CA-V2-01

Tracing through the system carefully, noting that B and C are computed from **old** values, while A uses the **newly computed** C: **Cycle 1** — Start: A=10, B=0, C=0 - B_new = 2×A = 20 - C_new = 3×B = 0 - A_new = A − C_new = 10 − 0 = 10 - → A=10, B=20, C=0 **Cycle 2** — Start: A=10, B=20, C=0 - B_new = 2×A = 20 - C_new = 3×B = 60 - A_new = A − C_new = 10 − 60 = −50 → **floored to 0** - → A=0, B=20, C=60 **Cycle 3** — Start: A=0, B=20, C=60 - B_new = 2×A = 2×0 = **0** - C_new = 3×B = 60 - A_new = A − C_new = 0 − 60 → floored to 0 - → A=0, B=0, C=60 **After 3 complete cycles, B = 0.** The balancing loop (A→B→C⊣A) dominates: C's inhibition of A drives A to zero by cycle 2, which starves B of input by cycle 3. D's amplification never activates because A never exceeds the threshold T=15. The system collapses to a fixed point at (A=0, B=0, C=60).

Tracing through the system step by step: **Rules:** B_new = 2·A, C_new = 3·B_old, A_new = max(0, A − C_new). D_boost only if A > 15. | Cycle | A_start | B_start | B_new = 2·A | C_new = 3·B_old | A_new = A − C_new (floor 0) | |-------|---------|---------|-------------|-----------------|------------------------------| | 1 | 10 | 0 | 20 | 0 | 10 | | 2 | 10 | 20 | 20 | 60 | 0 | | 3 | 0 | 20 | **0** | 60 | 0 | - **Cycle 3:** A=0 (no D_boost), so B_new = 2·0 = **0**. C_new = 3·20 = 60. A_new = 0 − 60 → floored to 0. **After 3 complete cycles, B = 0.** The balancing loop (A→B→C⊣A) kills itself: B drives C up, C crushes A to zero, and with A=0 the next cycle zeroes out B. The D_boost amplifier never activates because A never exceeds 15.