The SD&N (Shape–Dimension–Number) model encodes particle properties via topological shape and discrete numeric values, integrating them with scale and density to derive mass and interaction behaviors. This approach captures both geometric and algebraic aspects of fundamental particles, enabling a deeper link between quantum topology and physical observables. - FatherTimeSDKP/FatherTimeSDKP-SD-N-EOS-QCC GitHub Wiki

Shape–Dimension–Number (SD&N)

SD&N encodes particle properties in the SDKP framework through three mathematically significant components:

• Shape (s):
  Represented by topological invariants such as knot types or geometric descriptors. Shape influences particle symmetry and interaction topology.
  Examples include trefoil knots for electrons or unknots for protons.

• Dimension (d):
  The spatial or fractal dimensionality associated with the particle’s effective configuration space. This may be an integer or fractional dimension impacting scaling laws and interaction strength.

• Number (n):
  A quantized discrete parameter encoding particle identity, charge states, or multiplicity. Number acts as an index in the SDKP scaling functions.

Mathematical Role:

The combined SD&N parameters form the input to the SDKP mass scaling function:

[ m = f(n, s, d) = \rho^{\alpha(n)} \times s^{\beta(d)} \times g(n, s, d) ]

where:

• ( \rho ) = scale or density parameter,
• ( \alpha(n), \beta(d) ) = scaling exponents dependent on number and dimension,
• ( g(n, s, d) ) = shape-dependent geometric correction factor.

This framework allows rigorous, scalable modeling of particle masses and interactions grounded in topology (shape), dimensional physics, and discrete quantization (number).

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