Pith Number

pith:EP5SCLVA

pith:2009:EP5SCLVAAHYWKZ4HLPOBWGUXKG

not attested not anchored not stored refs pending

High accuracy semidefinite programming bounds for kissing numbers

Frank Vallentin, Hans D. Mittelmann

arxiv:0902.1105 v3 · 2009-02-06 · math.OC · math.MG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EP5SCLVAAHYWKZ4HLPOBWGUXKG}

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

1 paper in Pith

Variations on five-dimensional sphere packings

Receipt and verification

First computed	2026-07-05T00:17:23.654010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23fb212ea001f16567875bdc1b1a9751b945ae275522db366a0dde2fbbf54f0e

Aliases

arxiv: 0902.1105 · arxiv_version: 0902.1105v3 · doi: 10.48550/arxiv.0902.1105 · pith_short_12: EP5SCLVAAHYW · pith_short_16: EP5SCLVAAHYWKZ4H · pith_short_8: EP5SCLVA

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/EP5SCLVAAHYWKZ4HLPOBWGUXKG \
  | 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: 23fb212ea001f16567875bdc1b1a9751b945ae275522db366a0dde2fbbf54f0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b87c13320fc7f4857bbd5acce66f3d139b32e4fb7b3c08ee82f81e61ef22343",
    "cross_cats_sorted": [
      "math.MG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2009-02-06T17:15:35Z",
    "title_canon_sha256": "2cbe997e7bed58c1a221bc5b36cf24c9eb98284a31c333b86631131f6b9c2b4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.1105",
    "kind": "arxiv",
    "version": 3
  }
}