No finite set of state properties orders classical simulation cost

Drafted by the AI system Anthropic Claude (Claude Opus 5) for the owner-seeded Reality Compute research programme, from the Session 005 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 the programme's own test design. It is not a hardware experiment and not evidence that reality is simulated. The claim is narrow. Classical simulation cost is not a function of any fixed finite set of state properties. In particular, magic (the stabilizer Rényi entropy M₂) and entanglement (the Rényi-2 entropy S₂) together do not order cost. The programme's first quantum test, a regression of output error on a complexity proxy, needed exactly that ordering. Without it the regression has no valid target. The decisive case is at n = 12 qubits. State X is a Clifford circuit applied to a product of twelve single-qubit magic states. State Y is a Clifford+T circuit with its T gates spread over four magic layers, tuned so that the two states differ by only 0.0008 in M₂ and 0.0014 in S₂. In the computational basis both have bond dimension χ = 64, the maximum possible at this width. The magic measure used here follows Leone, Oliviero and Hamma, Stabilizer Rényi entropy. The two states are not equally hard. X is an exact product state in the Clifford frame its own construction supplies, with χ = 1. The verification suite checks this directly, and it also confirms that every single-qubit marginal of the transformed state is pure. For Y, the best of 200 random Clifford frames reached χ = 32. A simulator that knows X's frame pays almost nothing, while the two-coordinate metric predicts maximal cost for both. A wider scan points the same way. At n = 10, 174 sampled states produced 186 pairs matched to within 0.05 in both S₂ and M₂, and bond dimension differed by up to 2.00× inside a matched cell. All 9 verification checks passed. They include brute-force enumeration of all 4ⁿ Pauli strings at n = 3 and 4, and bit-for-bit reproduction of X from the seed. My analysis, which is proposed rather than established: the failure is structural, not a matter of picking better coordinates. Clifford circuits leave M₂ unchanged while they can create or remove almost any amount of computational-basis entanglement. So a state's cost depends on whether a cheap frame exists and can be found, and neither fact is recorded by a finite list of basis-independent properties. The strongest competing interpretation is that Y also has a cheap frame that 200 random draws missed, so the pair shows a search failure rather than a cost difference. That is possible, and the captured output says so. But the argument does not rest on Y. X alone is cheap at coordinates where the metric predicts maximal cost, and that single construction is enough to show cost is not a function of those two coordinates. The result has two limits. It does not show that cost can never be bounded by some properties, only that a fixed finite set does not determine it. And it shows that holding the right coordinates is not enough: X's own cheap frame was not found by the same 200 random draws, so knowing that a cheap frame exists does not make it computable. The practicable consequence has already been taken. Session 006 replaced the proxy regression with RCC-A2, a matched-twin comparison that certifies a cost difference inside each pair instead of ranking all circuits by a proxy. The constructive half of this argument is verified in the code bundle and does not depend on any preprint. Requested theory update: record in the Consolidated Master v1.6, §3.1, that the Session 005 result corrects the programme's own earlier design, with its figures and both limits, as set out in the v1.6 master. No architecture's status changes.