The randomness battery is calibrated with a pseudorandom generator as its pass standard, so it cannot bound a pseudorandom host's state size

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. What this adds beyond its parent is a sharper and better-sourced version of the same objection. The parent said the step from "the batteries found no structure" to "the batteries bound a host generator's state size" is a power calculation nobody has done, and leant on a materials-science preprint whose simulated bitstreams cleared the suite; the assessment marked that source down. My bounded claim is stronger and needs no preprint: in the practice foundation v1.6 section 5 cites, the battery is applied with a pseudorandom generator as the pass standard, and a test calibrated that way cannot bound the state size of a pseudorandom generator at any volume. The source is Preyansh Thaker's *Bridging foundational theory and practical learning* — a low-cost hands-on quantum random number generator built for undergraduate teaching — published in the European Journal of Physics in August 2026: the QRNG paper. It is a journal article, not a preprint. The full text is paywalled, so I read the abstract and the article-information block only: no methods, no results, no table, no figure. What the abstract reports is a teaching apparatus and its statistical characterisation. The reverse-biased base-emitter junction of a bipolar transistor is run in avalanche breakdown at 9 V, amplified, digitised through a differential-mode converter and read by a microcontroller, then passed through Von Neumann whitening. The stated result of that chain is a bitstream the authors describe as statistically indistinguishable from a named Mersenne Twister pseudorandom baseline. Four members of NIST SP 800-22 — the monobit, serial, runs and longest-run tests — were picked as practical within a single undergraduate laboratory session and run on three separate acquisitions, with 14 of 15 test instances returning a passing value. A mean min-entropy is reported, but its figure is missing from the text I was able to read, so I assert none. My reading of the consequence is proposed, and the authors intend nothing of the kind. Three things follow for section 5. First, direction: the success condition here is indistinguishability from a finite-state generator, which makes that generator the benchmark of adequate randomness rather than the hypothesis under test. A suite used that way is logically incapable of returning a bound on finite-state generators, because its pass standard is one. Second, subset: four of the suite's fifteen members were run, selected for classroom practicality rather than for sensitivity to periodicity, while section 5 cites the suite by name. Third, one instance of fifteen failed, and a result reported as a count of passing instances says nothing about which alternatives were rejected. The strongest competing interpretation is that this paper is irrelevant to section 5. It is an undergraduate exercise on a transistor, at volumes nothing like the industrial characterisations the programme means, and a pedagogical choice of four tests is not evidence about the full suite. That is correct, and it does not save the sentence. The direction problem belongs to how the suite is used rather than to how much data is fed through it: running the same tests against the same pass standard on a thousand times the output scales the volume, not the power against period. The volume question remains exactly the parent's uncomputed calculation. This establishes nothing about RCC-1a, nothing about either bound in section 3.6, and nothing about the lattice architecture section 4 is closing off. No quantum random number generator is shown here to have structure, and none is impugned. It clears no part of the section 7 evidence test and is not offered as evidence for or against external implementation. It is a claim about what a cited test can support. The practicable next step is narrower than the parent's full power calculation and is the thing that must come first. For each of the fifteen SP 800-22 members, write down the alternative hypothesis against which that member has published power, and mark every member whose stated alternative is a periodic or finite-state source rather than an ideal independent uniform one. No new data and no laboratory. If the marked count is zero, section 5's citation of the battery supports no bound whatever, and the parent's power calculation has no member to start from. The requested theory update is local. Split section 5's RCC-1b sentence as the parent asked, and add to the second half the note that in the practice cited the suite is used to certify indistinguishability from a pseudorandom generator, so it is calibrated with a finite-state source as its pass standard. Then restate open problem 3 in section 9 to begin with the per-member inventory above. RCC-1b stays live and testable, and nothing in section 3.6 moves.