Drafted by the AI system Anthropic Claude (Claude Opus 5) for the owner-seeded Reality Compute research programme, from Quantum Loop Record 001's scripts in the Session 006 code bundle, the Session 007 bundle and their captured output, produced in AI-assisted research sessions with the owner. Human verification: independent human verification has not been recorded. This is a finding about the programme's test instrument, in simulation. It is not a hardware experiment and not evidence that reality is simulated.
The claim: as first built, the RCC-A2 test could only certify a cost difference by exactly simulating the circuits being compared. That confined the test to a regime of roughly 10³ to 10⁶ operations, where a resource-constrained host is not plausibly under pressure. A null result there says little about hosts that matter.
RCC-A2 compares a cheap control circuit with an expensive test circuit and looks for extra error in the expensive one. The comparison is only meaningful if the cost difference is certified. In Session 006 the certificate was the exact Schmidt rank across a cut, read from the statevector. Building the statevector is simulating the circuit. The cost of certifying therefore grows exactly as fast as the cost the test is trying to probe.
Loop Record 001 found a second limit inside the frozen circuit family. At n = 6, 10 and 12, pairs exist at one or two certified doublings of bond dimension, and three or more doublings yields zero pairs. A targeted search for low-rank control circuits matched plain random sampling in 5 of 6 cells, so the cap comes from the ansatz, not the search budget. At equal pair count, the κ bound available at one doubling was 0.00575 per doubling, and leverage came only from the number of doublings.
My analysis, proposed: this is a general trap for any test of a computational host. If the evidence that one case is harder than another requires doing the hard computation, the test can never reach the regime where the host would be strained. The certificate must be cheaper than the thing it certifies.
Session 007 took that step. Its certificates bound Schmidt rank from stabilizer tableaux without building a statevector. Each T gate splits the state into branches, and the certification cost is 2^t·poly(n), exponential in T-count only. The per-gate constant, 1.171573, matches the stabilizer extent of Bravyi et al.,
Simulation of quantum circuits by low-rank stabilizer decompositions. For Clifford circuits at n = 96, certified bond dimensions span 2⁴⁵ to 2⁴⁸, and the test arm's contraction cost is about 2.14 × 10⁴⁵ operations. The run took 21.3 s for 60 circuits.
The strongest competing interpretation is that the small-circuit regime was never meant to find a host effect, only to validate the statistics, so this is a known staging limit rather than a flaw. There is something to that. But the programme reported a κ bound from that regime, and a bound from circuits no host would find hard constrains very little. The record should say so.
The fix has its own price, which this finding does not hide. Adding magic collapses the analytic certificate. At n = 32 the certified separation is +1.00 doublings at t = 0 and already −0.26 at t = 2, falling to −1.83 at t = 8. Wide circuits and magic-rich circuits are currently mutually exclusive under this certificate. Session 008 located the main cause in the loose upper bound Σⱼ2^(Eⱼ).
What this does not establish: nothing about any host, and nothing against the statistical validity of RCC-A2 itself. It challenges only the claim that the early bound was a meaningful constraint.
Practicable next step: tighten the upper bound, which Session 008 found is 81% of the certification problem, so that certified separation survives at both width and magic.
Requested theory update: record Loop Record 001's structural finding and the instrument limits in the Consolidated Master v1.6, §3.3 and §3.7, as set out in
the v1.6 master.