Pith Number

pith:45KJWMVX

pith:2011:45KJWMVXIINXD6BKHUSRMFZ6TY

not attested not anchored not stored refs pending

How dense can one pack spheres of arbitrary size distribution?

Hans J. Herrmann, Jos\'e S. Andrade Jr., Nuno A. M. Ara\'ujo, Saulo D. S. Reis

arxiv:1109.0966 v2 · 2011-09-05 · cond-mat.stat-mech · cond-mat.mtrl-sci · physics.comp-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{45KJWMVXIINXD6BKHUSRMFZ6TY}

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	2026-05-18T04:05:16.436940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7549b32b7421b71f82a3d2516173e9e3a17ca102b7fad98d398511dcb67d596

Aliases

arxiv: 1109.0966 · arxiv_version: 1109.0966v2 · doi: 10.48550/arxiv.1109.0966 · pith_short_12: 45KJWMVXIINX · pith_short_16: 45KJWMVXIINXD6BK · pith_short_8: 45KJWMVX

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/45KJWMVXIINXD6BKHUSRMFZ6TY \
  | 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: e7549b32b7421b71f82a3d2516173e9e3a17ca102b7fad98d398511dcb67d596

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d2f16cfbee94b38664555fed72eb60f7559f14b972f5f09b7063595b43ae6f2",
    "cross_cats_sorted": [
      "cond-mat.mtrl-sci",
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2011-09-05T17:18:13Z",
    "title_canon_sha256": "57a416b87dc3d71db8486ae2021fa87dfe094668ae97a7e60dbffbad5baa898b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0966",
    "kind": "arxiv",
    "version": 2
  }
}