Pith Number

pith:QBFRL2WC

pith:2026:QBFRL2WCC3QWTIS3IDGKVOMK75

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Semiclassical algebraic reconstruction for type III algebras

Haocheng Zhong

Semiclassical crossed product constructions extend the algebraic reconstruction theorem to type III algebras and yield an algebraic Ryu-Takayanagi formula for holographic duality.

arxiv:2605.13576 v1 · 2026-05-13 · hep-th · gr-qc · math-ph · math.MP

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Claims

C1strongest claim

By constructing holographic crossed product algebras for bulk and boundary type III factors, we extend the algebraic reconstruction theorem to include the algebraic Ryu-Takayanagi formula semiclassically, which provides a complete algebraic description of the reconstruction theorem as an intrinsic framework for the algebraic version of bulk-boundary correspondences in holographic duality.

C2weakest assumption

The claimed factorization of relative entropy in crossed product algebras into original algebra and observer wavefunction contributions is valid, and semiclassical approximations suffice to extend the theorem to type III cases without additional inconsistencies.

C3one line summary

Semiclassical crossed product constructions extend the algebraic reconstruction theorem to type III algebras and yield an algebraic Ryu-Takayanagi formula for holographic duality.

References

86 extracted · 86 resolved · 29 Pith anchors

[1] Witten, Gravity and the crossed product, JHEP 10 (2022), 008, [2112.12828] 2022

[2] V. Chandrasekaran, R. Longo, G. Penington and E. Witten,An algebra of observables for de Sitter space,JHEP02(2023) 082 [2206.10780] 2023

[3] K. Jensen, J. Sorce and A.J. Speranza,Generalized entropy for general subregions in quantum gravity,JHEP12(2023) 020 [2306.01837] 2023

[4] J. Kudler-Flam, S. Leutheusser, A.A. Rahman, G. Satishchandran and A.J. Speranza, Covariant regulator for entanglement entropy: Proofs of the Bekenstein bound and the quantum null energy condition,Phy 2025

[5] Algebras and Hilbert spaces from gravitational path integrals. Understanding Ryu-Takayanagi/HRT as entropy without AdS/CFT, 2024

Receipt and verification

First computed	2026-05-18T02:44:23.292527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

804b15eac216e169a25b40ccaab98aff7b86a94c689f7521cb29db75eab8888c

Aliases

arxiv: 2605.13576 · arxiv_version: 2605.13576v1 · doi: 10.48550/arxiv.2605.13576 · pith_short_12: QBFRL2WCC3QW · pith_short_16: QBFRL2WCC3QWTIS3 · pith_short_8: QBFRL2WC

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QBFRL2WCC3QWTIS3IDGKVOMK75 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 804b15eac216e169a25b40ccaab98aff7b86a94c689f7521cb29db75eab8888c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f62f8926afbc3f72ae16447d9830b99f9d43499265d77907abfa77662e6551a1",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-05-13T14:10:23Z",
    "title_canon_sha256": "de8986c3abacafda3fb822219447312977980e4e19ddfefc6c977a12ef85e47c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13576",
    "kind": "arxiv",
    "version": 1
  }
}