Difference between revisions of "Paper Symbols"
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=== Instantaneous configuration === | === Instantaneous configuration === | ||
| − | <!--no latex--><span class="tex">σ = (A, n, χ, u)<sub>instantaneous</sub></span><!--/no latex--><!--latex:\[ \sigma = (A,\,n,\,\chi,\,u)_{\mathrm{instantaneous}} | + | <!--no latex--><span class="tex">σ = (A, n, χ, u)<sub>instantaneous</sub></span><!--/no latex--><!--latex:\[ \sigma = (A,\,n,\,\chi,\,u)_{\mathrm{instantaneous}}\]--> |
| − | \]--> | + | |
=== Statistical configuration === | === Statistical configuration === | ||
| Line 78: | Line 77: | ||
<!--no latex--><span class="tex">EA = (ΔP<sub>A</sub>, ΔP<sub>n</sub>, ΔP<sub>χ</sub>, ΔP<sub>u</sub>)</span><!--/no latex--><!--latex:\[EA = (\Delta P_{A},\,\Delta P_{n},\,\Delta P_{\chi},\,\Delta P_{u})\]--> | <!--no latex--><span class="tex">EA = (ΔP<sub>A</sub>, ΔP<sub>n</sub>, ΔP<sub>χ</sub>, ΔP<sub>u</sub>)</span><!--/no latex--><!--latex:\[EA = (\Delta P_{A},\,\Delta P_{n},\,\Delta P_{\chi},\,\Delta P_{u})\]--> | ||
| − | + | <!--no latex--><span class="tex"><b>EA = (ΔP<sub>A</sub>, ΔP<sub>n</sub>, ΔP<sub>χ</sub>, ΔP<sub>u</sub>)</b></span><!--/no latex--><!--latex:\[\mathbf{EA} = (\mathbf{\Delta P_{A}},\,\mathbf{\Delta P_{n}},\,\mathbf{\Delta P_{\chi}},\,\mathbf{\Delta P_{u}})\]--> | |
| − | <!--no latex--><span class="tex">ΔP<sub> | + | <!--no latex--><span class="tex"><b>ΔP<sub>A</sub>, ΔP<sub>n</sub>, ΔP<sub>χ</sub>, ΔP<sub>u</sub></b></span><!--/no latex--><!--latex:\[\mathbf{\Delta P_{A}},\,\mathbf{\Delta P_{n}},\,\mathbf{\Delta P_{\chi}},\,\mathbf{\Delta P_{u}}\]--> |
| − | \[ | + | <!--no latex--><span class="tex">ΔP<sub>A</sub></span><!--/no latex--><!--latex:\[\Delta P_{A}\]--> |
| − | \Delta P_{ | + | <!--no latex--><span class="tex"><b>ΔP<sub>A</sub></b></span><!--/no latex--><!--latex:\[\mathbf{\Delta P_{A}}\]--> |
| − | + | ||
| − | \ | + | |
| − | \] | + | |
| − | --> | + | <!--no latex--><span class="tex">ΔP<sub>n</sub></span><!--/no latex--><!--latex:\[\Delta P_{n}\]--> |
| + | <!--no latex--><span class="tex"><b>ΔP<sub>n</sub></b></span><!--/no latex--><!--latex:\[\mathbf{\Delta P_{n}}\]--> | ||
| + | |||
| + | <!--no latex--><span class="tex">ΔP<sub>χ</sub></span><!--/no latex--><!--latex:\[\Delta P_{\chi}\]--> | ||
| + | <!--no latex--><span class="tex"><b>ΔP<sub>χ</sub></b></span><!--/no latex--><!--latex:\[\mathbf{\Delta P_{\chi}}\]--> | ||
| + | |||
| + | <!--no latex--><span class="tex">ΔP<sub>u</sub></span><!--/no latex--><!--latex:\[\Delta P_{u}\]--> | ||
| + | <!--no latex--><span class="tex"><b>ΔP<sub>u</sub></b></span><!--/no latex--><!--latex:\[\mathbf{\Delta P_{u}}\]--> | ||
| + | |||
| + | <!--no latex--><span class="tex">ΔP<sub>𝓲</sub> = τ<sub>𝓲</sub><sup>actual</sup> − τ<sub>𝓲</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:\[\Delta P_{\mathcal{i}} = \tau_{\mathcal{i}}^{\mathrm{actual}} - \tau_{\mathcal{i}}^{(\mathrm{stochastically\ symmetric})}\]--> | ||
| + | |||
| + | Stochastically symmetric => Stochastically symmetric reference τ(σ) distribution | ||
| + | |||
| + | When symmetry holds: | ||
| + | <!--no latex--><span class="tex">ΔP<sub>𝓲</sub> = 0</span><!--/no latex--><!--latex:\[\Delta P_{\mathcal{i}} = 0\]--> | ||
| + | |||
| + | When symmetry is broken: | ||
| + | <!--no latex--><span class="tex">ΔP<sub>𝓲</sub> ≠ 0</span><!--/no latex--><!--latex:\[\Delta P_{\mathcal{i}} \neq 0\]--> | ||
| + | |||
| + | <!--no latex--><span class="tex">(A, n, χ, u)</span><!--/no latex--><!--latex:\[(A,\,n,\,\chi,\,u)\]--> | ||
=== Modes / Components === | === Modes / Components === | ||
Latest revision as of 23:44, 14 July 2026
Contents
The Primary Source of Reality
Fundamental Force (FF)
F₀
Elementary Field (EF)
𝓕
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
kA — intensity resistance
kn — linear‑orientation resistance
kχ — chirality‑reorientation resistance
ku — intrinsic‑angular‑orientation resistance
{kA — intensity‑resistance, kn — linear‑orientation resistance, kχ — chirality‑reorientation resistance, ku — intrinsic‑angular‑orientation resistance}
{kA, kn, kχ, ku}
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)
EA = (ΔPA, ΔPn, ΔPχ, ΔPu)
ΔPA, ΔPn, ΔPχ, ΔPu
ΔPA ΔPA
ΔPn ΔPn
ΔPχ ΔPχ
ΔPu ΔPu
ΔP𝓲 = τ𝓲actual − τ𝓲stochastically symmetric
Stochastically symmetric => Stochastically symmetric reference τ(σ) distribution
When symmetry holds: ΔP𝓲 = 0
When symmetry is broken: ΔP𝓲 ≠ 0
(A, n, χ, u)
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
