Pith Number

pith:QZ3KR7Q4

pith:2004:QZ3KR7Q46WTONOWQPY2R6G672L

not attested not anchored not stored refs pending

Three-loop Phi-derivable Approximation in QED

Jens O. Andersen, Michael Strickland

arxiv:hep-ph/0406163 v2 · 2004-06-15 · hep-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{QZ3KR7Q46WTONOWQPY2R6G672L}

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

Consistent Thermal Resummation and Phase Transitions with 2PI Methods

Receipt and verification

First computed	2026-07-04T16:48:16.353246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8676a8fe1cf5a6e6bad07e351f1bdfd2c751b5cb445b76d928e9ca5f51dac2c5

Aliases

arxiv: hep-ph/0406163 · arxiv_version: hep-ph/0406163v2 · doi: 10.48550/arxiv.hep-ph/0406163 · pith_short_12: QZ3KR7Q46WTO · pith_short_16: QZ3KR7Q46WTONOWQ · pith_short_8: QZ3KR7Q4

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/QZ3KR7Q46WTONOWQPY2R6G672L \
  | 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: 8676a8fe1cf5a6e6bad07e351f1bdfd2c751b5cb445b76d928e9ca5f51dac2c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45b42b58bc120549559b0cf0a0050ef49c171409ddebf26f2f94f573f6f876e6",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2004-06-15T14:13:35Z",
    "title_canon_sha256": "88d87d0d75bd1d77bdb075d6de1ee99af106aff4a09093286d40c32f1a5dc9b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0406163",
    "kind": "arxiv",
    "version": 2
  }
}