE(\mathit{x},\tau)=\delta\mathcal{F}(\mathit{x},\tau)\]--> |
| − | + | ||
| − | \[ | + | |
| − | EE(\mathit{x},\tau)=\delta\mathcal{F}(\mathit{x},\tau) | + | |
| − | \] | + | |
| − | + | ||
| − | --> | + | |
=== Response of the Field === | === Response of the Field === | ||
| − | <!--no latex--><span class="tex"> | + | <!--no latex--><span class="tex">EE(𝑥,τ)= δ𝓕(𝑥,τ) = Resp<sub>𝓕</sub>(𝑥,τ; F₀, k<sub>A</sub>, k<sub>n</sub>, k<sub>χ</sub>, k<sub>u</sub>)</span><!--/no latex--><!--latex:\[EE(\mathit{x},\tau)= \delta\mathcal{F}(\mathit{x},\tau) = \mathrm{Resp}_{\mathcal{F}}\!\left(\mathit{x},\tau;\,F_{0},k_{A},k_{n},k_{\chi},k_{u}\right)\]--> |
| − | EE(𝑥,τ)= δ𝓕(𝑥,τ) | + | |
| − | = Resp<sub>𝓕</sub>(𝑥,τ; F₀, k<sub>A</sub>, k<sub>n</sub>, k<sub>χ</sub>, k<sub>u</sub>) | + | |
| − | </span><!--/no latex--><!--latex: | + | |
| − | + | ||
| − | \[ | + | |
| − | EE(\mathit{x},\tau)= \delta\mathcal{F}(\mathit{x},\tau)= | + | |
| − | \mathrm{Resp}_{\mathcal{F}}\!\left(\mathit{x},\tau;\,F_{0},k_{A},k_{n},k_{\chi},k_{u}\right) | + | |
| − | \] | + | |
| − | + | ||
| − | --> | + | |
=== Decomposition === | === Decomposition === | ||
| − | <!--no latex--><span class="tex">EE = {A, n, χ, u}</span><!--/no latex--><!--latex: | + | <!--no latex--><span class="tex">EE = {A, n, χ, u}</span><!--/no latex--><!--latex:\[EE = \{A,\,n,\,\chi,\,u\}\]--> |
| − | + | ||
| − | \[ | + | |
| − | EE = \{A,\,n,\,\chi,\,u\} | + | |
| − | \] | + | |
| − | + | ||
| − | --> | + | |
=== Instantaneous configuration === | === Instantaneous configuration === | ||
| − | <!--no latex--><span class="tex">σ = (A, n, χ, u)<sub>instantaneous</sub></span><!--/no latex--><!--latex: | + | <!--no latex--><span class="tex">σ = (A, n, χ, u)<sub>instantaneous</sub></span><!--/no latex--><!--latex:\[ \sigma = (A,\,n,\,\chi,\,u)_{\mathrm{instantaneous}} |
| − | + | \]--> | |
| − | \[ | + | |
| − | \sigma = (A,\,n,\,\chi,\,u)_{\mathrm{instantaneous}} | + | |
| − | \] | + | |
| − | + | ||
| − | --> | + | |
=== Statistical configuration === | === Statistical configuration === | ||
| − | <!--no latex--><span class="tex">(A(τ), n(τ), χ(τ), u(τ))</span><!--/no latex--><!--latex: | + | <!--no latex--><span class="tex">(A(τ), n(τ), χ(τ), u(τ))</span><!--/no latex--><!--latex:\[(A(\tau),\,n(\tau),\,\chi(\tau),\,u(\tau))\]--> |
| − | + | ||
| − | \[ | + | |
| − | (A(\tau),\,n(\tau),\,\chi(\tau),\,u(\tau)) | + | |
| − | \] | + | |
| − | + | ||
| − | --> | + | |
== Elementary Action == | == Elementary Action == | ||
Revision as of 22:21, 13 July 2026
Contents
The Primary Source of Reality
Fundamental Force (FF)
F₀
Elementary Field (EF)
𝓕 = F₀ (A, n, χ, u; kA, kn, kχ, ku)
Structure of resistances
k𝓲 = k𝓲(intrinsic) + k𝓲(dynamic), 𝓲 ∈ {A,n,χ,u}
Resistance parameters
kA, kn — proto‑stress resistances
kχ, ku — proto‑vorticity resistances
Operational hypotheses (to be refined)
kχ ≈ ε0
ku ≈ μ0
Event-point(s) (EP)
EP = infinitesimal analytical sampling locus of the Field at label 𝑥
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)instantaneous
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)
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
