Pith Number

pith:TT3M33EU

pith:2003:TT3M33EUGB2JJEA5DTC52LNLO3

not attested not anchored not stored refs pending

Uniqueness and Symmetry in Problems of Optimally Dense Packings

Charles Holton, Charles Radin, Lewis Bowen, Lorenzo Sadun

arxiv:math/0302056 v2 · 2003-02-05 · math.MG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TT3M33EUGB2JJEA5DTC52LNLO3}

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	2026-05-18T00:11:07.491101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cf6cdec94307494901d1cc5dd2dab76c33a92a2432dc9f8e22f31d1aa2e6a51

Aliases

arxiv: math/0302056 · arxiv_version: math/0302056v2 · doi: 10.48550/arxiv.math/0302056 · pith_short_12: TT3M33EUGB2J · pith_short_16: TT3M33EUGB2JJEA5 · pith_short_8: TT3M33EU

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/TT3M33EUGB2JJEA5DTC52LNLO3 \
  | 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: 9cf6cdec94307494901d1cc5dd2dab76c33a92a2432dc9f8e22f31d1aa2e6a51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8f9203f9b98fcedca2aeb2ac36647c720445d89047470e335c7069c1e9340b0",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2003-02-05T21:43:48Z",
    "title_canon_sha256": "c3417d1f5bc4cca0e055bff64fcff3c26f17d5d3ddbb2c3dc0003270f5856eaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0302056",
    "kind": "arxiv",
    "version": 2
  }
}