Pith Number

pith:YKKY3XII

pith:2011:YKKY3XII2ID72RK6SZ44XKYNZS

not attested not anchored not stored refs pending

Densest binary sphere packings

Adam B. Hopkins, Frank H. Stillinger, Salvatore Torquato

arxiv:1111.4917 v2 · 2011-11-21 · cond-mat.stat-mech · cond-mat.mtrl-sci · cond-mat.soft

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YKKY3XII2ID72RK6SZ44XKYNZS}

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	2026-05-18T01:59:27.428879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2958ddd08d207fd455e9679cbab0dcc87effeaa1162bd2af2cae7e9caeb2c5b

Aliases

arxiv: 1111.4917 · arxiv_version: 1111.4917v2 · doi: 10.48550/arxiv.1111.4917 · pith_short_12: YKKY3XII2ID7 · pith_short_16: YKKY3XII2ID72RK6 · pith_short_8: YKKY3XII

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/YKKY3XII2ID72RK6SZ44XKYNZS \
  | 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: c2958ddd08d207fd455e9679cbab0dcc87effeaa1162bd2af2cae7e9caeb2c5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d731476a908c1f16e6345ba391cb64f0d6830259961d43bd8437a532cfedcd9",
    "cross_cats_sorted": [
      "cond-mat.mtrl-sci",
      "cond-mat.soft"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2011-11-21T16:22:23Z",
    "title_canon_sha256": "1036b1237fbde101e63cd534c4fe47c70acd4eff69444e919ba345cd241a6e60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4917",
    "kind": "arxiv",
    "version": 2
  }
}