Pith Number

pith:AA3ITZTC

pith:2012:AA3ITZTC4DGT3HA55EC6YKTRWW

not attested not anchored not stored refs pending

The 3-ball is a local pessimum for packing

Yoav Kallus

arxiv:1212.2551 v3 · 2012-12-11 · math.MG · cond-mat.soft · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AA3ITZTC4DGT3HA55EC6YKTRWW}

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	2026-05-18T02:45:58.407691Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

003689e662e0cd3d9c1de905ec2a71b5ab46334dbca8c33cea79219e1ce58359

Aliases

arxiv: 1212.2551 · arxiv_version: 1212.2551v3 · doi: 10.48550/arxiv.1212.2551 · pith_short_12: AA3ITZTC4DGT · pith_short_16: AA3ITZTC4DGT3HA5 · pith_short_8: AA3ITZTC

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/AA3ITZTC4DGT3HA55EC6YKTRWW \
  | 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: 003689e662e0cd3d9c1de905ec2a71b5ab46334dbca8c33cea79219e1ce58359

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6689bf71b0ea649748ca3ae904850ac67225cde745171f4beed97599fb377493",
    "cross_cats_sorted": [
      "cond-mat.soft",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-12-11T17:39:29Z",
    "title_canon_sha256": "b631d326cd2723bf0a3ff5d6a4b00c9c0e4b4bd40c8b96c735208de1660969fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2551",
    "kind": "arxiv",
    "version": 3
  }
}