Pith Number

pith:IWM6BP5W

pith:2011:IWM6BP5WPJYWASTB3HZIJX5PRJ

not attested not anchored not stored refs pending

Contact numbers for congruent sphere packings in Euclidean 3-space

Karoly Bezdek

arxiv:1102.1198 v2 · 2011-02-06 · 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{IWM6BP5WPJYWASTB3HZIJX5PRJ}

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	2026-05-18T03:34:00.155921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4599e0bfb67a71604a61d9f284dfaf8a7850202335e510fc29bac1a2d8349294

Aliases

arxiv: 1102.1198 · arxiv_version: 1102.1198v2 · doi: 10.48550/arxiv.1102.1198 · pith_short_12: IWM6BP5WPJYW · pith_short_16: IWM6BP5WPJYWASTB · pith_short_8: IWM6BP5W

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/IWM6BP5WPJYWASTB3HZIJX5PRJ \
  | 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: 4599e0bfb67a71604a61d9f284dfaf8a7850202335e510fc29bac1a2d8349294

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4817d7c27860919348699eb337ef1be3e2a9a3a0529b6a1ba630e1cc02154f46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2011-02-06T20:28:09Z",
    "title_canon_sha256": "4fdcb5c1e32d7fba112baca2f14c8ee8ed39fb775c6e3623acf4f96e092288b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1198",
    "kind": "arxiv",
    "version": 2
  }
}