Pith Number

pith:ERCPP4JO

pith:2025:ERCPP4JONDNJYRRZVSQVSHD7TI

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Callan-Symanzik-like equation in information theory

Mehdi Sadeghi, Mojtaba Shahbazi

The complexity growth rate in holographic models satisfies a Callan-Symanzik-like equation near phase transitions.

arxiv:2508.13330 v3 · 2025-08-18 · quant-ph · hep-th

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\pithnumber{ERCPP4JONDNJYRRZVSQVSHD7TI}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations 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 show that the CGR satisfies a Callan-Symanzik-like equation near the transitions. Our results provide a new information-theoretic interpretation of the Callan-Symanzik equation, with the CGR running with the energy scale.

C2weakest assumption

The fluid-gravity correspondence accurately translates the dynamics of the bulk fields that control the jumps in complexity growth rate into the boundary energy-momentum tensor, and that this translation remains valid exactly at the critical points where the jumps occur.

C3one line summary

Holographic complexity growth rate satisfies a Callan-Symanzik-like equation near phase-transition points, giving an information-theoretic interpretation of the renormalization-group equation with the rate running against energy scale.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-29T01:04:55.180108Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2444f7f12e68da9c4639aca1591c7f9a3ad532dc059ae852a17ff599d1919bce

Aliases

arxiv: 2508.13330 · arxiv_version: 2508.13330v3 · doi: 10.48550/arxiv.2508.13330 · pith_short_12: ERCPP4JONDNJ · pith_short_16: ERCPP4JONDNJYRRZ · pith_short_8: ERCPP4JO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ERCPP4JONDNJYRRZVSQVSHD7TI \
  | 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: 2444f7f12e68da9c4639aca1591c7f9a3ad532dc059ae852a17ff599d1919bce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c411354301f61ff19cbbcf488eed2121b7333c6ee0e4957d632619a6b60d893c",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-08-18T19:25:43Z",
    "title_canon_sha256": "eee10e081b63a1725f31c7d16bc68e3e03acbbcf2553193273d6ea1af2d8859b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.13330",
    "kind": "arxiv",
    "version": 3
  }
}