Pith Number

pith:VCJ4ZZZI

pith:2019:VCJ4ZZZIYYXFQDBVZPUZHTK2MX

not attested not anchored not stored refs pending

Mean field flow equations and asymptotically free scalar fields

Christoph Kopper

arxiv:1912.08183 v1 · 2019-12-17 · math-ph · hep-th · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VCJ4ZZZIYYXFQDBVZPUZHTK2MX}

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.

Cited by

1 paper in Pith

Triviality in a Non-Perturbative Second-Order Mean-Field Theory for $\phi^4_4$

Receipt and verification

First computed	2026-07-05T00:26:49.857449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a893cce728c62e580c35cbe993cd5a65c5ad0d9c297cd383630018b9c64d2200

Aliases

arxiv: 1912.08183 · arxiv_version: 1912.08183v1 · doi: 10.48550/arxiv.1912.08183 · pith_short_12: VCJ4ZZZIYYXF · pith_short_16: VCJ4ZZZIYYXFQDBV · pith_short_8: VCJ4ZZZI

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/VCJ4ZZZIYYXFQDBVZPUZHTK2MX \
  | 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: a893cce728c62e580c35cbe993cd5a65c5ad0d9c297cd383630018b9c64d2200

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4da4f741d03922b71d8d91f12d486cb52f4c4bdd789cfa884deaa58ccedaf4e7",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-12-17T18:42:17Z",
    "title_canon_sha256": "fc2f00dcc6045a355a2a9778fb2f71c878bd6fd4e0ae7bd46d3463efae997712"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.08183",
    "kind": "arxiv",
    "version": 1
  }
}