Pith Number

pith:2IQ67SCM

pith:2026:2IQ67SCMMOVIC5IX36GPCNXB7Q

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A general proof of integer R\'enyi QNEC

Pratik Roy, Tanay Kibe

The sandwiched Rényi divergence obeys a null energy condition for every integer order two and higher in algebras equipped with half-sided modular inclusions.

arxiv:2605.15272 v1 · 2026-05-14 · hep-th · math-ph · math.MP · math.OA · quant-ph

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\usepackage{pith}
\pithnumber{2IQ67SCMMOVIC5IX36GPCNXB7Q}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove Rényi QNEC for all integer Rényi parameters n≥2 for von Neumann algebras carrying a half-sided modular inclusion structure. The only assumption on the excited state is finiteness of its SRD relative to the vacuum.

C2weakest assumption

The algebra must carry a half-sided modular inclusion that generates the null-translation semigroup; without this structure the log-convexity argument does not apply (abstract, paragraph beginning 'Concretely, for any σ-finite von Neumann algebra').

C3one line summary

Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.

References

63 extracted · 63 resolved · 18 Pith anchors

[1] A Quantum Focussing Conjecture 2016 · arXiv:1506.02669

[2] Proof of the Quantum Null Energy Condition 2016 · arXiv:1509.02542

[3] T.A. Malik and R. Lopez-Mobilia,Proof of the quantum null energy condition for free fermionic field theories,Phys. Rev. D101(2020) 066028 [1910.07594] 2020

[4] Holographic Proof of the Quantum Null Energy Condition 2016 · arXiv:1512.06109

[5] S. Balakrishnan, T. Faulkner, Z.U. Khandker and H. Wang,A General Proof of the Quantum Null Energy Condition,JHEP09(2019) 020 [1706.09432] 2019

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:49.905337Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d221efc84c63aa817517df8cf136e1fc137c02502cb27e5c41eb5cef5c2984fe

Aliases

arxiv: 2605.15272 · arxiv_version: 2605.15272v1 · doi: 10.48550/arxiv.2605.15272 · pith_short_12: 2IQ67SCMMOVI · pith_short_16: 2IQ67SCMMOVIC5IX · pith_short_8: 2IQ67SCM

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2IQ67SCMMOVIC5IX36GPCNXB7Q \
  | 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: d221efc84c63aa817517df8cf136e1fc137c02502cb27e5c41eb5cef5c2984fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83124c5c680d782dd32c9f4fde53c9634333a3544ce2d9674ab16c1a101eeb3f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2026-05-14T18:00:02Z",
    "title_canon_sha256": "898a08ddd8429294bfdad68b6bb6b834b0501f7f1fd63278590bcf9efd403320"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15272",
    "kind": "arxiv",
    "version": 1
  }
}