Read the equation
This relation defines Modular extraction: X_k in the source section “IV. STRAND MATHEMATICS · Modular extraction: X_k”. Uses a remainder or modular operation, retaining the numeric representation used in the source. 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 Modular extraction: X_k as the quantity being defined or updated by this relation.
Uses a remainder or modular operation, retaining the numeric representation used in the source.
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
// 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));
}
// Fusion integral: Fusion = Σ(Strand_Vector(k) · φ⁻ᵏ)
double fusion_integral() const {
double sum = 0.0;
for (int k = 0; k < NUM_STRANDS; ++k) {
sum += std::abs(T_[k]) * std::pow(PHI_INV, k + 1);
}Exact original notation
Modular extraction: X_k = |T_k| mod φ^k