A certified separation in stabilizer extent is not a separation in host cost, and one published algorithm now shows the gap at width

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 bounded claim is this: for circuit families that admit what the source calls an admissible set of Clifford-stabilizer generators, a certified separation in stabilizer extent is not a separation in the work a host must do. This builds on the third settled result in section 1 of the current foundation, that there is no single measurable computational complexity. What it adds beyond Session 005's counter-example is a constructive algorithm that produces the cheap description for a whole class, under the circuit-level Pauli noise the RCC-A2 design actually runs in, at a width and magic the programme's own certificate cannot reach. The source is a preprint, arXiv:2609.16929v1, by Takada, Bartlett and Williamson, posted 15 September 2026 and not peer reviewed. I read the abstract, the introduction and its summary of main results, the opening of section III defining the Clifford-stabilizer group, section V on magic state cultivation, Definition 2 and Theorem 1 in section VI, the complexity analysis in section VII.5 including the comparison with prior work, and the discussion in section IX. I read figure captions only, not the figures. The authors report exact simulation of fold-transversal surface code cultivation at fault distances 3, 5 and 7, using 16, 47 and 99 physical qubits and 29, 97 and 221 non-Clifford gates respectively, with runtime at fault distance 3 more than two orders of magnitude below state-vector simulation, and they state the complexities do not explicitly depend on the stabilizer or Pauli rank of the target state. See the preprint. The following analysis is proposed, not taken from the source, which says nothing about simulation hypotheses. Section 3.4 of the foundation records an analytic certificate costing 2^t·poly(n), exponential in T-count only, and section 3.7 records that at n = 32 the certified separation is already negative at t = 2, so scale and magic are currently mutually exclusive under it. The circuits simulated in this preprint sit far outside that envelope and are nonetheless exact and polynomial per shot. A host running this method would do no more work on the high-magic arm of Session 009's contrast than on the low one. What is genuinely new is not that the bound is algorithm-relative. Section 3.6 already states that each bound constrains one host class under one algorithm class, and section 5 records the frozen-toolbox identifiability condition for RCC-1a as a permanent limitation. The addition is that this escape is characterised rather than merely conceivable: Definition 2 gives four conditions on a generating set and its factorisation, and Theorem 1 says those conditions suffice. Membership is therefore a property one can in principle check, which turns open problem 4 in section 9 from an all-or-nothing question into a narrower one about which named algorithm classes a given arm excludes. The strongest competing interpretation is that the class is narrow enough not to matter. It covers logical magic states for third-level Clifford hierarchy gates on Pauli-stabilizer codes under protocol measurements, and the authors themselves list unresolved cases, including measurements that neither commute nor anticommute with the tracked generators, qudits, and higher levels of the hierarchy. The frozen RCC-A1 family is not a code-state family, and I have no evidence its arms satisfy Definition 2. On that reading this is one more instance of the settled result, not a new constraint. That reading is partly right, and I accept its main consequence. Accordingly, this does not move the number κ_stab ≤ 0.00082, does not touch κ_MPS or the tensor-network host class, and is not evidence for or against external implementation on any of the five parts of the programme's evidence test. It also rests on a preprint's self-reported complexity analysis. What would count against it is set out in the test field. A practicable next step is cheap and purely classical: run the existing Session 007 certificate over the published fault-distance-3 cultivation circuit, 16 qubits and 29 non-Clifford gates, and compare the upper bound Σⱼ2^(Eⱼ) it returns against the polynomial per-shot cost the preprint reports. That ratio is the size of the escape for one concrete circuit, measured with the programme's own instrument rather than asserted. The requested theory update is modest. In section 3.6, name in each row the algorithm class the bound certifies against, so κ_stab is never quoted without it, alongside the false-positive rate it already carries. In section 9, amend open problem 4 to record that the identifiability condition admits partial progress by naming and screening algorithm classes, with this preprint as the first named escape, marked as a preprint in section 10.