Pith Number

pith:UKE7JEF3

pith:2010:UKE7JEF3PTJKOKSXOO3LS4XTNM

not attested not anchored not stored refs pending

Renormalization and asymptotic expansion of Dirac's polarized vacuum

Eric s\'er\'e (CEREMADE), Mathieu Lewin (AGM), Philippe Gravejat (CEREMADE)

arxiv:1004.1734 v1 · 2010-04-10 · math-ph · 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{UKE7JEF3PTJKOKSXOO3LS4XTNM}

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	2026-05-18T04:17:15.439202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a289f490bb7cd2a72a5773b6b972f36b1ed29cde4963790d1edbe21853e784d0

Aliases

arxiv: 1004.1734 · arxiv_version: 1004.1734v1 · doi: 10.48550/arxiv.1004.1734 · pith_short_12: UKE7JEF3PTJK · pith_short_16: UKE7JEF3PTJKOKSX · pith_short_8: UKE7JEF3

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/UKE7JEF3PTJKOKSXOO3LS4XTNM \
  | 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: a289f490bb7cd2a72a5773b6b972f36b1ed29cde4963790d1edbe21853e784d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e980b2a2ad688473614ca7439efc6d3a5d0b396a15f933815d2a57efb2c8024",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-04-10T19:03:11Z",
    "title_canon_sha256": "7e14f68be64a7f4ab77d83d441c36672bdbe0e75035fc7e622973f1df99ed1d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.1734",
    "kind": "arxiv",
    "version": 1
  }
}