Pith Number

pith:7I5SF3UV

pith:1998:7I5SF3UVE2IDQHJ3CW7LW2A4DU

not attested not anchored not stored refs pending

Thermal Renormalization Group-Equations and the Phase-Transition of Scalar O(N)-Theories

Bastian Bergerhoff, Juergen Reingruber

arxiv:hep-ph/9809251 v1 · 1998-09-03 · hep-ph · cond-mat · nucl-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7I5SF3UVE2IDQHJ3CW7LW2A4DU}

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

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.

Receipt and verification

First computed	2026-05-18T04:17:37.201381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa3b22ee952690381d3b15bebb681c1d3b02251f613a4e3ebd9992017677e8ad

Aliases

arxiv: hep-ph/9809251 · arxiv_version: hep-ph/9809251v1 · doi: 10.48550/arxiv.hep-ph/9809251 · pith_short_12: 7I5SF3UVE2ID · pith_short_16: 7I5SF3UVE2IDQHJ3 · pith_short_8: 7I5SF3UV

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/7I5SF3UVE2IDQHJ3CW7LW2A4DU \
  | 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: fa3b22ee952690381d3b15bebb681c1d3b02251f613a4e3ebd9992017677e8ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a04450742d1d4c6efd647a8ccc728d1258d6d08ff1beafe41a47a82b112e5076",
    "cross_cats_sorted": [
      "cond-mat",
      "nucl-th"
    ],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1998-09-03T16:00:31Z",
    "title_canon_sha256": "3ba8e3bb077187b196b84d12fc94c98ee44ade198a0cf0113e9ca6277f46b879"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9809251",
    "kind": "arxiv",
    "version": 1
  }
}