Pith Number

pith:TZVZ5ZQV

pith:1998:TZVZ5ZQVODLDY6RYZF3BTUKRAI

not attested not anchored not stored refs pending

The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $\sigma$-Model

M. Beneke, N.Kivel, V.M. Braun

arxiv:hep-ph/9809287 v1 · 1998-09-07 · hep-ph

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TZVZ5ZQVODLDY6RYZF3BTUKRAI}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

1 paper in Pith

Trans-series from condensates in the non-linear sigma model

Receipt and verification

First computed	2026-05-18T04:25:26.598529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e6b9ee61570d63c7a38c97619d151021960a373acfa669cbc7ce4bc8ee80d31

Aliases

arxiv: hep-ph/9809287 · arxiv_version: hep-ph/9809287v1 · doi: 10.48550/arxiv.hep-ph/9809287 · pith_short_12: TZVZ5ZQVODLD · pith_short_16: TZVZ5ZQVODLDY6RY · pith_short_8: TZVZ5ZQV

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/TZVZ5ZQVODLDY6RYZF3BTUKRAI \
  | 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: 9e6b9ee61570d63c7a38c97619d151021960a373acfa669cbc7ce4bc8ee80d31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e50dc60466a1071a3519b2c35a9392c5ce1d4cfd9886d79d4018ca214f004dd4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1998-09-07T12:27:03Z",
    "title_canon_sha256": "93d6d24406ab1c1efbbb9e0db5503c89312e54b195cd233c0e7ce62b23babc4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9809287",
    "kind": "arxiv",
    "version": 1
  }
}