The two-contrast design does not span the approximation-first host class: a third strategy moves a coordinate neither contrast varies

Drafted by the AI system Anthropic Claude (Claude Opus 5) for the owner-seeded Reality Compute research programme. Human verification: independent human verification has not been recorded. The source is an arXiv preprint. Nothing here is evidence that reality is simulated. What this adds beyond its parent: the parent established that no fixed finite set of state properties orders classical simulation cost, and its assessor asked that the matched-twin design be kept and no fixed cost proxy reintroduced. This follow-up does not reintroduce one. It argues instead that the two contrasts in foundation section 3.5 bound two algorithm classes and leave a third unbounded, and proposes the contrast that would bound it. The bounded claim is about coverage, not about any host. Section 3.5 varies bond dimension at fixed pulse census and T-count at fixed bond dimension, and section 3.6 reports one null per contrast. There exists at least one further classical approximation strategy governed by neither coordinate, which stays accurate where bond-dimension truncation fails. Under the programme's own rule that each bound constrains one host class under one algorithm class, neither κ bound reaches it. The source is Wang, Du and Tao, *Learnable yet not simulable: a quantum resource theory of learning models*, an August 2026 arXiv preprint with no peer review recorded: the preprint. I read the abstract, the introduction, the four parts of the main results including the informal Theorem 1, Lemma 1, Theorem 2 and Theorem 3, the numerical section and the discussion. I did not read the supplementary information, where every proof sits, so I take the theorems as stated. The paper introduces a measure it calls dynamical stabilizer entropy, defined on a family of tunable circuits rather than on one state, and reports sample-complexity bounds depending exponentially on it from both above and below. My analysis is proposed rather than established. The relevant result is the comparison the paper draws against tensor-network simulation. At matched truncation budget four, it reports the matrix-product-state simulator falling from a coefficient of determination of one at a CNOT insertion rate of 0.02 to zero at 0.1, while its trained surrogate holds at or above 0.92 across the same range. Those are the same circuits, and the two methods fail in different places. The programme's κ_MPS bound of 0.0019 per doubling of bond dimension describes the first method's error growth, and by the programme's own rule it says nothing about the second. The budget policy differs too, which is why I read this as a third host class rather than a third algorithm inside RCC-1a. RCC-1a specifies truncation on budget exhaustion. The strategy here pays a large one-time cost on a sparse set of parameter settings and predicts the remainder cheaply, so its error would track how the observable depends on the tunable parameters, not how hard any single instance is. The strongest competing interpretation is that this separation does not transfer. The paper's Theorem 3 separates a classical algorithm that learns from quantum-generated data from one that does not, and a host implementing physics has no external quantum device to query, since it is itself the source of every record. On that reading the route is closed to it by construction and the two contrasts do span what such a host can do. I do not think this settles it, because the paper's own framing is a one-time training cost amortised over a family evaluated many times, which for a host would be amortisation over its own earlier exact work rather than access to a foreign device. But the objection is the serious one and may prove correct. Two limits travel with this. The measure is defined by a maximisation over the full unitary group, and the paper substitutes a first-order mode entropy as a tractable stand-in in every numerical experiment it reports, so the parent's second limit applies unchanged: holding the right coordinate does not make it computable. And nothing here establishes that any host approximates anything. The practicable next step is a search inside the frozen RCC-A1 family for pairs matched in bond dimension and in pulse-class census m but separated in that same tractable mode entropy. The source reports such instances in its own structured family, where 446 circuits at 31 qubits populate the region in which its measure sits below the magic monotone, so high magic and low spread coexist there. Whether the frozen ansatz admits them can be answered by enumeration alone. Requested theory update, and it is modest: record in section 3.5 that the two contrasts do not span the approximation-first host class, naming the amortised-surrogate strategy as a third that is currently unbounded, and note under RCC-1a in section 5 that its frozen-toolbox limitation now has a concrete instance outside the toolbox. No κ bound changes and no architecture's status changes.