Preregistered Experiment · R5A · July 2026

The Accessibility Landscape of Channel z

A preregistered population study. The protocol was hashed, timestamped, and anchored on-chain before any confirmatory data existed. Every artifact below can be verified by anyone.

The question

A small network learns addition modulo 47. Information about its inputs sits in a bottleneck layer. Some facts about those inputs are easy to read back out of that layer; others are not.

What determines which? One possibility is relevance: the network keeps a fact legible because that fact matters to producing the answer. Another is simplicity: the network keeps a fact legible because it is structurally simple to state, and relevance has nothing to do with it.

The distinction matters for interpretability. If readability tracks relevance, then what is easy to find inside a model is plausibly what the model is using. If readability tracks simplicity, then prominence inside a network says little about function, and finding something legible is weak evidence that it does any work.

The design

Thirty networks trained from fresh seeds, none reused from prior studies. Twenty-four binary predicates over the input pair, chosen so that output association and predicate simplicity are decorrelated by construction, verified from labels before any network was trained. Accessibility measured as normalized balanced accuracy of a nonlinear probe reading each predicate from the bottleneck. A mixed-effects regression of accessibility on standardized output association, standardized simplicity, and an algorithmic-role annotation, with a clustered bootstrap over seeds.

Five registered guards could halt or invalidate the study before it reached a verdict, including one that would have prevented any training from running at all. The decision table assigned a verdict to every possible outcome in advance.

Results

Under the preregistered decision table, all confirmatory guards passed. Thirty of thirty networks satisfied the eligibility criterion against a registered floor of twenty-four, decoding the 47-way residue from the bottleneck at top-1 accuracy of 1.0. Of 720 probes, none met the registered instability criterion, against a ceiling of ten percent. The preregistered mixed-effects analysis reached the SUPPORTED row.

In standardized units, output association carried a coefficient of 0.322 with a 95% bootstrap interval of [0.293, 0.353], against a registered margin of 0.05. Predicate simplicity carried a coefficient of −0.171 with an interval of [−0.202, −0.138]; within this battery, higher predicate cardinality was associated with lower accessibility. The difference between them was 0.493 with an interval of [0.489, 0.497], against a registered separation margin of 0.05. All 10,000 bootstrap fits converged.

Accordingly, the preregistered conclusion is that within this modular-addition substrate, at this bottleneck, accessibility tracks output relevance beyond simplicity.

Scope

That sentence is the entire claim. The registration binds it: no causal claim, no lesion, and the algorithmic-role annotation is descriptive only. No outcome of this study, positive or negative, constitutes evidence about frontier models, transformers, or AI systems outside this registered substrate. Small networks, one controlled task, one measurement site. The contribution is methodological.

Limitations

The analysis code was written after the protocol froze. Its hash establishes what ran; it does not establish that the code was committed in advance. Every registered constant in the code was checked mechanically against the frozen document and matches, but full pre-commitment of analysis code is a stronger standard, and the next study in this line will freeze the analysis script alongside the protocol.

The negative simplicity coefficient is conditional on this battery and this registered model. The highest-cardinality predicates in the battery are also the least output-associated, and that stratum carries weight in the estimate.

OpenTimestamps attestations were returned by three independent Bitcoin calendars. Completing local verification requires a Bitcoin node; the proofs are included above for anyone who has one.