Read the equation
This relation defines Transform: T_k in the source section “IV. STRAND MATHEMATICS · Transform: T_k”. Evaluates oscillatory sine or cosine terms using the stated phase or frequency. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read Transform: T_k as the quantity being defined or updated by this relation.
Evaluates oscillatory sine or cosine terms using the stated phase or frequency.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.
Original context
Read the surrounding source passage
// Complex strand representation: S_k = D_k · e^{ikφ}
void compute_transforms() {
for (int k = 0; k < NUM_STRANDS; ++k) {
double phase = (k + 1) * PHI;
S_[k] = D_[k] * std::exp(std::complex<double>(0, phase));
// Transform: T_k = S_k · (cos(k) + i·sin(k))
double angle = k + 1;
T_[k] = S_[k] * std::complex<double>(std::cos(angle), std::sin(angle));
}
}
// Modular extraction: X_k = |T_k| mod φ^k
double modular_extraction(int k) const {
return std::fmod(std::abs(T_[k-1]), std::pow(PHI, k));
}
Exact original notation
Transform: T_k = S_k · (cos(k) + i·sin(k))