Pith Number

pith:WO5JK2AT

pith:2005:WO5JK2ATEEEVLPGKP7UVUTEZ7K

not attested not anchored not stored refs pending

The Mean-Field Approximation in Quantum Electrodynamics. The no-photon case

Christian Hainzl, Jan Philip Solovej, Mathieu Lewin

arxiv:math-ph/0503075 v2 · 2005-03-31 · math-ph · hep-th · math.MP · physics.atom-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WO5JK2ATEEEVLPGKP7UVUTEZ7K}

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	2026-07-04T14:50:06.055177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3ba956813210955bcca7fe95a4c99fab105b2d1b7b3c395318225a86bd783ed

Aliases

arxiv: math-ph/0503075 · arxiv_version: math-ph/0503075v2 · doi: 10.48550/arxiv.math-ph/0503075 · pith_short_12: WO5JK2ATEEEV · pith_short_16: WO5JK2ATEEEVLPGK · pith_short_8: WO5JK2AT

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/WO5JK2ATEEEVLPGKP7UVUTEZ7K \
  | 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: b3ba956813210955bcca7fe95a4c99fab105b2d1b7b3c395318225a86bd783ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb5d20cb9015b03424aaf760e8d4c614f134991fc2602e48e4effa0f54935d19",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP",
      "physics.atom-ph"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-03-31T16:37:06Z",
    "title_canon_sha256": "f92bfd57292571c0ecf3051f3094f4014cda3613a95ea214be2b6c25a33eee26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0503075",
    "kind": "arxiv",
    "version": 2
  }
}