Difference between revisions of "Paper Symbols"
From Evolutionary Knowledge Base
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=== Elementary Field (EF) === | === Elementary Field (EF) === | ||
| − | <!--no latex--><span class="tex">𝓕 = F₀(A, n, χ, u; k<sub>A</sub>, k<sub>n</sub>, k<sub>χ</sub>, k<sub>u</sub>)</span><!--/no latex--><!--latex:\[\mathcal{F} = F_{0}(A,n,\chi,u;\,k_{A},k_{n},k_{\chi},k_{u})\]--> | + | <!--no latex--><span class="tex">𝓕 = F₀ (A, n, χ, u; k<sub>A</sub>, k<sub>n</sub>, k<sub>χ</sub>, k<sub>u</sub>)</span><!--/no latex--><!--latex:\[\mathcal{F} = F_{0}(A,n,\chi,u;\,k_{A},k_{n},k_{\chi},k_{u})\]--> |
==== Structure of resistances ==== | ==== Structure of resistances ==== | ||
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<!--no latex--><span class="tex"> | <!--no latex--><span class="tex"> | ||
k<sub>𝓲</sub> = k<sub>𝓲</sub><sup>(intrinsic)</sup> + k<sub>𝓲</sub><sup>(dynamic)</sup>, 𝓲 ∈ {A,n,χ,u} | k<sub>𝓲</sub> = k<sub>𝓲</sub><sup>(intrinsic)</sup> + k<sub>𝓲</sub><sup>(dynamic)</sup>, 𝓲 ∈ {A,n,χ,u} | ||
| − | </span><!--/no latex--><!--latex: | + | </span><!--/no latex--><!--latex:\[k_{\mathcal{i}} = k_{\mathcal{i}}^{(\mathrm{intrinsic})} + k_{\mathcal{i}}^{(\mathrm{dynamic})}, \qquad \mathcal{i} \in \{A,\,n,\,\chi,\,u\}\]--> |
| − | + | ||
| − | \[ | + | |
| − | k_{\mathcal{i}} = k_{\mathcal{i}}^{(\mathrm{intrinsic})} + k_{\mathcal{i}}^{(\mathrm{dynamic})}, | + | |
| − | \qquad | + | |
| − | \mathcal{i} \in \{A,\,n,\,\chi,\,u\} | + | |
| − | \] | + | |
| − | + | ||
| − | --> | + | |
==== Resistance parameters ==== | ==== Resistance parameters ==== | ||
<!--no latex--><span class="tex">k<sub>A</sub>, k<sub>n</sub> — proto‑stress resistances</span><br/> | <!--no latex--><span class="tex">k<sub>A</sub>, k<sub>n</sub> — proto‑stress resistances</span><br/> | ||
| − | <span class="tex">k<sub>χ</sub>, k<sub>u</sub> — proto‑vorticity resistances</span><!--/no latex--><!--latex: | + | <span class="tex">k<sub>χ</sub>, k<sub>u</sub> — proto‑vorticity resistances</span><!--/no latex--><!--latex:\[k_{A},\,k_{n}\ \text{— proto‑stress resistances} |
| − | + | \] \[k_{\chi},\,k_{u}\ \text{— proto‑vorticity resistances}\]--> | |
| − | \[ | + | |
| − | k_{A},\,k_{n}\ \text{— proto‑stress resistances} | + | |
| − | \] | + | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | \[ | + | |
| − | k_{\chi},\,k_{u}\ \text{— proto‑vorticity resistances} | + | |
| − | \] | + | |
| − | + | ||
| − | --> | + | |
==== Operational hypotheses (to be refined) ==== | ==== Operational hypotheses (to be refined) ==== | ||
| − | <!--no latex--><span class="tex">k<sub>χ</sub> ≈ ε<sub>0</sub></span><br/> | + | <!--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:\[ |
| − | <span class="tex">k<sub>u</sub> ≈ μ<sub>0</sub></span><!--/no latex--><!--latex: | + | k_{\chi} \approx \varepsilon_{0}\] \[k_{u} \approx \mu_{0}\]--> |
| − | + | ||
| − | \[ | + | |
| − | k_{\chi} \approx \varepsilon_{0} | + | |
| − | \] | + | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | \[ | + | |
| − | k_{u} \approx \mu_{0} | + | |
| − | \] | + | |
| − | + | ||
| − | --> | + | |
== Event-point(s) (EP) == | == Event-point(s) (EP) == | ||
Revision as of 22:19, 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
