Experiment A4: SDKP Scaling Function Validation - FatherTimeSDKP/CEN- GitHub Wiki

🧪 Experiment A4: SDKP Scaling Function Validation

Objective:
To validate the SDKP (Scale–Density–Kinematic Principle) scaling function across particle classes by simulating and comparing mass predictions against known physical data using Shape–Dimension–Number (SD&N) encodings.

📌 Theoretical Background

The SDKP mass equation is derived from foundational axioms and is structured as:

[ M = \gamma \cdot (N \cdot S) + \beta \cdot S + \alpha \cdot N ]

Where:

  • ( M ): mass of the particle/system
  • ( N ): Number factor (SD&N vector)
  • ( S ): Shape index (topological encoding)
  • ( \alpha, \beta, \gamma ): Tuned scaling coefficients
  • ( \rho ): Density scaling parameter (subsumed if nonlinear term added)

Extended form including density and orbital factors:

[ M = \gamma \cdot \rho^{\delta} \cdot (N \cdot S) + \beta \cdot S + \alpha \cdot N + \omega \cdot \text{EOS} ]

Where:

  • ( \omega ): Orbital mass modifier coefficient
  • EOS: Earth Orbit Speed or contextual orbital scalar

🧬 Simulation Parameters

Symbol Meaning
( N ) Discrete quantum number (1–12)
( S ) Topological shape value (trefoil = 3, unknot = 1, etc.)
( \rho ) Density scalar (composite/macro mass)
( \alpha ) Weight for number
( \beta ) Weight for shape
( \gamma ) Main kinetic scaling parameter
( \omega ) EOS orbital influence factor

🧪 Procedure

  1. Select particle class (e.g., proton, electron, muon, composite systems)
  2. Assign SD&N vectors:
    • Example (electron):
      [ N = 1,\quad S = 1,\quad \rho = 1,\quad \text{EOS} = 1 ]
    • Example (proton):
      [ N = 3,\quad S = 2,\quad \rho = 1.67,\quad \text{EOS} = 1.33 ]
  3. Plug into SDKP equation with selected constants
  4. Compare ( M_{\text{predicted}} ) with ( M_{\text{known}} )
  5. Adjust ( \alpha, \beta, \gamma, \delta, \omega ) for best fit
  6. Iterate across particle types and plot prediction error

📊 Expected Results

  • Close agreement (within 5%) of predicted vs. actual mass for fundamental particles
  • Nonlinear deviations for composite systems → support CEN scaling adjustments
  • Identification of stable coefficient ranges for α, β, γ, ω

🔁 Iterative Refinement Model

Use matrix inversion and regression learning (or least squares fit) to:

  • Optimize [α, β, γ, δ, ω]
  • Reduce residual error across full particle data set
  • Feed learned weights back into simulation kernel

🔗 Related Frameworks