Pith Number

pith:PL3CNJV3

pith:2016:PL3CNJV3AKC57PVJNXD7V5AJFC

not attested not anchored not stored refs pending

An Addendum to the Heisenberg-Euler effective action beyond one loop

Felix Karbstein, Holger Gies

arxiv:1612.07251 v5 · 2016-12-21 · hep-th · 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{PL3CNJV3AKC57PVJNXD7V5AJFC}

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

2 papers in Pith

Hard cutoff and gauge theories

Leading low-temperature correction to the Heisenberg-Euler Lagrangian

Receipt and verification

First computed	2026-07-05T04:28:04.870924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7af626a6bb0285dfbea96dc7faf409289702174d98e0dfdb275ca1989eef4550

Aliases

arxiv: 1612.07251 · arxiv_version: 1612.07251v5 · doi: 10.48550/arxiv.1612.07251 · pith_short_12: PL3CNJV3AKC5 · pith_short_16: PL3CNJV3AKC57PVJ · pith_short_8: PL3CNJV3

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/PL3CNJV3AKC57PVJNXD7V5AJFC \
  | 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: 7af626a6bb0285dfbea96dc7faf409289702174d98e0dfdb275ca1989eef4550

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "feace61e264f1169ed3fb7e66c6674e298dc77acc4b87ec3d2a563f8133bc08c",
    "cross_cats_sorted": [
      "hep-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2016-12-21T17:43:57Z",
    "title_canon_sha256": "aeb94b387837356bee3cfc9c16b6f9adc139e37193db11f477e40655202eae31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07251",
    "kind": "arxiv",
    "version": 5
  }
}