Pith Number

pith:COOWP7FD

pith:2014:COOWP7FDB27NIDRSVGG663RZQT

not attested not anchored not stored refs pending

Renormalized Energy and Asymptotic Expansion of Optimal Logarithmic Energy on the Sphere

Etienne Sandier (LAMA), Laurent B\'etermin

arxiv:1404.4485 v5 · 2014-04-17 · math.AP · 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{COOWP7FDB27NIDRSVGG663RZQT}

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	2026-05-18T00:18:27.261198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

139d67fca30ebed40e32a98def6e3984d1291becfd722274e410b26a13038e91

Aliases

arxiv: 1404.4485 · arxiv_version: 1404.4485v5 · doi: 10.48550/arxiv.1404.4485 · pith_short_12: COOWP7FDB27N · pith_short_16: COOWP7FDB27NIDRS · pith_short_8: COOWP7FD

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/COOWP7FDB27NIDRSVGG663RZQT \
  | 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: 139d67fca30ebed40e32a98def6e3984d1291becfd722274e410b26a13038e91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "976ebec396df64220ec2b5a0cc3b4ed6118a957cc59c0715a954ae950f3bead5",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-04-17T11:06:27Z",
    "title_canon_sha256": "cdfeb04a85a9a313e9385e3578a1b15f69d804e6cc2c6a9327726d9f2051b841"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.4485",
    "kind": "arxiv",
    "version": 5
  }
}