TL;DR. Part 34 left branch 3 with a well-posed question: does HWM’s ten-step abstract-action transition graph carry more structure — higher SI above a degree-matched null — than the one-step primitive-action graph over the same latents? The answer came back looking like the best result this project has ever produced: coarse beats fine on 20 of 20 maps, p < 0.0001, with the ground-truth gate passed before we measured anything. One control killed it. The raw effect is a sensitivity artifact of the estimator, correlating r = +0.987 with off-diagonal graph mass; with self-loops zeroed the coarse graph is not more structured at all (+0.021, p = 0.45, 11/20 maps). We are reporting the 20/20 result and then reporting that it means nothing, because the control is the story.

The measurement

Setup, per Part 34’s reframing: 20 maze2d maps, 5050 frames each, run through the released HWM checkpoint to get its (single, shared) 18×43×43 latent space — 36,980 dimensions, k-means into 48 discrete states per map. From the same latent sequence we build transition graphs at five horizons: skip ∈ {1, 2, 5, 10, 20} steps per edge, where skip=1 is the primitive-action graph and skip=10 is the model’s trained l2_step_skip. For each graph we compute SI above a degree-matched null. Twenty maps give twenty paired replicates.

The gate ran first: a linear probe from the latents recovers agent position with R² = 1.000 on every one of the 20 maps. After the SE-JEPA episode — where the “true by construction” nuisance axis turned out to occlude the object being measured — no measurement here runs before the axis it depends on is verified model-free. The latents genuinely encode position. Hold that thought.

The result that looked like a slam dunk

 skip   offdiag        SI-null raw
    1      0.07       0.076 ± 0.014
    2      0.13       0.175 ± 0.026
    5      0.31       0.378 ± 0.071
   10      0.53       0.570 ± 0.107
   20      0.74       0.683 ± 0.133

SI above the null rises nine-fold from the one-step graph to the twenty-step graph. Paired at the horizons that matter — coarse (skip=10, the trained abstraction) against fine (skip=1):

raw: mean difference +0.494, p < 0.0001, coarse wins on 20 of 20 maps.

Every replicate. A permutation p-value with no ties to argue about. The preregistered-looking answer to Part 34’s question, in the direction that would have given hierarchical world models a mechanism: the coarse level’s transitions carry more structure, so that is what hierarchy buys.

This is the point in previous campaigns where the number went in the abstract.

The control that killed it

Look at the second column of that table. Off-diagonal mass — the fraction of transitions that leave their cluster — climbs from 0.07 to 0.74 across the same sweep. Of course it does: at skip=1, consecutive frames almost always land in the same k-means cluster, so the graph is mostly self-loops; at skip=20 the agent has moved. That is not structure. That is what a longer horizon does to any discretised trajectory, structured or not.

And SI-above-null is not equally sensitive everywhere. A graph that is 93% self-loops has almost no off-diagonal mass for the estimator to find community structure in; the same estimator on a graph with 74% off-diagonal mass has ten times the material to work with. The null model is degree-matched — it equalises the marginals — but matching marginals does not equalise the estimator’s power, and here power tracks the very variable we swept. Correlating the raw effect against off-diagonal mass across the five horizons:

r = +0.987.

The raw rise essentially is the mass curve. So the control: zero the self-loops in every graph, renormalise, recompute SI above the (re-matched) null, and pair coarse against fine again on the structure that remains:

 skip   SI-null nodiag
    1      1.180 ± 0.163
    2      1.250 ± 0.159
    5      1.233 ± 0.208
   10      1.201 ± 0.167
   20      1.057 ± 0.151

nodiag: mean difference +0.021, p = 0.45, coarse wins on 11 of 20 maps.

Flat. A coin flip. Once both graphs are scored on their off-diagonal structure alone, the ten-step abstract-action graph is exactly as structured as the one-step primitive graph. The 20/20, p < 0.0001 effect was the estimator’s sensitivity curve wearing the costume of a finding.

Two lessons we intend to keep

A degree-matched null is not enough when the swept variable moves the estimator’s sensitivity. The null answers “is this graph more structured than a random graph with the same marginals?” — and it answers it honestly at every horizon. What it cannot answer is “is the difference between two horizons structure, or power?” When the thing you vary (horizon) also varies how much signal the estimator can see (off-diagonal mass), the paired comparison inherits the confound even though every individual measurement is clean. The r = +0.987 check costs one line and should run whenever the compared conditions differ in graph density. Worth being honest about how it was caught: not because the raw result looked suspicious — it looked perfect — but because self-loop handling has burned SE measurements in this project before, so the control was on the checklist regardless of how the headline number looked.

A clean ground-truth gate does not protect against a sensitivity confound. The gate did its job: unlike SE-JEPA’s occluded cube, these latents demonstrably encode position, R² = 1.000, all 20 maps. Every frame of the pipeline upstream of the estimator was sound — and the result was still an artifact, because the failure was not in the representation, it was in how the measure’s power interacts with the design. Gates validate axes. They do not validate comparisons.

What this means for branch 3, and the campaign

Part 34 set the stakes explicitly: if the coarse level is more structured, that is a mechanism for why hierarchical planning helps and a target a better architecture could optimise; if the two are equally structured, the benefit is search-space reduction, which Hi-LeWM has already argued, and we would be adding nothing.

It is the second one. On this model, the hierarchy’s coarse level carries no additional transition structure — its benefit, whatever it is, is consistent with plain search-space reduction over a shared representation. There is no mechanism here for us to claim, and we are not claiming one.

The three-branch campaign is closed, with all three branches answered:

branch answer status
1 — planner economics value = “having a planner” + “extra search”; only the first varies decomposition; two-factor account survives 3/4 tasks, not claimed confirmed
2 — capacity sets planning value flat across 128× (rho = +0.064, p = 0.82) refuted, as preregistered
3 — coarse graph is more structured 20/20, p < 0.0001 raw — killed by the self-loop control artifact

One decomposition, one refutation, one artifact. No positive claims. That is not the campaign failing — the point of Yoon’s critique was that this project kept producing measurements without hypotheses sharp enough to die. All three of these were sharp enough to die, and two of them did, cleanly and cheaply, on a single 3090 Ti.

Repro: python3 repro/b3_analyze.py data/b3_graph.jsonl in SuuTTT/world-model-paper, branch results/three-branch-2026-08-20 (data 439e9a8).