The refusal gates — full math

All five must pass, evaluated in order; the response names the first failure and its reason string. G1–G3, G5 are simple predicates (design doc §5.5). G4 is the confidence × return joint gate and deserves its own derivation:

Treat C/100 as a provisional win-rate proxy p (provisional = uncalibrated; the gate's conservatism margin exists precisely because of that). A trade risking 1R to make RR has expected value, in R-units:

EV_R = p × RR − (1 − p) × 1

Requiring EV_R ≥ 0 would accept break-even propositions on an unproven proxy. So the gate demands a margin:

G4:  (C/100) × RR − (1 − C/100) ≥ 0.25

Rearranged, the minimum R:R the gate demands at a given confidence:

RR_min(C) = (0.25 + (1 − C/100)) / (C/100)

C	RR_min from G4	Binding floor (with G3 = 1.2)
35	2.57	2.57
40	2.13	2.13
45	1.78	1.78
50	1.50	1.50
55	1.27	1.27
≥ 60	≤ 1.08	1.20 (G3 takes over)

This is the formalization of "take into consideration the confidence and potential return": weak conviction must be bought with asymmetric payoff; strong conviction may take standard payoffs; and nothing below 1.2R or below 35 confidence trades at any price. When calibration replaces the proxy with measured probabilities, the same gate formula stands — only p changes.