Pith Number

pith:IFOKCVWT

pith:2012:IFOKCVWTWKWBSKJ4FJ66EINLJS

not attested not anchored not stored refs pending

The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere

D. P. Hardin, E. B. Saff, J. S. Brauchart

arxiv:1202.4037 v1 · 2012-02-17 · 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{IFOKCVWTWKWBSKJ4FJ66EINLJS}

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	2026-05-18T02:59:06.606288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

415ca156d3b2ac19293c2a7de221ab4c86311b37617f67b17f27c8a8b837842f

Aliases

arxiv: 1202.4037 · arxiv_version: 1202.4037v1 · doi: 10.48550/arxiv.1202.4037 · pith_short_12: IFOKCVWTWKWB · pith_short_16: IFOKCVWTWKWBSKJ4 · pith_short_8: IFOKCVWT

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/IFOKCVWTWKWBSKJ4FJ66EINLJS \
  | 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: 415ca156d3b2ac19293c2a7de221ab4c86311b37617f67b17f27c8a8b837842f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9875ea82e86be16de037a3dc1284371681d6ea5ca11d1c2d4a16173b8a90013",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-02-17T23:14:31Z",
    "title_canon_sha256": "b071a06f729ae24f05591c0088ec5b2a295da2d942899ace58dee7b71c0d4bb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.4037",
    "kind": "arxiv",
    "version": 1
  }
}