The Clock on a Flat Set

A monitor who has given up paying attention is excused to the attribution protocol’s floor, and the floor is the same whatever his sense of duty. On the set of duty weights that give up at a given task, the material payoff therefore contains no duty weight at all, and selection is exactly neutral. A parent paper shows that the distribution of conscience surviving on that set is the distribution that was there when the dynamics began. Exact neutrality is not robustness but the absence of any force, so any second force decides the answer. This paper adds imperfect transmission of the duty weight and asks what it costs. Where the population ends up is already known and is credited rather than claimed: on a set where selection is blind the limit is fixed by the set’s own structure and not by the rate. What is open is how long, and the received answer has the right shape and the wrong constant. The memory decays at the mutation rate multiplied by the set’s own share of the kernel — and because this set is narrow precisely because giving up is rare, that divisor buys the parent’s result between one and a half and two orders of magnitude of extra life, according to which reading of the set’s edge is taken. Its memory result is therefore not false but dated: intact at every horizon its own model reaches, and lost only in a limit that model never takes. Three further results follow. Which survivor appears is decided by the kernel’s range against the set’s width rather than by its shape, and only in the narrow-kernel régime does the boundary rule for the weight become expensive. Over the stretch of tasks where the ledger prefers the monitor who is just working, noise moves the surviving conscience upward rather than down. And a finite population destroys the same memory in an opposite way, preserving its mean in expectation while fixing every individual history on a single weight. What the paper does not measure is the value of the surviving conscience as a reservoir, since it never lets a task become cheap again.