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The denominator adds one to a sum of squared discrepancies across the selected sites. The score is one when every discrepancy is zero and decreases as their total squared magnitude grows. Its calibration changes with site count and discrepancy scale, so the name C5000 identifies its project role rather than a universal measure.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| C_5000 | Project discrepancy score |
| d_i | Per-site discrepancy |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
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Original context
Read the surrounding source passage
* - Differential Geometry: Fisher metric, geodesics, Ricci curvature
* - Category Theory: functors, natural transformations, monads
* - Stochastic Calculus: Itô SDE, Fokker-Planck
* - Optimal Transport: Wasserstein distance, Kantorovich duality
* - Gate5000 Binary Substrate (G1-G11):
* - G4: sᵢ(t+1) = H(Σw_{ji}·sⱼ - θᵢ)
* - G5: aᵢ(t+1) = tanh(α·Σu_{ji}·aⱼ + β)
* - G10: C₅₀₀₀(t) = 1/(1 + Σdᵢ(t)²)
* - G11: 16 DNA Families × 5000 Substrates = 80,000 sites
*/
#pragma once
#include <cmath>
#include <array>
#include <vector>
#include <complex>
#include <algorithm>Exact original notation
- G10: C₅₀₀₀(t) = 1/(1 + Σdᵢ(t)²)