Pith Number

pith:WSKNRXTI

pith:2015:WSKNRXTICDIWJPLV3FQE6VK5AG

not attested not anchored not stored refs pending

Universal lower bounds for potential energy of spherical codes

D. P. Hardin, E. B. Saff, M. M. Stoyanova, P. D. Dragnev, P. G. Boyvalenkov

arxiv:1503.07228 v1 · 2015-03-24 · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WSKNRXTICDIWJPLV3FQE6VK5AG}

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	2026-05-18T02:20:28.013138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b494d8de6810d164bd75d9604f555d01a271ee2c430273434596a1d1d2f86c63

Aliases

arxiv: 1503.07228 · arxiv_version: 1503.07228v1 · doi: 10.48550/arxiv.1503.07228 · pith_short_12: WSKNRXTICDIW · pith_short_16: WSKNRXTICDIWJPLV · pith_short_8: WSKNRXTI

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/WSKNRXTICDIWJPLV3FQE6VK5AG \
  | 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: b494d8de6810d164bd75d9604f555d01a271ee2c430273434596a1d1d2f86c63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffe22066e6b7d8892098c22bdb914796738071aecb43d7e7ac17089e44428f7e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-03-24T23:05:36Z",
    "title_canon_sha256": "22c06e9ae107ac680c50fac9bbdf451279b394c61de6c3065f4c5242b7962b23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.07228",
    "kind": "arxiv",
    "version": 1
  }
}