Difference between revisions of "Paper Symbols"

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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</span><!--/no latex--><!--latex:\[\mathcal{F}\]-->
  
−
==== Total resistances ====
+
<!--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">k<sub>𝓲</sub> = k<sub>𝓲</sub><sup>intr</sup> + k<sub>𝓲</sub><sup>dyn</sup></span><!--/no latex--><!--latex:\[k_{\mathcal{i}} = k_{\mathcal{i}}^{\mathrm{intr}} + k_{\mathcal{i}}^{\mathrm{dyn}}\]-->
+
==== Structure of resistances ====
 +
 
 +
<!--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}
 +
</span><!--/no latex--><!--latex:\[k_{\mathcal{i}} = k_{\mathcal{i}}^{(\mathrm{intrinsic})} + k_{\mathcal{i}}^{(\mathrm{dynamic})}, \qquad \mathcal{i} \in \{A,\,n,\,\chi,\,u\}\]-->
 +
 
 +
==== Resistance parameters ====
 +
 
 +
<!--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:\[k_{A},\,k_{n}\ \text{— proto‑stress resistances}
 +
\] \[k_{\chi},\,k_{u}\ \text{— proto‑vorticity resistances}\]-->
 +
 
 +
<!--no latex--><span class="tex">k<sub>A</sub> — intensity resistance</span><!--/no latex--><!--latex:\[k_{A}\ \text{— intensity resistance}\]-->
 +
 
 +
<!--no latex--><span class="tex">k<sub>n</sub> — linear‑orientation resistance</span><!--/no latex--><!--latex:\[k_{n}\ \text{— linear‑orientation resistance}\]
 +
-->
 +
 
 +
<!--no latex--><span class="tex">k<sub>χ</sub> — chirality‑reorientation resistance</span><!--/no latex--><!--latex:\[k_{\chi}\ \text{— chirality‑reorientation resistance}\]-->
 +
 
 +
<!--no latex--><span class="tex">k<sub>u</sub> — intrinsic‑angular‑orientation resistance</span><!--/no latex--><!--latex:\[k_{u}\ \text{— intrinsic‑angular‑orientation resistance}\]-->
 +
 
 +
{<!--no latex--><span class="tex">k<sub>A</sub> — intensity‑resistance</span><!--/no latex--><!--latex:\[k_{A}\ \text{— intensity‑resistance}\]-->, <!--no latex--><span class="tex">k<sub>n</sub> — linear‑orientation resistance</span><!--/no latex--><!--latex:\[k_{n}\ \text{— linear‑orientation resistance}\]-->, <!--no latex--><span class="tex">k<sub>χ</sub> — chirality‑reorientation resistance</span><!--/no latex--><!--latex:\[k_{\chi}\ \text{— chirality‑reorientation resistance}\]-->, <!--no latex--><span class="tex">k<sub>u</sub> — intrinsic‑angular‑orientation resistance</span><!--/no latex--><!--latex:\[k_{u}\ \text{— intrinsic‑angular‑orientation resistance}\]-->}
 +
 
 +
{<!--no latex--><span class="tex">k<sub>A</sub></span><!--/no latex--><!--latex:\[k_{A}\]-->, <!--no latex--><span class="tex">k<sub>n</sub></span><!--/no latex--><!--latex:\[k_{n}\]-->, <!--no latex--><span class="tex">k<sub>χ</sub></span><!--/no latex--><!--latex:\[k_{\chi}\]-->, <!--no latex--><span class="tex">k<sub>u</sub></span><!--/no latex--><!--latex:\[k_{u}\]-->}
 +
 
 +
==== Operational hypotheses (to be refined) ====
 +
 
 +
<!--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) ==
  
−
nn
+
<!--no latex--><span class="tex">
 +
EP = infinitesimal analytical sampling locus of the Field at label 𝑥
 +
</span><!--/no latex--><!--latex:
 +
 
 +
\[
 +
EP = \text{infinitesimal analytical sampling locus of the Field at label }\mathit{x}
 +
\]
 +
 
 +
-->
  
 
== Elementary Events (EE) ==
 
== Elementary Events (EE) ==
  
−
<!--no latex--><span class="tex">EE(𝑥,τ)= δ𝓕(𝑥,τ)</span><!--/no latex--><!--latex:\[EE(𝑥,\tau)=\delta\mathcal{F}(𝑥,\tau)\]-->
+
<!--no latex--><span class="tex">EE(𝑥,τ)= δ𝓕(𝑥,τ)</span><!--/no latex--><!--latex:\[EE(\mathit{x},\tau)=\delta\mathcal{F}(\mathit{x},\tau)\]-->
  
 
=== 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:\[EE(x,\tau)= \delta\mathcal{F}(x,\tau)= \mathrm{Resp}_{\mathcal{F}}\!\left(x,\tau;\,F_{0},k_{A},k_{n},k_{\chi},k_{u}\right)\]-->
+
  
−
=== Aspects ===
+
=== Decomposition ===
  
−
?
+
<!--no latex--><span class="tex">EE = {A, n, χ, u}</span><!--/no latex--><!--latex:\[EE = \{A,\,n,\,\chi,\,u\}\]-->
 +
 
 +
=== Instantaneous configuration ===
 +
 
 +
<!--no latex--><span class="tex">σ = (A, n, χ, u)<sub>instantaneous</sub></span><!--/no latex--><!--latex:\[ \sigma = (A,\,n,\,\chi,\,u)_{\mathrm{instantaneous}}\]-->
 +
 
 +
=== Statistical configuration ===
 +
 
 +
<!--no latex--><span class="tex">(A(τ), n(τ), χ(τ), u(τ))</span><!--/no latex--><!--latex:\[(A(\tau),\,n(\tau),\,\chi(\tau),\,u(\tau))\]-->
  
 
== Elementary Action ==
 
== Elementary Action ==
Line 36: 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">ΔP<sub>𝓲</sub> = τ<sub>𝓲</sub><sup>actual</sup> − τ<sub>𝓲</sub><sup>stoch.sym.</sup></span><!--/no latex--><!--latex:
+
<!--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"><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:\[\Delta P_{A}\]-->
 +
<!--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 ===
 +
 
 +
* Perturbation: <!--no latex--><span class="tex">ΔP<sub>A</sub> = τ<sub>A</sub><sup>actual</sup> − τ<sub>A</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:\[\Delta P_{A} = \tau_{A}^{\mathrm{actual}} -
 +
\tau_{A}^{(\mathrm{stochastically\ symmetric})}\]-->
 +
 
 +
* Translation: <!--no latex--><span class="tex">ΔP<sub>n</sub> = τ<sub>n</sub><sup>actual</sup> − τ<sub>n</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:\[\Delta P_{n} =
 +
\tau_{n}^{\mathrm{actual}} -\tau_{n}^{(\mathrm{stochastically\ symmetric})}\]-->
 +
 
 +
* Rotation: Chirality: <!--no latex--><span class="tex">ΔP<sub>χ</sub> = τ<sub>χ</sub><sup>actual</sup> − τ<sub>χ</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:\[\Delta P_{\chi} =
 +
\tau_{\chi}^{\mathrm{actual}} -\tau_{\chi}^{(\mathrm{stochastically\ symmetric})}\]-->
 +
 
 +
* Rotation: AxisOrientation: <!--no latex--><span class="tex">ΔP<sub>u</sub> = τ<sub>u</sub><sup>actual</sup> − τ<sub>u</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:\[\Delta P_{u} =
 +
\tau_{u}^{\mathrm{actual}} -\tau_{u}^{(\mathrm{stochastically\ symmetric})}\]-->
 +
 
 +
== Information / Energy (Potentials) ==
 +
 
 +
=== Equilibrium conditions ===
 +
 
 +
<!--no latex--><span class="tex">𝓒<sub>M</sub> = 𝓒(ΔP<sub>A</sub>) = 0</span><!--/no latex--><!--latex:
  
 
\[
 
\[
−
\Delta P_{\mathcal{i}}
+
\mathcal{C}_{M} = \mathcal{C}(\Delta P_{A}) = 0
−
= \tau_{\mathcal{i}}^{\mathrm{actual}}
+
−
- \tau_{\mathcal{i}}^{(\mathrm{stoch.\ sym.})}
+
 
\]
 
\]
  
 
-->
 
-->
  
−
<!--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:
+
<!--no latex--><span class="tex">𝓒<sub>A</sub> = 𝓒(ΔP<sub>n</sub>) = 0</span><!--/no latex--><!--latex:
  
 
\[
 
\[
−
\Delta P_{\mathcal{i}}
+
\mathcal{C}_{A} = \mathcal{C}(\Delta P_{n}) = 0
−
= \tau_{\mathcal{i}}^{\mathrm{actual}}
+
−
- \tau_{\mathcal{i}}^{(\mathrm{stochastically\ symmetric})}
+
 
\]
 
\]
  
 
-->
 
-->
  
−
=== Modes / Components ===
+
<!--no latex--><span class="tex">𝓒<sub>E</sub> = 𝓒(ΔP<sub>χ</sub>) = 0</span><!--/no latex--><!--latex:
 +
 
 +
\[
 +
\mathcal{C}_{E} = \mathcal{C}(\Delta P_{\chi}) = 0
 +
\]
 +
 
 +
-->
 +
 
 +
<!--no latex--><span class="tex">𝓒<sub>B</sub> = 𝓒(ΔP<sub>u</sub>) = 0</span><!--/no latex--><!--latex:
 +
 
 +
\[
 +
\mathcal{C}_{B} = \mathcal{C}(\Delta P_{u}) = 0
 +
\]
 +
 
 +
-->
 +
 
 +
=== Diffuse solutions ===
 +
 
 +
<!--no latex--><span class="tex">Φ<sub>M</sub>, Φ<sub>A</sub>, Φ<sub>E</sub>, Φ<sub>B</sub> ∈ Sol(𝓒)</span><!--/no latex--><!--latex:
 +
 
 +
\[
 +
\Phi_{M},\;\Phi_{A},\;\Phi_{E},\;\Phi_{B} \in \mathrm{Sol}(\mathcal{C})
 +
\]
 +
 
 +
-->
 +
 
 +
== InfoStructures ==
 +
 
 +
=== Wave‑like InfoStructures ===
 +
 
 +
==== Derived from ====
 +
 
 +
<!--no latex--><span class="tex">ΔP<sub>n</sub>, ΔP<sub>u</sub></span><!--/no latex--><!--latex:
 +
 
 +
\[
 +
\Delta P_{n},\;\Delta P_{u}
 +
\]
 +
 
 +
-->
 +
 
 +
==== Equilibrium condition ====
 +
 
 +
<!--no latex--><span class="tex">𝓒<sub>wave</sub> (ΔP<sub>n</sub>, ΔP<sub>u</sub>) = 0</span><!--/no latex--><!--latex:\[\mathcal{C}_{wave}(\Delta P_{n},\,\Delta P_{u}) = 0\]-->
 +
 
 +
==== Proto‑wave equation ====
 +
 
 +
<!--no latex--><span class="tex">𝓦 [Ψ; ΔP<sub>n</sub>, ΔP<sub>u</sub>] = 0</span><!--/no latex--><!--latex:\[\mathcal{W}[\Psi;\,\Delta P_{n},\,\Delta P_{u}] = 0
 +
\]-->
 +
 
 +
=== Vortex‑like InfoStructures ===
 +
 
 +
==== Derived from ====
 +
 
 +
<!--no latex--><span class="tex">ΔP<sub>A</sub>, ΔP<sub>n</sub>, ΔP<sub>χ</sub>, ΔP<sub>u</sub></span><!--/no latex--><!--latex:
 +
 
 +
\[
 +
\Delta P_{A},\;\Delta P_{n},\;\Delta P_{\chi},\;\Delta P_{u}
 +
\]
 +
 
 +
-->
 +
 
 +
==== Equilibrium condition ====
 +
 
 +
<!--no latex--><span class="tex">𝓒<sub>vortex</sub> (ΔP<sub>A</sub>, ΔP<sub>n</sub>, ΔP<sub>χ</sub>, ΔP<sub>u</sub>) = 0</span><!--/no latex--><!--latex:\[
 +
\mathcal{C}_{vortex}(\Delta P_{A},\,\Delta P_{n},\,\Delta P_{\chi},\,\Delta P_{u}) = 0\]-->
 +
 
 +
==== Proto‑vortex equation ====
 +
 
 +
<!--no latex--><span class="tex">𝓥 [Ξ; ΔP<sub>A</sub>, ΔP<sub>n</sub>, ΔP<sub>χ</sub>, ΔP<sub>u</sub>] = 0</span><!--/no latex--><!--latex:\[\mathcal{V}[\Xi;\,\Delta P_{A},\,\Delta P_{n},\,\Delta P_{\chi},\,\Delta P_{u}] = 0\]-->
 +
 
 +
=== Interaction‑mediating InfoStructures ===
 +
 
 +
==== Relational equilibrium ====
 +
 
 +
<!--no latex--><span class="tex">𝓒<sub>int </sub>(Ψ, Ξ) = 0</span><!--/no latex--><!--latex:\[\mathcal{C}_{int}(\Psi,\,\Xi) = 0\]-->
 +
 
 +
==== Proto‑interaction equation ====
 +
 
 +
<!--no latex--><span class="tex">𝓘 [Ψ, Ξ] = 0</span><!--/no latex--><!--latex:\[\mathcal{I}[\Psi,\,\Xi] = 0\]-->
 +
 
 +
== Geometric Projection ==
 +
 
 +
=== Wave projection ===
 +
 
 +
<!--no latex--><span class="tex">Proj(𝓦) → QM wave equations</span><!--/no latex--><!--latex:
 +
 
 +
\[
 +
\mathrm{Proj}(\mathcal{W}) \longrightarrow \text{QM wave equations}
 +
\]
 +
 
 +
-->
 +
 
 +
=== Vortex projection ===
 +
 
 +
<!--no latex--><span class="tex">Proj(𝓥) → spinor equations</span><!--/no latex--><!--latex:
 +
 
 +
\[
 +
\mathrm{Proj}(\mathcal{V}) \longrightarrow \text{spinor equations}
 +
\]
 +
 
 +
-->
 +
 
 +
=== Interaction projection ===
 +
 
 +
<!--no latex--><span class="tex">Proj(𝓘) → gauge equations</span><!--/no latex--><!--latex:
 +
 
 +
\[
 +
\mathrm{Proj}(\mathcal{I}) \longrightarrow \text{gauge equations}
 +
\]
 +
 
 +
-->
 +
 
 +
== Forms ==
  
−
* Perturbation
+
No new fundamental equation
−
* Translation
+
−
* Rotation:Chirality
+
−
* Rotation:AxisOrientation
+

Latest revision as of 23:44, 14 July 2026

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