Zero Worlds · claim ZW-C502 · Observation rung · Empirical benchmarks

Spekkens' toy theory reproduces a wide variety of quantum phenomena — interference analogues, no-cloning, teleportation, entanglement-like correlations — from classical states plus an epistemic restriction, while explicitly failing to reproduce Bell-inequality violation and Kochen–Specker contextuality.

Not featured in the current editionAI-extractedorigin: Spekkens 2007, abstract (arXiv quant-ph/0401052)

source anchor

Physical Review A 75, 032110 (2007), abstract

“A wide variety of quantum phenomena are found to have analogues within this toy theory.”

Evidence

Supports· strongZW-E015

Spekkens 2007: how much quantum 'look' a non-quantum theory can fake

what the source states: A toy theory built from classical states plus a restriction on knowledge finds that "a wide variety of quantum phenomena... have analogues within this toy theory" — interference-like behavior, no-cloning, teleportation, entanglement analogues — while explicitly failing to reproduce Bell-inequality violations and Kochen–Specker contextuality.
what we infer: The calibration standard this case applies to every "quantum-like" result in the observer-first literature: wave equations, complex numbers, branching, and interference-resemblance are all obtainable without quantum mechanics. The bar is the genuinely nonclassical correlation structure, and nothing below it counts.
limitations: The toy theory targets ψ-epistemic interpretations, not idealism; its use here as a general calibration device is an editorial application.

Spekkens, R. W. (2007)AI-verified citation

Supports· strongZW-E023

Müller 2026 (conclusions): quantum phenomena are the framework's test, and resemblance does not count

what the source states: In the paper's conclusions Müller names "two main open technical problems". The first is the bit model's lack of forgetting, "which is unmotivated, unrealistic, and an artefact of the way that Solomonoff induction has been formulated in Algorithmic Information Theory". The second is that "a successful formalization of algorithmic idealism should predict some phenomenal aspects of Quantum Theory". Its target is "phenomena that are genuinely quantum, such as the violation of Bell inequalities together with compliance with the no-signalling principle" (p. 28). An explanation of Bell violation "has been sketched in [2], but it needs further elaboration". He adds: "Note that it is not enough to point at mathematical elements" that resemble those of quantum theory, since "the main question is whether the statistical results of experiments are predicted to behave in genuinely nonclassical ways". Building the formalism in would defeat the test: "it would be methodologically wrong to build the quantum formalism into algorithmic idealism by construction" (p. 29).
what we infer: The framework's peer-reviewed statement agrees with the case on two points. It names the quantum derivation as open (ZW-C002), and it sets the same bar this case borrows from Spekkens (ZW-C502): nonclassical statistics, not resembling equations. This record also supersedes the abstract-level characterization in ZW-E002 with the paper's own words, and quotes the erasure problem (ZW-C504) from the published paper rather than the author's web page.
limitations: Read from the arXiv version dated 24 July 2025. The Springer version was not separately compared.
The proponent setting his own test is not evidence that the test can or cannot be passed.

Müller, M. P. (2026)AI-verified citation

an honest empty state

This claim is in the ledger but not in the current edition's featured set. Nothing here has been assessed — that absence is information, not an oversight.

Still missing: plain-language gloss, credibility assessment, diagnosticity assessment, strongest objection, what would change our mind. A claim gains them when an edition features it and the edition's adopted assessment supplies the full treatment — a decision the panel reviews, not a field anyone flips.