Witten's 2023/2025 paper states, in his own words, a two-part 'universal no-boundary state' hypothesis for general spacetimes

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In §4.2 of "A Background-Independent Algebra in Quantum Gravity" (first posted to arXiv as 2308.03663 in August 2023, subsequently published as Witten, General Relativity and Gravitation 57(1):17, 2025), titled "A Universal No Boundary State?", Edward Witten states a hypothesis with two parts about the Hartle-Hawking no-boundary state ΨHH, enriched to include an observer. The first part asserts that ΨHH makes sense universally as a state (more precisely a weight) on the observer's algebra A_obs, regardless of which spacetime M the observer lives in — one can define the expectation value ⟨ΨHH|a|ΨHH⟩ for any operator a in A_obs. The second part asserts that ΨHH can be regarded as a universal maximum-entropy state.

Witten is explicit that this is a hypothesis, not an established result: "Everything about [the no boundary state] can be questioned," and the claim is rigorously checked only in the restricted case of de Sitter vacua with different values of the cosmological constant, not for a fully general spacetime. This is a distinct claim from the one Vinck & De Haro (2026) test against three philosophical definitions of background-independence — that claim concerns whether the CLPW crossed-product algebra itself is "background-independent"; this one concerns whether a specific state on that algebra generalizes universally across spacetimes. Both appear in Witten's broader 2023–2025 research program but are separable claims that could hold or fail independently of each other.