# Reality Compute

## Consolidated Master — v1.5

FOUNDATION DOCUMENT

**Prepared for:** Alex Whayman
**Date:** 12 September 2026
**Supersedes:** v1.3 (7 September 2026) as the current position
**Status:** Research record. External simulation is not established. Nothing in this document is evidence that reality is simulated.

**What changed since v1.3.** Five research sessions, one anomaly ledger, and one structural correction. The programme now records, for the first time, the strongest existing evidence *against* its own best\-specified architecture — a gap v1.3 had. The quantum branch has a working test design and a newly located bottleneck. One new architecture is proposed.

* * *

## 1\. Current position

Reality Compute asks whether a resource\-constrained computational implementation of physical law would produce observable departures from calibrated physics, and whether such an implementation can be distinguished from ordinary explanations at all.

The honest summary: **no observation currently favours external implementation.** The programme has produced useful formal results, a statistically sound test design, and a clearer map of what would and would not count as evidence. It has not produced evidence.

Three results constrain everything else and are treated as settled:

1. **Faithful implementations are unreachable.** If an implementation reproduces the same distribution of accessible records, every likelihood ratio is exactly 1. No internal experiment can distinguish it, ever. Only *lossy* implementations are testable.
2. **External slowdown is invisible.** A host that pauses all internal processes consistently changes no internal clock comparison. "Demanding physics should lag" is false without a further assumption.
3. **There is no single measurable computational complexity.** State\-preparation cost, classical simulation cost, entanglement and non\-stabilizer resource are four different quantities. Session 005 strengthened this: classical simulation cost is not a function of any fixed finite set of state properties.

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## 2\. Changelog from v1.3

| Area | v1.3 | v1.5 |
| --- | --- | --- |
| Architecture spec | Not chosen | RCC\-1a specified (approximation\-first, truncation policy) |
| Quantum test | Draft protocol, unexecuted | RCC\-A2 designed, feasibility executed, false\-positive mechanism identified and designed out |
| Cost certificates | None | Analytic bounds, exponential in T\-count only; bottleneck now located |
| Evidence against | **Absent** | Section 4 — Lorentz and UHECR nulls recorded as standing constraints |
| Architectures | One implicit | Four specified, one new, each with status |
| Evidence criteria | Informal | Five\-point test, Section 7 |
| Anomaly base rate | Not addressed | Section 8, from the ledger |

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## 3\. The quantum branch, Sessions 004–008

### 3\.1 What was established

**Session 004 — the false\-positive mechanism.** The proposed regression test's error rate is governed by one quantity nobody had named: the correlation between the baseline observable and the complexity proxy. Below |r| ≈ 0.35 it holds its nominal rate; at |r| ≈ 0.73, ordinary depolarizing noise with *no effect present* produces a spurious result four times the detection threshold and rejects the null **100% of the time**. Decorrelating the baseline from the proxy is what makes incoherent confounds orthogonal to the tested regressor.

**Session 005 — no finite cost metric exists.** At n \= 12, two states matched to |ΔM₂| \= 0.0008 and |ΔS₂| \= 0.0014 differ by ≥ 32× in true simulation cost. Any fixed finite set of state properties fails to order cost. This killed the proxy\-regression design and forced a replacement.

**Session 006 — RCC\-A2.** A matched\-twin two\-point design that needs no cost ordering. Against the identical confound generator: RCC\-A1 false\-positives at 97.8–100%; **RCC\-A2 stays at 1.2% against a nominal 1%.**

**Session 007 — analytic certificates.** Stabilizer\-decomposition bounds costing 2^t·poly(n) — exponential in T\-count only, never in width. Runs at n \= 96 in \~0.35 s/circuit. Limitation: certified separation crosses at t \= 2–4, so the test was effectively Clifford\-only.

### 3\.2 Session 008 — the loop named the wrong target

Loop Record 001 identified "tighten the analytic lower bound" as the highest\-value next step, on the basis that it reached only \~0.40 of the exact Schmidt rank. That work was carried out. The result is more useful than the intended one.

**Result A — the looseness is deterministic, not statistical.** The Session 007 operator\-norm bound satisfies

```math
L_1/r_{\text{exact}} = \xi^{-t}, \qquad \xi = 1.171573
```

where ξ is the stabilizer extent of the magic state and *t* is the T\-count. Verified to 10⁻¹⁵ at t \= 0 and exactly at the median for t \= 2, 4. The bound loses **0\.2284 bits per T gate**, predictably.

**Result B — a new bound, derived and validated.** Nuclear\-norm duality gives, for any stabilizer state φ,

```math
r \ge |\langle\psi|\phi\rangle|^2 \cdot 2^{E_\phi}
```

read as: a state overlapping strongly with a highly entangled stabilizer state cannot have low rank. It costs the same 2^t and strictly improves the worst cases (0.364 → 0.729 of exact).

**Result C — the purity bound is essentially exact.** The participation\-ratio bound r ≥ 1/Tr\[ρ\_A²\] reached the exact rank in 43 of 45 circuits tested, and is provably never worse than the operator\-norm bound. It costs 2^{4t}·poly(n) — still exponential in T\-count only, at 65,536 stabilizer terms for t \= 4, which is affordable.

**Result D — and this is the finding that matters.** Measuring where the looseness actually sits:

| T\-count | Upper bound is off by | Lower bound is off by |
| ---: | ---: | ---: |
| 0 | 1\.0× | 1\.00× |
| 2 | 4\.0× | 1\.37× |
| 4 | **16\.0×** | 1\.88× |

The upper bound Σⱼ2^{Eⱼ} doubles per T gate — **1\.000 bits per gate**. The lower bound loses 0.2284 bits per gate. So tightening the lower bound addresses at most **19% of the problem**, and the crossing that made the test Clifford\-only is driven overwhelmingly by the *upper* bound.

**Redirect.** Σⱼ2^{Eⱼ} is the triangle inequality on Schmidt rank, and the true rank of a superposition is typically far below the sum of its branch ranks — 16× below at t \= 4 here. The programme's next technical step is tightening the **upper** bound, not the lower one. The lower\-bound work is now done and banked; it buys back 0.23 bits per gate that were previously lost.

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## 4\. Standing evidence against

**This section did not exist in v1.3 and should have.** The programme documented supporting leads without recording the strongest published constraint on its own best\-specified architecture.

The clearest architecture — a discrete spacetime lattice (Beane, Davoudi & Savage, [arXiv:1210.1847](https://arxiv.org/abs/1210.1847)) — makes a concrete prediction: energy\-dependent photon propagation. Two independent programmes have looked.

| Test | Observable | Result |
| --- | --- | --- |
| Gamma\-ray burst dispersion | Energy\-dependent arrival times over cosmological baselines | **Null.** Constrained beyond the Planck scale |
| GRB polarization | Birefringence from Lorentz violation | **Null** |
| UHECR spectrum & anisotropy | Directional structure correlated with a fixed spatial axis | **Null.** GZK suppression as expected |

These are the only two observational programmes with direct bearing on any Reality Compute architecture, and both report nothing. Under the programme's own rules this is evidence against the lattice architecture and must be recorded as such. It does not constrain non\-lattice implementations.

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## 5\. Architectures

A specification is only research\-grade if it predicts something that could come out either way. Four are now specified.

### RCC\-1a — approximation\-first classical host

Host classically approximates the internal quantum dynamics using methods whose cost is governed by non\-stabilizer resource. On budget exhaustion it **truncates** rather than pausing — the only budget policy that writes anything into the record.

**Predicts:** excess output error above a certified cost threshold. **Testable:** yes, in the lab, via RCC\-A2. **Status:** live; κ (suppression per doubling of certified bond dimension) bounded at ≤ 0.0019. **Identifiability condition:** only targets hosts using methods in the frozen toolbox — untestable from inside, and a permanent limitation.

### RCC\-1b — pseudorandom\-outcome host *(new in v1.5)*

A deterministic host must generate every quantum measurement outcome in the universe. True randomness is unavailable to it, so outcomes come from a pseudorandom generator with finite state *s*.

**Predicts:** measurement\-outcome sequences have period ≤ 2^s and admit a polynomial\-time distinguisher given sufficient output. **Testable:** yes, and cheaply — quantum random number generators are already subjected to large statistical batteries (NIST SP 800\-22, TestU01, Dieharder) on enormous output volumes, with no structure detected.

**Why it bites.** A cryptographically secure PRNG is by construction indistinguishable in polynomial time, so this test cannot exclude an unlimited host. But the programme's entire premise is a **resource\-constrained** host — and a constrained host cannot afford cryptographic\-grade generation for every measurement outcome in a universe. The test therefore bites precisely on the hypothesis the programme actually holds, which is unusual and worth exploiting.

**Prior art:** the question predates the simulation framing — see [quant\-ph/0006079](https://arxiv.org/html/quant-ph/0006079) on whether quantum randomness arises from deterministic chaos.

**Status:** live, and the existing null results are already a constraint the programme should quantify.

### RCC\-1c — discrete lattice

**Predicts:** photon dispersion, cosmic\-ray anisotropy. **Status:** being closed off — see Section 4.

### RCC\-0 — faithful implementation

**Predicts:** nothing. **Status:** permanently untestable, by result 1 of Section 1. Retained only to mark the boundary.

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## 6\. What the programme should not do

Carried forward from v1.3 and reinforced by the anomaly ledger:

- No additive evidence scores pooling unrelated streams.
- Update only the hypothesis actually tested.
- Separate the five explanations — documented human development, lost technique, precursor civilisation, nonhuman agents within the world, operator intervention. Evidence for one is not evidence for the others.
- A model that can always relocate its threshold beyond the next experiment is unconstrained, not surviving.
- Discovery\-tool record counts are not evidence counts.

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## 7\. The evidence test

A finding counts as evidence for external implementation only if it clears all five:

1. **Large, not marginal** — a factor\-scale effect, not a 3σ excess in a favourable bin.
2. **Confirmed in an independent channel** — a different observable, not more of the same data.
3. **Growing with better data**, not blurring.
4. **Found incidentally**, by researchers measuring something else.
5. **Matching a specified architecture's signature** — right sign, scale and threshold behaviour — rather than merely being unexplained.

Criteria 1–4 are what separated the anomalies that survived from those that died. Criterion 5 is what separates "our model is incomplete" from "this is an implementation artifact." **Nothing currently known clears even the first four.**

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## 8\. Base rate

From the anomaly ledger: of the headline cosmological anomalies of the last fifteen years, most shrank or died. Two mechanisms account for nearly all of it — the theoretical prediction moved, or the search space was larger than reported. BICEP2 was announced at roughly 7σ and was galactic dust. The claimed CMB Hawking points fell from 99.98% to about 87% once 52 tested annulus configurations were properly marginalised — the same look\-elsewhere error Session 004 quantified, in print, in MNRAS.

The counterweight matters equally. The solar neutrino deficit was attributed to a faulty solar model for **thirty\-three years** and turned out to be real physics; SNO settled it in 2001 by measuring total flux alongside electron\-flavour flux. Accelerating expansion was found by two rival teams who set out to measure deceleration. Reflexive dismissal is the same error as credulity with the sign reversed.

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## 9\. Open problems, ranked

1. **Tighten the upper bound** Σⱼ2^{Eⱼ}. Session 008 shows this is 81% of the certification problem. Everything else in the quantum branch waits on it.
2. **Quantify the RCC\-1b constraint.** Convert existing QRNG test volumes into a lower bound on host generator state size. Cheap, and the data already exists.
3. **Resolve the identifiability condition** for RCC\-1a, or state permanently that it cannot be resolved from inside.
4. **Non\-quantum tracks** — the bounded transmission analogue, and one properly bounded archaeological or geological case study.

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## 10\. Provenance

The v1.3 foundation and its downloadable files are preserved unchanged. This document supersedes v1.3 as the current position; v1.3 remains the archive of the originating theory and the full evidence review.

Sessions 004–008 each produced a reproducible code bundle (seeds 20260907–20260911), all pure\-numpy with no third\-party quantum libraries, and each validated against an independent exact simulator. Session 008's validity checks: 45 circuits, zero cases where a lower bound exceeded the exact rank or an upper bound fell below it.

Nothing in this document establishes external implementation, nested ancestry, or creator motives.