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  "slug": "booklet-cosmological-states-as-random-tensor-codes-recovery-bounds-and-entropic-",
  "title": "Booklet Cosmological States as Random-Tensor Codes: Recovery Bounds and Entropic Diagnostics for Multi-Boundary Baby Universes",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Cosmological states in holography can contain closed \"baby\" universes inaccessible to any single asymptotic boundary, raising the question of whether the information they carry is recoverable, and from where. The booklet cosmology construction extends the two-boundary cosmological-state proposal of Antonini, Sasieta and Swingle to three or more holographic CFTs glued along a common interface, and models the resulting cosmology-to-boundary map by a circular complex Gaussian random tensor, i.e., a tripartite Haar-like state in flat energy windows. We treat this Gaussian model as a quantum error-correcting code whose logical system is the central closed universe and whose three arms are recovery regions. Working entirely within the stated Gaussian model, we derive explicit diagnostics with fully shown arithmetic: the expected purity of a single-arm reduced state via the Page formula, its excess over the maximally mixed value (scaling as 1/b²), the single-arm von Neumann entropy with Page correction, and the recovery error for a code of dimension K from any two arms, scaling linearly as K/b. [...]",
  "abstract_markdown": "Cosmological states in holography can contain closed \"baby\" universes inaccessible to any single asymptotic boundary, raising the question of whether the information they carry is recoverable, and from where. The booklet cosmology construction extends the two-boundary cosmological-state proposal of Antonini, Sasieta and Swingle to three or more holographic CFTs glued along a common interface, and models the resulting cosmology-to-boundary map by a circular complex Gaussian random tensor, i.e., a tripartite Haar-like state in flat energy windows. We treat this Gaussian model as a quantum error-correcting code whose logical system is the central closed universe and whose three arms are recovery regions. Working entirely within the stated Gaussian model, we derive explicit diagnostics with fully shown arithmetic: the expected purity of a single-arm reduced state via the Page formula, its excess over the maximally mixed value (scaling as $1/b^{2}$), the single-arm von Neumann entropy with Page correction, and the recovery error for a code of dimension $K$ from any two arms, scaling linearly as $K/b$. [...]",
  "date": "2026-10-09",
  "first_published": "2026-10-09",
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  "url": "https://papers.qnfo.org/papers/booklet-cosmological-states-as-random-tensor-codes-recovery-bounds-and-entropic-",
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    "titles": [
      {
        "title": "Booklet Cosmological States as Random-Tensor Codes: Recovery Bounds and Entropic Diagnostics for Multi-Boundary Baby Universes"
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        "description": "Cosmological states in holography can contain closed \"baby\" universes inaccessible to any single asymptotic boundary, raising the question of whether the information they carry is recoverable, and from where. The booklet cosmology construction extends the two-boundary cosmological-state proposal of Antonini, Sasieta and Swingle to three or more holographic CFTs glued along a common interface, and models the resulting cosmology-to-boundary map by a circular complex Gaussian random tensor, i.e., a tripartite Haar-like state in flat energy windows. We treat this Gaussian model as a quantum error-correcting code whose logical system is the central closed universe and whose three arms are recovery regions. Working entirely within the stated Gaussian model, we derive explicit diagnostics with fully shown arithmetic: the expected purity of a single-arm reduced state via the Page formula, its excess over the maximally mixed value (scaling as 1/b²), the single-arm von Neumann entropy with Page correction, and the recovery error for a code of dimension K from any two arms, scaling linearly as K/b. [...]",
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