Pith Number

pith:CJSPKXHF

pith:2010:CJSPKXHF22G4FS3CG42TTS2BN5

not attested not anchored not stored refs pending

Spherical codes, maximal local packing density, and the golden ratio

A. B. Hopkins, F. H. Stillinger, S. Torquato

arxiv:1003.3604 v1 · 2010-03-18 · cond-mat.stat-mech · cond-mat.soft · 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{CJSPKXHF22G4FS3CG42TTS2BN5}

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	2026-05-18T02:08:25.959199Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1264f55ce5d68dc2cb62373539cb416f72dbb25aa65d0c62c38547d951a11fcc

Aliases

arxiv: 1003.3604 · arxiv_version: 1003.3604v1 · doi: 10.48550/arxiv.1003.3604 · pith_short_12: CJSPKXHF22G4 · pith_short_16: CJSPKXHF22G4FS3C · pith_short_8: CJSPKXHF

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/CJSPKXHF22G4FS3CG42TTS2BN5 \
  | 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: 1264f55ce5d68dc2cb62373539cb416f72dbb25aa65d0c62c38547d951a11fcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d21efa661820e2c08083b97502211b3a57d47a4625784477de9b4dd04082dfe7",
    "cross_cats_sorted": [
      "cond-mat.soft",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2010-03-18T15:13:02Z",
    "title_canon_sha256": "fc1ed76053e81fe8624ca2b906508fb5f0d5956163e00e857275ca643ae87570"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.3604",
    "kind": "arxiv",
    "version": 1
  }
}