All Equations Index - FatherTimeSDKP/CEN- GitHub Wiki

All Equations Index

Purpose

This page provides a unified index of all major equations that form the mathematical backbone of the FatherTime SDKP framework and its integration into NFT license metadata, mass models, timestamp verification systems, and quantum-causal simulations. These expressions govern how physics interacts with code.

SDKP (Scale–Density–Kinematic Principle)

1. Mass Equation (Composite Particles):

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

  • N: Numerical encoding of Shape-Dimension complexity
  • S: Density-Scale coupling parameter
  • γ, β, α: Tunable coefficients (calibrated to known masses or causal fields)
  • Used In: SDKPMassLib.sol, NFT license visualization

SD&N (Shape–Dimension–Number)

2. Shape-Dimension Number Mapping:

[ N = \sum_{i=1}^k w_i \cdot f_i(\text{topology}_i) ]

  • Each fundamental topology (e.g. unknot, trefoil, Möbius) is mapped to an f_i function
  • Weights w_i define influence of each shape
  • Used in assigning values for N in the mass equation

EOS (Earth Orbital Speed)

3. EOS Reference Constant:

[ c_{EOS} = v_{orbit} = 29.78 , \text{km/s} ]

  • Replaces the traditional speed of light c in causality calculations
  • Foundation for "local relativistic timing" in TimeSeal simulations
  • Used in: TimeSeal offset calibration, timestamp adjustment

4. TimeSeal Drift Equation:

[ \Delta t = \frac{r_{orbital}}{c_{EOS}} \cdot f_{sync}(x) ]

  • Governs drift between orbital-based time and machine-based UTC
  • Used in timestamp verification logic via Chainlink oracle requests

QCC (Quantum Computerization of Consciousness)

5. QCC Kernel Compression:

[ K_C(t) = \min_{\Omega} {H(\phi(\Omega_t)) ,|, \Omega \in \text{causal paths} } ]

  • Finds minimal entropy representation for causal sequences at time t
  • φ(Ωₜ) = projection of causal flow under consciousness embedding
  • Used in: QCC metadata embedding and Chainlink-based microstate hashing

6. NFT Entropic License Hash:

[ \text{hash}_{\text{license}} = H(\text{SVG} , || , \text{SD&N vector} , || , K_C) ]

  • Canonical hash of license data for verification and immutability
  • Combines graphical, physical, and causal identity into one proof

NFT System-Level Calculations

7. On-Chain Royalty Split:

[ R = \begin{cases} 0.175 \cdot P, & \text{Commercial license} \ 0.115 \cdot P, & \text{Residential/AI license} \end{cases} ]

  • P: Price of sale
  • R: Royalty portion routed to 0x311540cD…B4Bf7
  • Used in: royaltyInfo() override in ERC-1155 contract

8. Metadata URI Resolver (ERC-1155):

[ \text{URI}_{tokenId} = \text{ipfs://CID/} + \text{tokenId} + \text{.json} ]

  • Token ID maps directly to fixed IPFS metadata endpoint
  • Used in: uri(uint256 tokenId) in contract and frontend SVG rendering

Summary

These equations not only underpin the theoretical physics embedded in the licenses but also define how those theories are encoded, timestamped, visualized, and verified across the blockchain. Each formula is a functional part of the NFT framework’s causal-verifiable engine.

Author:
Donald Paul Smith aka FatherTime
Timestamped Origin: January 18, 2025

Last updated: 2025-05-29