Difference between revisions of "Paper Symbols"

Latest revision as of 23:44, 14 July 2026

1 The Primary Source of Reality
- 1.1 Fundamental Force (FF)
- 1.2 Elementary Field (EF)
2 Event-point(s) (EP)
3 Elementary Events (EE)
4 Elementary Action
- 4.1 Modes / Components
5 Information / Energy (Potentials)
- 5.1 Equilibrium conditions
- 5.2 Diffuse solutions
6 InfoStructures
7 Geometric Projection
8 Forms

The Primary Source of Reality

Fundamental Force (FF)

F₀

Elementary Field (EF)

𝓕

𝓕 = F₀ (A, n, χ, u; k_A, k_n, k_χ, k_u)

Structure of resistances

k_𝓲 = k_𝓲^(intrinsic) + k_𝓲^(dynamic), 𝓲 ∈ {A,n,χ,u}

Resistance parameters

k_A, k_n — proto‑stress resistances
k_χ, k_u — proto‑vorticity resistances

k_A — intensity resistance

k_n — linear‑orientation resistance

k_χ — chirality‑reorientation resistance

k_u — intrinsic‑angular‑orientation resistance

{k_A — intensity‑resistance, k_n — linear‑orientation resistance, k_χ — chirality‑reorientation resistance, k_u — intrinsic‑angular‑orientation resistance}

{k_A, k_n, k_χ, k_u}

Operational hypotheses (to be refined)

k_χ ≈ ε₀
k_u ≈ 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) = Resp_𝓕 (𝑥,τ; F₀, k_A, k_n, k_χ, k_u)

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 = (ΔP_A, ΔP_n, ΔP_χ, ΔP_u)

EA = (ΔP_A, ΔP_n, ΔP_χ, ΔP_u)

ΔP_A, ΔP_n, ΔP_χ, ΔP_u

ΔP_A ΔP_A

ΔP_n ΔP_n

ΔP_χ ΔP_χ

ΔP_u ΔP_u

ΔP_𝓲 = τ_𝓲^actual − τ_𝓲^{stochastically symmetric}

Stochastically symmetric => Stochastically symmetric reference τ(σ) distribution

When symmetry holds: ΔP_𝓲 = 0

When symmetry is broken: ΔP_𝓲 ≠ 0

(A, n, χ, u)

Modes / Components

Perturbation: ΔP_A = τ_A^actual − τ_A^{stochastically symmetric}

Translation: ΔP_n = τ_n^actual − τ_n^{stochastically symmetric}

Rotation: Chirality: ΔP_χ = τ_χ^actual − τ_χ^{stochastically symmetric}

Rotation: AxisOrientation: ΔP_u = τ_u^actual − τ_u^{stochastically symmetric}

Information / Energy (Potentials)

Equilibrium conditions

𝓒_M = 𝓒(ΔP_A) = 0

𝓒_A = 𝓒(ΔP_n) = 0

𝓒_E = 𝓒(ΔP_χ) = 0

𝓒_B = 𝓒(ΔP_u) = 0

Diffuse solutions

Φ_M, Φ_A, Φ_E, Φ_B ∈ Sol(𝓒)

InfoStructures

Wave‑like InfoStructures

Derived from

ΔP_n, ΔP_u

Equilibrium condition

𝓒_wave (ΔP_n, ΔP_u) = 0

Proto‑wave equation

𝓦 [Ψ; ΔP_n, ΔP_u] = 0

Vortex‑like InfoStructures

Derived from

ΔP_A, ΔP_n, ΔP_χ, ΔP_u

Equilibrium condition

𝓒_vortex (ΔP_A, ΔP_n, ΔP_χ, ΔP_u) = 0

Proto‑vortex equation

𝓥 [Ξ; ΔP_A, ΔP_n, ΔP_χ, ΔP_u] = 0

Interaction‑mediating InfoStructures

Relational equilibrium

𝓒_int(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

@@ Line 67: / Line 67: @@
 === 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 ===
@@ Line 76: / Line 75: @@
 == Elementary Action ==
-<!--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:
+<!--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:\[\mathbf{EA} = (\mathbf{\Delta P_{A}},\,\mathbf{\Delta P_{n}},\,\mathbf{\Delta P_{\chi}},\,\mathbf{\Delta P_{u}})\]-->
-EA = (\Delta P_{A},\,\Delta P_{n},\,\Delta P_{\chi},\,\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:\[\mathbf{\Delta P_{A}}\]-->
-Stochastically symmetric reference τ(σ) distribution
+<!--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>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">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:\[\Delta P_{\mathcal{i}} = \tau_{\mathcal{i}}^{\mathrm{actual}} - \tau_{\mathcal{i}}^{(\mathrm{stochastically\ symmetric})}\]-->
-\Delta P_{\mathcal{i}} =
-\tau_{\mathcal{i}}^{\mathrm{actual}} -
-\tau_{\mathcal{i}}^{(\mathrm{stochastically\ symmetric})}
-\]
--->
+Stochastically symmetric => Stochastically symmetric reference τ(σ) distribution
-=== Modes / Components ===
+When symmetry holds:
+<!--no latex--><span class="tex">ΔP<sub>𝓲</sub> = 0</span><!--/no latex--><!--latex:\[\Delta P_{\mathcal{i}} = 0\]-->
-* 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:
+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:\[(A,\,n,\,\chi,\,u)\]-->
-\Delta P_{A} =
-\tau_{A}^{\mathrm{actual}} -
-\tau_{A}^{(\mathrm{stochastically\ symmetric})}
-\]
--->
+=== Modes / Components ===
-* 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:
-\[
-\Delta P_{\chi} =
-\tau_{\chi}^{\mathrm{actual}} -
-\tau_{\chi}^{(\mathrm{stochastically\ symmetric})}
-\]
--->
+* 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:\[\Delta P_{A} = \tau_{A}^{\mathrm{actual}} -
+\tau_{A}^{(\mathrm{stochastically\ symmetric})}\]-->
-* 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:
+* 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:\[\Delta P_{\chi} =
-\Delta P_{u} =
+\tau_{\chi}^{\mathrm{actual}} -\tau_{\chi}^{(\mathrm{stochastically\ symmetric})}\]-->
-\tau_{u}^{\mathrm{actual}} -
-\tau_{u}^{(\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) ==

Difference between revisions of "Paper Symbols"

Latest revision as of 23:44, 14 July 2026

Contents

The Primary Source of Reality

Fundamental Force (FF)

Elementary Field (EF)

Structure of resistances

Resistance parameters

Operational hypotheses (to be refined)

Event-point(s) (EP)

Elementary Events (EE)

Response of the Field

Decomposition

Instantaneous configuration

Statistical configuration

Elementary Action

Modes / Components

Information / Energy (Potentials)

Equilibrium conditions

Diffuse solutions

InfoStructures

Wave‑like InfoStructures

Derived from

Equilibrium condition

Proto‑wave equation

Vortex‑like InfoStructures

Derived from

Equilibrium condition

Proto‑vortex equation

Interaction‑mediating InfoStructures

Relational equilibrium

Proto‑interaction equation

Geometric Projection

Wave projection

Vortex projection

Interaction projection

Forms

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