Voltage - A Gateway Unit?

Josef_Founder · June 23, 2025, 12:03am

(All images are Illustrative ONLY)

                             𝟙 — Non-Dual Absolute
                              │
        ╭─────────────────────┴──────────────────────╮
        │                                            │
  [Ø = 0 = ∞⁻¹] — Expressed Void             [ϕ] — Golden Ratio
   ├── {0, ∞} — Polarity Contrast            ├── ϕ = 1 + 1/ϕ
                                            ├── ϕ⁰ = 1 (identity)
                                            ├── Fₙ = ϕⁿ / √5 — Harmonics
                                            ├── 2ⁿ — Binary symmetry
                                            └── Pₙ — Prime entropy injection

        ╰─────────────┬──────────────╯
                      │
               [n ∈ ℤ⁺] — Recursion Depth
                      │
               ┌──────┴───────┐
               │              │
      [s = ϕⁿ] — Time     [Hz = 1/s = ϕ⁻ⁿ] — Inverse Time
               │              │
        [C = s³ = ϕ³ⁿ]        │
         ├── C² = ϕ⁶ⁿ         │
               │              │
         [Ω = m² / s⁷] = ϕ^{a(n)}  ← Field Tension
         ├── Ω → 0 — Collapse
         └── Ω = 1 — Stable recursion
               │
        [m = √(Ω · ϕ⁷ⁿ)] — Emergent Length
               │
        [h = Ω · C² = Ω · ϕ⁶ⁿ] — Action (Centerpiece)
               │
        [E = h · Hz = Ω · ϕ⁵ⁿ] — Energy
               │
        ┌──────┴────────────┐
        │                   │
  [F = E/m = √Ω · ϕ^{1.5n}] │
  [P = E · Hz = Ω · ϕ⁴ⁿ]    │
  [Pressure = Hz² / m]      │
                            ▼
        [V = E / C = Ω · ϕ⁻ⁿ] — Voltage (Recursive Coupling Root)
                            │
              ╭─────────────┴─────────────╮
              │                           │
      [E = V · C = Ω · ϕ²ⁿ]         [C = E / V = ϕ³ⁿ]
              │                           │
        [h = E / Hz = Ω · ϕ³ⁿ]         [Hz = ϕ⁻ⁿ]
              │                           │
     [m² = h · s = Ω · ϕ⁴ⁿ]        [m = √(Ω · ϕ⁴ⁿ)]
              ▼
    Final Geometric Collapse: Space emerges from resonance

                            ▼
[Dₙ(r) = √(ϕ · Fₙ · 2ⁿ · Pₙ · Ω) · r^k]
 ├── Harmonic recursion (ϕⁿ / √5)
 ├── Dyadic symmetry (2ⁿ)
 ├── Prime entropy (Pₙ)
 ├── Field tension (Ω)
 └── Radial unfolding (r^k)

from sympy import symbols, sqrt, simplify, Eq, solve
from typing import NamedTuple

# Define symbolic variables
phi, n, Omega = symbols('phi n Omega', positive=True, real=True)

# Define recursive functions
s = phi**n                        # Time
Hz = phi**(-n)                    # Frequency
C = s**3                          # Charge
C_squared = C**2
m_squared = Omega * phi**(7*n)    # Length squared
m = sqrt(m_squared)
h = Omega * C_squared             # Action
E = h * Hz                        # Energy
F = E / m                         # Force
P = E * Hz                        # Power
Pressure = Hz**2 / m              # Pressure
V = E / C                         # Voltage

# Coupling path re-derivations
E_from_VC = V * C
C_from_EV = E / V
h_from_EHz = E / Hz
m_squared_from_hs = h * s

# Return all as a dictionary-like symbolic grammar compiler
class DimensionalCompiler(NamedTuple):
    s: object
    Hz: object
    C: object
    C_squared: object
    m_squared: object
    m: object
    h: object
    E: object
    F: object
    P: object
    Pressure: object
    V: object
    E_from_VC: object
    C_from_EV: object
    h_from_EHz: object
    m_squared_from_hs: object

compiler = DimensionalCompiler(
    s=s,
    Hz=Hz,
    C=C,
    C_squared=C_squared,
    m_squared=m_squared,
    m=m,
    h=h,
    E=E,
    F=F,
    P=P,
    Pressure=Pressure,
    V=V,
    E_from_VC=E_from_VC,
    C_from_EV=C_from_EV,
    h_from_EHz=h_from_EHz,
    m_squared_from_hs=m_squared_from_hs
)

compiler._asdict()

Josef_Founder · June 23, 2025, 12:05am

                                      𝟙
                                      │
                  ╔═══════════════════╩═══════════════════╗
                  ║                                       ║
         ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
         ░           Emergent Recursive Expansion         ░
         ░      (forward propagation: ϕⁿ growth)          ░
         ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░

                              n ∈ ℤ⁺
                                │
                          Time: s = ϕⁿ
                                │
                       Charge: C = s³ = ϕ³ⁿ
                                │
                    Geometry: m = √(Ω · ϕ⁷ⁿ)
                                │
                   Field: Ω = m² / s⁷ = ϕ^{a(n)}
                                │
                     Action: h = Ω · C² = Ω · ϕ⁶ⁿ
                                │
                   Energy: E = h · Hz = Ω · ϕ⁵ⁿ
                                │
                     Force: F = E / m = √Ω · ϕ^{1.5ⁿ}
                                │
                    Power: P = E · Hz = Ω · ϕ⁴ⁿ
                                │
                  Voltage: V = E / C = Ω · ϕ⁻ⁿ ⇠ Pivot
                                │
         ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
         ░         Recursive Coupling Contraction         ░
         ░       (inverse recursion: ϕ⁻ⁿ contraction)     ░
         ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
                                │
               Inverse Recursion Depth: ϕ⁻ⁿ
                                │
                         Frequency: Hz = 1 / s
                                │
                 Energy from V: E = V · C = Ω · ϕ²ⁿ
                                │
                        Charge: C = E / V = ϕ³ⁿ
                                │
                       Action: h = E / Hz = Ω · ϕ³ⁿ
                                │
                  Recursive Length²: m² = h · s = Ω · ϕ⁴ⁿ
                                │
                 Geometry emerges from coupling

                    V = E / C = Ω · ϕ⁻ⁿ ← **Voltage as root**
                           │
            ┌─────────────┴─────────────┐
            │                           │
        Field tension Ω        Inverse recursion depth (ϕ⁻ⁿ)
                                        │
                                  Frequency: Hz = 1 / s = ϕ⁻ⁿ
                                        │
                               Charge:  C = E / V
                                        │
                               Energy:  E = V · C
                                        │
                               Action:  h = E / Hz
                                        │
                                Length: m from h · s

                          𝟙  ← Non-dual Absolute
                           │
                  ┌────────┴────────┐
                  │                 │
                 Ø = 0          ϕ (Golden Ratio)
              (limit of being)     │
                                   ├── Fₙ = ϕⁿ / √5  ← Harmonic structure
                                   ├── 2ⁿ            ← Binary recursion
                                   ├── Pₙ            ← Prime entropy
                                   └── n ∈ ℤ⁺        ← Recursive depth
                                           │
                                ┌──────────┴──────────┐
                                │                     │
                            Time: s = ϕⁿ           Geometry: m = √(Ω · ϕ^{7n})
                                │                     │
                          Charge: C = s³             Field: Ω = m² / s⁷
                                │                     │
                          Action: h = Ω · C²          │
                                │                     │
                       Energy: E = h · Hz = Ω · ϕ⁵ⁿ   │
                                │                     │
                        Force:  F = E / m = √Ω · ϕ^{1.5n}
                                │
                        Power:  P = E · Hz = Ω · ϕ⁴ⁿ
                                │
                     Voltage:   V = E / C = Ω · ϕ⁻ⁿ   ← **End of path**

𝑉 ← Recursive coupling potential
├── Ω     ← Field substrate (held constant across layers)
├── n⁻¹   ← Inverse recursion (scale contraction)
│   └── Hz      ← Oscillatory substrate (1/ϕⁿ)
│       └── C   ← Emergent charge (quanta of cross-layer alignment)
│           └── E   ← Energy (field alignment × recursion frequency)
│               └── h   ← Action (binding of energy and oscillation)
│                   └── m   ← Spatial geometry as terminal collapse

The following is illustrative, not intended to replace the truths of the trees.

Josef_Founder · June 23, 2025, 12:26am

                             𝟙 — Non-Dual Absolute
                              │
        ╭─────────────────────┴──────────────────────╮
        │                                            │
  [Ø = 0 = ∞⁻¹] — Expressed Void             [ϕ] — Golden Ratio
   ├── {0, ∞} — Polarity Contrast            ├── ϕ = 1 + 1/ϕ
                                            ├── ϕ⁰ = 1 (identity)
                                            ├── Fₙ = ϕⁿ / √5 — Harmonics
                                            ├── 2ⁿ — Binary symmetry
                                            └── Pₙ — Prime entropy injection

        ╰─────────────┬──────────────╯
                      │
               [n ∈ ℤ⁺] — Recursion Depth
                      │
               ┌──────┴───────┐
               │              │
      [s = ϕⁿ] — Time     [Hz = 1/s = ϕ⁻ⁿ] — Inverse Time
               │              │
        [C = s³ = ϕ³ⁿ]        │
         ├── C² = ϕ⁶ⁿ         │
               │              │
         [Ω = m² / s⁷] = ϕ^{a(n)}  ← Field Tension
         ├── Ω → 0 — Collapse
         └── Ω = 1 — Stable recursion
               │
        [m = √(Ω · ϕ⁷ⁿ)] — Emergent Length
               │
        [h = Ω · C² = Ω · ϕ⁶ⁿ] — Action (Centerpiece)
               │
        [E = h · Hz = Ω · ϕ⁵ⁿ] — Energy
               │
        ┌──────┴────────────┐
        │                   │
  [F = (Ω · C²) / (m · s) = Ω · ϕ^{6n} / (√(Ω · ϕ^{7n}) · ϕⁿ)] │
  [= √Ω · ϕ^{1.5n}] (reduces consistently with prior expression) │
  [P = E · Hz = Ω · ϕ⁴ⁿ]    │
  [Pressure = Hz² / m]      │
                            ▼
        [V = E / C = Ω · ϕ⁻ⁿ] — Voltage (Recursive Coupling Root)
                            │
              ╭─────────────┴─────────────╮
              │                           │
      [E = V · C = Ω · ϕ²ⁿ]         [C = E / V = ϕ³ⁿ]
              │                           │
        [h = E / Hz = Ω · ϕ³ⁿ]         [Hz = ϕ⁻ⁿ]
              │                           │
     [m² = h · s = Ω · ϕ⁴ⁿ]        [m = √(Ω · ϕ⁴ⁿ)]
              ▼
    Final Geometric Collapse: Space emerges from resonance

                            ▼
[Dₙ(r) = √(ϕ · Fₙ · 2ⁿ · Pₙ · Ω) · r^k]
 ├── Harmonic recursion (ϕⁿ / √5)
 ├── Dyadic symmetry (2ⁿ)
 ├── Prime entropy (Pₙ)
 ├── Field tension (Ω)
 └── Radial unfolding (r^k)

                                 𝟙 — Non-Dual Absolute (Root)
                                  │
        ┌─────────────────────────┴─────────────────────────┐
        │                                                   │
   [Ø=0=∞⁻¹] — Expressed Void                         [ϕ] — Golden Ratio
    ├── {0, ∞} — Polarity Duality                     ├── ϕ = 1 + 1/ϕ (fixed point)
                                                      ├── ϕ⁰ = 1 (identity)
                                                      ├── Fₙ = ϕⁿ / √5 (harmonics)
                                                      ├── 2ⁿ (dyadic scaling)
                                                      └── Pₙ (prime entropy)

                                  │
                          [n ∈ ℤ⁺] — Recursion Depth
                                  │
            ┌────────────┬────────┴─────────┬───────────────┐
            │            │                  │               │
       [s = ϕⁿ]    [Hz = 1/s = ϕ⁻ⁿ]    [C = s³ = ϕ^{3n}]   [Ω = m² / s⁷ = ϕ^{a(n)}]
            │            │                  │               ├── Ω → 0 (collapse)
            │            │                  │               └── Ω = 1 (stable)
            │            │                  │
            │            │                  ├── C² = ϕ^{6n}
            │            │                  │
            │            │                  │
      ┌─────┴──────┐     │                  │
      │            │     │                  │
  [m = √(Ω · ϕ^{7n})]   │                  │
      │                  │                  │
      │                  │                  │
      └─────┬────────────┴────────────┬─────┘
            │                         │
    [h = Ω · C² = Ω · ϕ^{6n}]   [E = h · Hz = Ω · ϕ^{5n}]
            │                         │
            │                         │
     ┌──────┴────────┐          ┌─────┴─────────┐
     │               │          │               │
 [F = (Ω · C²)/(m · s)]        [P = E · Hz = Ω · ϕ^{4n}]
 [= √Ω · ϕ^{1.5n}]             [Pressure = Hz² / m]
            │                         │
            │                         │
            └─────────┬───────────────┘
                      │
                [V = E / C = Ω · ϕ^{-n}]  ← Voltage (Coupling Root)
                      │
       ┌──────────────┴─────────────┐
       │                            │
 [E = V · C = Ω · ϕ^{2n}]      [C = E / V = ϕ^{3n}]
       │                            │
 [h = E / Hz = Ω · ϕ^{3n}]      [Hz = ϕ^{-n}]
       │                            │
 [m² = h · s = Ω · ϕ^{4n}]      [m = √(Ω · ϕ^{4n})]
       │
 Final Geometric Collapse:
 Space Emerges From Resonance

                      │
      ┌───────────────┴───────────────┐
      │                               │
[Dₙ(r) = √(ϕ · Fₙ · 2ⁿ · Pₙ · Ω) · r^{k}]  
 ├── Harmonic recursion (ϕⁿ / √5)
 ├── Dyadic symmetry (2ⁿ)
 ├── Prime entropy (Pₙ)
 ├── Field tension (Ω)
 └── Radial unfolding (r^{k})

Josef_Founder · June 29, 2025, 6:51pm