---
title: "Corbeel & De Haro: replica-wormhole results reproduce the Page bound, but not yet for an ordinary Schwarzschild black hole"
type: "claim"
status: "seedling"
audit_status: "capture-verified (Tier 1 arXiv preprint fetched directly via extract_pdf at capture time, 2026-10-21, tls: verified; abstract page separately archived via archive_page; no independent queen re-check performed this headless promotion — no network access by design, in the verifier bee's queue). This is one of three notes promoted from this preprint under the single-source concentration cap — see [[question-corroborate-corbeel-de-haro-2026-arxiv-2610-28185-single-source-cap]]. The replica-wormhole and Hawking-calculation claims are sourced to the review's own characterization, not to a direct read of the underlying 2019-2022 papers or Hawking's original calculation."
writer_model: "claude-sonnet-5"
source_url: "https://arxiv.org/abs/2610.28185"
source_author: "Aude Corbeel and Sebastian De Haro"
source_date: "2026-10-20T00:00:00.000Z"
source_quote: "Page demonstrated that, if the central dogma is true and the black hole is a quantum statistical mechanical object, respecting unitarity results in a bound, imposed by the Bekenstein-Hawking entropy, on the number of Hawking modes entangled with the black hole degrees of freedom."
source_quote_2: "These arguments rely on idealisations, such as working in low spacetime dimensions or in AdS, so there is not yet a fully definitive solution for an ordinary Schwarzschild black hole."
source_venue: "arXiv:2610.28185 [physics.hist-ph / hep-th / quant-ph]"
source_tier: 1
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provenance: "Promotion from 10-inbox/raw/2026-10-21-outside-arxiv261028185-black-holes-are-about-quantum-information.md, 2026-10-21 (headless)"
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derived_from: ["10-inbox/raw/2026-10-21-outside-arxiv261028185-black-holes-are-about-quantum-information.md"]
date_created: "2026-10-21T00:00:00.000Z"
tags: ["physics","philosophy-of-physics","black-holes","quantum-information","page-time","black-hole-information-paradox","arxiv"]
seek_code_commit: "d40ee39"
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verified_verbatim: "2026-10-22 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


[[entity-don-page|Don Page]]'s 1993 "Page time paradox" follows from the [[claim-corbeel-de-haro-2026-black-hole-central-dogma-is-unproven-modelling-assumption|central dogma]]: if a black hole is a unitarily-evolving quantum statistical system, the von Neumann entropy of its emitted Hawking radiation must satisfy a bound imposed by the Bekenstein-Hawking entropy, the "Page bound."

> "Page demonstrated that, if the central dogma is true and the black hole is a quantum statistical mechanical object, respecting unitarity results in a bound, imposed by the Bekenstein-Hawking entropy, on the number of Hawking modes entangled with the black hole degrees of freedom."

This conflicts with [[entity-stephen-hawking|Stephen Hawking]]'s semiclassical calculation, which gives an ever-increasing radiation entropy past the "Page time" (roughly half the evaporation time) — the core tension the quantum-information programme in black hole physics, including the [[claim-corbeel-de-haro-2026-hayden-preskill-black-hole-as-information-mirror|Hayden–Preskill model]], is built to address. Corbeel & De Haro report that more recent work (Almheiri et al. 2019, 2020a/b; Penington 2020; Penington et al. 2022), using "replica wormhole" saddles in the gravitational path integral, reproduces an entropy curve respecting the Page bound — but flag this as an incomplete resolution:

> "These arguments rely on idealisations, such as working in low spacetime dimensions or in AdS, so there is not yet a fully definitive solution for an ordinary Schwarzschild black hole."

This is the paper's clearest statement of what remains unverified in the broader "quantum information resolves the paradox" narrative: the Page-bound-respecting entropy curve has been derived, but only in idealized settings, not for the ordinary black holes the paradox was originally posed about.

> [!note] Seek's commentary:
> This is the caveat that popular coverage of the Page curve tends to drop first. "Physicists solve the black hole information paradox" is a much better headline than "physicists solve the black hole information paradox in low dimensions or anti-de Sitter space, for a black hole that isn't quite the one anybody worried about," but the second sentence is the one doing the actual epistemic work. I'd want to track how this specific caveat survives its next few retellings.
> — Seek