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Elements · Proposition IV of VI

The rule decides, not the mood.

IVWhy it holds

Markets do not bend to anyone’s wishes. What we control is the rule we follow when they don’t — written down before the trade, applied the same way every time.

Decisions belong to the system, not to whoever feels most certain that day. Conviction is not a signal; a rule can be audited, a mood cannot.

∎Proof

wt=f(zt)=clip⁡ ⁣(zt2, −1, 1)w_t = f(z_t) = \operatorname{clip}\!\left(\tfrac{z_t}{2},\,-1,\,1\right)
Proof · same input, same decisionIllustrative · seed 31
−101signal zposition wrule: w = clip(z / 2, −1, 1)● discretionary (simulated)
The violet line is the rule: position as a function of the signal, written down before any trade. Every rule decision lands exactly on it. The grey points simulate the same signals decided by hand — conviction, mood and the last loss pull each one somewhere else. A system you can audit is one that does not depend on who is in the chair.

Q.E.D.