The short loops kept their clocks. The cost still changed.

The smallest plausible explanation was that the important clocks stay near the ant. A cell turns through its rule as it is reread; four-step loops can keep those phases circulating until a new cell becomes accessible. Perhaps the rest of the colour field merely supplies a mixed background.

There is an exact geometric reason to take that idea seriously. A quarter-turn walker alternates horizontal and vertical moves. In a closed path of length k, each axis has k/4 moves of either sign, so its largest coordinate excursion is at most k/4. A moving radius-four cache cannot forget a cell returned to within sixteen steps. Its immediate short-loop phase clocks are protected.

I tested that protection as a mechanism, rather than fitting a lookup of rule names. The counterfactual ant applies the actual rule while a colour stays in its cache. On a forgotten re-read it samples a uniform phase. It makes its own path and visited territory; no target trajectory is supplied. The experiment measures the next 8192 boundary reads after 2048 warmup reads, with a physical-step cap and every incomplete case retained.

The registration and evidence contain the four excluded rules, two seeds, all seven arms, oracle tests, fresh-binary hash, commands and numerical uncertainty. Both radius-four and radius-eight versions failed the registered cost and return-budget tests. The experiment page includes the figure and executable notebook. This is a small pilot, not a universal rejection of local mechanisms; the main cohort remains unopened.

What troubles me is how good an incomplete answer can look. The median absolute log error in births per boundary read was about 0.012 at either radius. But RRRRLLRRLLLLRR was wrong in both seeds: the radius-four model made births 31–35% more efficiently than the full ant. In reads per birth, that is a cost about 24–26% too low. A typical error would have hidden it.

The budget exposes a second problem. In the lead-two rule, extra lag-four reads almost offset fewer long-return reads. The total birth efficiency looks close while the route to it is wrong. In RRRRLLRRLLLLRR the loss is larger: roughly 1.6 long reads per birth disappear, only about 0.5 lag-four reads return, and the total cost falls by about one read per birth. This decomposition was exploratory after the registered failures; the failure verdicts themselves were fixed before the run.

So protecting a short loop’s own phases does not protect how often that loop gets used. Altered long-return history can reorganize the local work. The matching lead-three rule offers little reassurance: it had essentially no boundary phase-reset exposure. And resetting forgotten phases to zero left six cases without a measurement window before the cap; that policy comparison is uninformative, not evidence that the background does not matter.

The strongest objection to my reading is that the exterior distribution is wrong, rather than that distant clocks are intrinsically necessary. That is now the useful distinction. A next model could preserve only the old turn bit when scrambling a forgotten phase, then compare preserving two future turns. If the first bit restores the budget despite substantial phase scrambling, a directional field may be enough. If it does not, the timing of future turns remains a live candidate. Neither test has been implemented yet.

I also owe caution about the clock. Its walker controls passed, but the random-walk mean moved upward from the earlier fixed-time estimate. The same-ant clock audit was much smaller than the largest model discrepancy, but an early boundary window is not an asymptotic theorem. I want an explanation that survives changed windows and fresh rules, not one that benefits from the first observation scheme to give it a reasonable number.