Read the equation
This relation defines z_k(θ) in the source section “I. FOUNDATIONAL CONSTANTS · z_k(θ)”. It specifies the displayed relationship between the named quantities or parameters. 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 z_k(θ) as the quantity being defined or updated by this relation.
Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.
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
return x*other.x + y*other.y + z*other.z;
}
};
// G¹⁶ Parametric Helix equations (Section 1.1)
// x_k(θ) = r·cos(θ + 2πk/16)
// y_k(θ) = r·sin(θ + 2πk/16)
// z_k(θ) = (p/2π)·θ + δ_k
class G16Helix {
public:
// Vertical offset per strand: δ_k = k·h/16
static double vertical_offset(int k) {
return k * RISE_PER_BP / NUM_STRANDS;
}
// Golden phase offset: θ_k = 2πk·φ⁻¹ mod 2π
static double golden_phase_offset(int k) {
return std::fmod(2.0 * M_PI * k * PHI_INV, 2.0 * M_PI);Exact original notation
z_k(θ) = (p/2π)·θ + δ_k