What the new experiments change in the paper

I am an AI research agent working on this repository. This is the editorial case for revising the manuscript after the latest experiments, written before making those revisions. The cube-root growth census stands. What changes is which transport regularities we can predict, what our measurements mean, and how much of the apparent explanation survives a serious attempt to break it.

A short rule feature earns its place

Let m be the number of identical turns at the beginning of a rule: RLL has m = 1, RRLL has m = 2. Let c be births per boundary step, where a birth is a step onto never-visited ground. Across 2,185 stationary census blobs, the fitted relation is 1/c = 1.363 + 0.696m, with m capped at eight in this fit.

That relation predicted c on 176 fresh stationary rules of lengths 13–14 with R² = 0.877 and median absolute relative error 4.1%. The fresh fitted slope was 0.683, with a rule-bootstrap 95% interval [0.658, 0.707]. A later, broader validation retained 378 of 600 candidates of lengths 11–16 and gave R² = 0.711, below the registered 0.80 threshold. The candidates were retained by a growth filter; this is a different selection from the stationary cohort. Both scores belong in the paper. Choosing only the first would exaggerate how far the law travels.

The chiral-edge experiment contains the registration and frozen predictions; its c-law summary records seed 20261019 and 2,000 rule bootstraps. The mechanism experiment records the broader validation and its exclusions.

The edge result has substance, but the constants are still a puzzle

The attractive picture was that repeated same-handed turns circulate around young boundary cells until an opposite turn sends the ant into fresh ground. Some of that picture survives: 78.4% of the tested circulating-colour boundary reads with a prior read return after exactly four steps (47 rules, 1.90 million reads). That is a description of these selected reads, not a fraction of all ant steps.

The more discriminating comparison moved the ants to a torus with a flat band of fresh ground beside previsited ground. On the 60-rule comparison, the fitted slope was 0.678 and the intercept 1.399. Replacing the previsited interior with zero, young or old colours changed c by only about 0.3% at the median among retained rules. The original run exhausted the band before its measurement window; the replacement window-selection rule and exclusions are disclosed in the record. These are finite-window tests of robustness to initial interior colours, not proof that the evolving bulk never matters.

I find this stronger evidence for a fresh-ground contribution than another successful regression would be. Yet the proposed flat read-cost plateau, near-certain birth at the first opposite turn, and transition-kernel accuracy targets failed. We have not derived 1.36 or 0.70. The pinned results and provenance preserve those failures alongside the successful tests.

A predictive association that almost became an explanation

The opening run also seemed to predict higher boundary occupation, κ, after controlling for early area. But area is produced jointly by edge entry and occupation. Among ants reaching the same area, one with lower c may need higher κ. Selecting on their shared outcome can create an association even when the opening run has no direct effect on occupation.

The registered check on 176 fresh rules made this concern quantitative. The observed conditional lead coefficient was +0.148; a permutation model with no direct effect gave +0.145, with central 95% interval [0.137, 0.153]. Including ln c left +0.014, with rule-bootstrap interval [−0.045, +0.062]. In 177 retained pairs, early letter flips that preserved the opening run changed ln κ by −0.007 on average, interval [−0.078, +0.060].

The manuscript’s prefix lookup remains a measured predictor in its selected stationary cohort. Its gain beyond early area does not establish an independent transport mechanism. Nor have we proved that the opening run has no direct effect: this is one survivor-selected cohort and one occupation window. The shortening mutation’s total κ drop remains unexplained and is confounded with flip direction. Stage 4 of the mechanism record gives seed 20261019, 2,000 resamples, the exact commands and the saved summaries; its full probe replay requires regenerating ignored dumps.

Uniform occupation needs a moving reference

The probe divides boundary time averaged over an octave by the boundary’s fraction of the territory at the octave’s end. A uniformly occupying walker therefore need not report κ = 1. With area exponent a and perimeter exponent β, its reference is 2 ∫ from 1/2 to 1 of x^−a(1−β) dx. For a = 2/3 and β = 1/2, this is 1.1101.

The uniform-by-construction control gave κ = 1.118 ± 0.009 across eight seeds, against a reference of 1.107 using its measured exponents. The typical ant is about 0.81 times its own reference. Memoryless controls give 1.24–1.32 and the late rotor about 1.80, each against its own reference. The walker comparison reports eight seeds per setting and between-seed spread. Memoryless windows end earlier than the census, and noisy rotors at small noise are drifting. These qualifications prevent turning a useful contrast into an ant-specific theorem. They also prevent extending it to all memory models: earlier reinforced walkers had low, declining occupation in a different growth regime.

What the revision should say

The paper should promote the opening-run c law, correct the uniform reference, and explain the conditioning problem beside the prefix prediction. It should record that the tested same-turn square-loop mechanism failed, that its gated surgery was closed unrun, and that the growth-clock test failed its support gate and supplied no effect estimate. These are three different outcomes.

The strongest case against my preferred local-edge story is that the simple kernels missed their targets and the broader validation weakened. A useful next test would predict the law’s constants from independently measured return probabilities and score new rules without refitting. That is a proposal, not a registration or a result. For κ, direction-balanced mutations and a second cohort would be more revealing than another area-conditioned fit.

The manuscript gains a sharper empirical law and a more honest account of occupation. The reason the ants settle into cube-root growth remains open.