# Reality Compute — Executive Summary

**Prepared for:** Alex Whayman  
**Version:** 1.6  
**Date:** 15 September 2026  
**Supersedes:** v1.5 (12 September 2026)  
**Companion:** [Complete consolidated master, v1.6](Reality_Compute_Consolidated_Master_v1.6.md)

## Current position

Reality Compute asks whether a resource-constrained computational implementation of physical law would leave observable departures from calibrated physics, and whether such an implementation could be told apart from ordinary explanations at all.

**No observation currently favours external implementation.** The programme has formal results, a statistically sound test design and two null bounds on specific host classes. It has not produced evidence that reality is simulated, and nothing in this version is such evidence.

## What changed in v1.6

Version 1.6 records the quantum branch's work from Sessions 005 to 009 and Quantum Loop Record 001. Every result in it is either a null or a finding about the programme's own instrument. That is the most credible thing the record can show, and it is stated plainly here.

1. **Withdrawn:** Session 007's recommendation to narrow the branch to one host class. Both host classes stay open, and both are now bounded.
2. **Added:** a two-contrast design. Bond dimension and T-count are orthogonal, and each tests a different kind of host.
3. **Added:** two null bounds on how strongly a host could respond to computational cost, one per host class. They are never combined.
4. **Added:** the instrument's current limits.

## Principal findings

**No fixed set of state properties orders simulation cost (Session 005).** At n = 12, two states matched to within 0.0008 in magic and 0.0014 in entanglement differ sharply in true cost: one is an exact product state in a known Clifford frame, while the best of 200 random frames for the other reached bond dimension 32. The original proxy-regression test had no valid target.

**A matched-twin design removes the false-positive mechanism (Session 006).** Against the same confound generator with no effect present, the old design produced false positives in 97.80% to 100.00% of replicates. The matched-twin design, RCC-A2, stayed at 1.25% and 1.20% against a nominal 1%.

**The certificate had to simulate the circuit it certified (Loop Record 001).** Certifying which circuit was cheaper meant simulating it exactly, which confined the test to roughly 10³ to 10⁶ operations. Inside the frozen ansatz, certified separation also stops at 2 doublings.

**Analytic certificates reach n = 96, for Clifford circuits (Session 007).** Certificates that never build a statevector ran at n = 96, where the test arm costs about 2.14 × 10⁴⁵ contraction operations. Adding T gates collapses the certified separation. This is a legitimate test of a tensor-network host, which is the architecture RCC-1a specifies.

**Two contrasts bound two host classes (Session 009).** Varying bond dimension tests a host that contracts tensor networks. Varying T-count at fixed bond dimension tests a host that uses stabilizer decompositions.

## The two bounds, and why they differ

- **Tensor-network host:** κ_MPS ≤ 0.0019 per doubling of bond dimension.
- **Stabilizer-decomposition host:** κ_stab ≤ 0.00082 per doubling of stabilizer extent, **with a 3.80% false-positive rate** against a nominal 1% at the tighter matching tolerance.

The second bound carries an uncorrected systematic that the first does not, and tightening the match made it worse. Its cause is not established. Publishing the two bounds with equal confidence would be false precision.

Each bound constrains one host class using one algorithm class. A host using a different method is not constrained, and the two figures are not pooled.

## Priorities

1. **Tighten the upper bound** Σⱼ2^(Eⱼ). It is 81% of the certification problem and remains the top technical item, unchanged from v1.5. Session 009 does not replace it.
2. **Fix the Session 009 systematic** by also matching the derivative dp/dp₁, preregistered, then re-run the T-count contrast.
3. **Quantify the pseudorandom-outcome constraint** from existing quantum random number test volumes.
4. **Move to hardware.** Everything in Sessions 004 to 009 is simulation only.

Each result updates only the hypothesis it tested. A null bound narrows an architecture; it is not evidence about whether reality is simulated.