Pith Number

pith:XPXGS25K

pith:2009:XPXGS25KF3OAJJBFELNH3KPXCZ

not attested not anchored not stored refs pending

Minimal Riesz energy on the sphere for axis-supported external fields

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

arxiv:0902.1558 v1 · 2009-02-09 · 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{XPXGS25KF3OAJJBFELNH3KPXCZ}

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	2026-05-18T02:59:06.936919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbee696baa2edc04a42522da7da9f71672c7cc5df2539c0de226064cc8980272

Aliases

arxiv: 0902.1558 · arxiv_version: 0902.1558v1 · doi: 10.48550/arxiv.0902.1558 · pith_short_12: XPXGS25KF3OA · pith_short_16: XPXGS25KF3OAJJBF · pith_short_8: XPXGS25K

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/XPXGS25KF3OAJJBFELNH3KPXCZ \
  | 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: bbee696baa2edc04a42522da7da9f71672c7cc5df2539c0de226064cc8980272

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a82d171edabb1c2f5d3c27b59991b2e48c6e6f1cb6761c8eb15f4fdf65040c1",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-02-09T23:12:07Z",
    "title_canon_sha256": "3c178cde2c2c6591833031b1eb95615b49ec4b206bed9f076154d6bf0cf22d03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.1558",
    "kind": "arxiv",
    "version": 1
  }
}