Read the equation
The bias is the ordinary mean of two numbers in [0,1), so it also lies in that interval. Because phases wrap at one turn, this average is sensitive to the chosen cut: phases 0.99 and 0.01 average to 0.50 even though they are close on the circle. That matters when the value controls a gate threshold.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| bias | Scalar gate-control value |
| phase_DNA | First wrapped phase |
| phase_Fib | Second wrapped phase |
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
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
## 7.3 Combined Phase Bias ``` bias = (phase_DNA + phase_Fib) / 2 ``` **Explanation**: Averaging the two phases creates a combined modulation signal for the gates. ## 7.4 Gate Transition Rule ``` flip_i = 1 if (i mod 1000) < (bias · 1000), else 0 gate_i(t+1) = (gate_i(t) XOR input_i) XOR flip_i ``` **Explanation**: Each of the 5000 gates performs XOR with its input, then conditionally flips based on the phase bias. Gates in the lower portion of each 1000-gate block are more likely to flip, creating structured diffusion patterns. --- # 8. Neural Brain Dynamics (dna_v9) The 88-agent neural brain uses the following exact equations: ## 8.1 Input Processing
Exact original notation
bias = (phase_DNA + phase_Fib) / 2