A matched-twin design removes the false-positive mechanism in the quantum test

Drafted by the AI system Anthropic Claude (Claude Opus 5) for the owner-seeded Reality Compute research programme, from the Session 006 code bundle and its captured output, produced in AI-assisted research sessions with the owner. Human verification: independent human verification has not been recorded. This reports a simulation result about test design. It is not a hardware experiment and not evidence that reality is simulated. The claim: a matched-twin comparison, RCC-A2, holds its nominal error rate under the confound that broke the programme's first quantum test design, RCC-A1. It does so because it never asks a cost proxy to rank circuits. The head-to-head result, with no external-computation effect present: | Confound | RCC-A1 scan, baseline–proxy r ≈ +0.85 | RCC-A2 twins | | ---: | ---: | ---: | | 3 × 10⁻³ | 97.80% false positives | 1.25% | | 1 × 10⁻² | 100.00% false positives | 1.20% | Both designs ran against the same Session 004 generator: 195 pairs (390 circuits), 20 000 shots per circuit, 2 000 replicates, at a nominal two-sided level of 1%. The mechanism comes from Session 004. RCC-A1 regresses output error on a complexity proxy across many circuits. When the baseline observable is correlated with the proxy, an ordinary pulse-asymmetry noise effect loads onto the proxy coefficient and looks like a host effect. Session 005 then showed that no fixed proxy orders cost anyway. RCC-A2 removes both problems. Each pair has a control and a test circuit with an identical pulse-class census (Δm = 0 exactly), matched ideal output (max |Δp_ideal| = 0.000817) and matched magic (max |ΔM₂| = 0.00819). Only the certified bond dimension differs. Noise that depends on the census or the ideal output acts equally on both arms, so the paired difference does not see it. The design has the statistical properties it should. Under pure shot noise the empirical 99th percentile of |t| is 2.596, close to the nominal cutoff of 2.576. The minimum detectable effect is 0.00575 logit units at 79.5% power, against a target of 80%. Across matching tolerances from 0.05 to 0.001 the false-positive rate stays between 0.55% and 1.60%. An injected effect is recovered without meaningful bias, and all 11 verification checks pass. It also fails where it should. When the p_ideal match is deliberately dropped, the false-positive rate rises to 10.15% with a bias of +0.00800. That is the design's load-bearing assumption, stated as a failure mode rather than hidden. My analysis, proposed: the general lesson is that a paired design with exact matching on every confound-relevant quantity is more robust than a regression on a proxy, because it does not need to know the confound's functional form. It only needs the confound to depend on quantities that can be matched. The strongest competing interpretation is that RCC-A2 only works against this one confound generator, and a noise process that depends on bond dimension itself would pass straight through it. That is correct. Such noise is indistinguishable from a host effect in this design, and no internal test can separate them without an independent handle on the noise. What this does not establish: nothing about any host. It shows the instrument can hold its error rate in simulation. Loop Record 001 later found that its cost certificate needed exact simulation of each circuit, which confined the test to small circuits until Session 007's analytic certificates. Practicable next step: preregister the matching tolerances and the confound families the design is claimed to survive before any hardware run, and add noise processes that scale with circuit structure to the stress suite. Requested theory update: record RCC-A2's head-to-head table and its failure mode in the Consolidated Master v1.6, §3.1, as the programme's working test design, as set out in the v1.6 master.