Pith Number

pith:L4JGK5QM

pith:2010:L4JGK5QMOKIIGEZWUUG5JW3BEE

not attested not anchored not stored refs pending

Optimal asymptotic bounds for spherical designs

Andriy Bondarenko, Danylo Radchenko, Maryna Viazovska

arxiv:1009.4407 v3 · 2010-09-22 · math.MG · math.CO · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L4JGK5QMOKIIGEZWUUG5JW3BEE}

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.

Cited by

2 papers in Pith

The most discriminable quantum states in the multicopy regime

Receipt and verification

First computed	2026-05-18T04:27:17.802818Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f1265760c7290831336a50dd4db6121312439ea1df75449dd66614b293df3b5

Aliases

arxiv: 1009.4407 · arxiv_version: 1009.4407v3 · doi: 10.48550/arxiv.1009.4407 · pith_short_12: L4JGK5QMOKII · pith_short_16: L4JGK5QMOKIIGEZW · pith_short_8: L4JGK5QM

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/L4JGK5QMOKIIGEZWUUG5JW3BEE \
  | 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: 5f1265760c7290831336a50dd4db6121312439ea1df75449dd66614b293df3b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "059c33550ee27ef20adb41f0a69490730bd72f795eafba3d0295c64859ebcc7e",
    "cross_cats_sorted": [
      "math.CO",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-09-22T16:16:51Z",
    "title_canon_sha256": "b1ad2236a9405f4e60484b81ca6bcb8fdd23662a19ef90bbd4fd122bc1e8b774"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4407",
    "kind": "arxiv",
    "version": 3
  }
}