Pith Number

pith:ANUKNTRK

pith:2009:ANUKNTRKHMA3YZBVXDQVCQTBB3

not attested not anchored not stored refs pending

Dense Packings of Polyhedra: Platonic and Archimedean Solids

S. Torquato, Y. Jiao

arxiv:0909.0940 v3 · 2009-09-04 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ANUKNTRKHMA3YZBVXDQVCQTBB3}

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	2026-05-18T02:11:59.616632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0368a6ce2a3b01bc6435b8e15142610edee44bbe02a73fded7b20624a82958f3

Aliases

arxiv: 0909.0940 · arxiv_version: 0909.0940v3 · doi: 10.48550/arxiv.0909.0940 · pith_short_12: ANUKNTRKHMA3 · pith_short_16: ANUKNTRKHMA3YZBV · pith_short_8: ANUKNTRK

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/ANUKNTRKHMA3YZBVXDQVCQTBB3 \
  | 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: 0368a6ce2a3b01bc6435b8e15142610edee44bbe02a73fded7b20624a82958f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a73c4091e82b0d0fa711890fa62d06c3941186c4a8f1533f5bd7ca7fc497ea6",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-09-04T19:43:51Z",
    "title_canon_sha256": "5028a262217c2f02822a36681e2eb25e0152fdd97da3fa0ecea022fd770837d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0940",
    "kind": "arxiv",
    "version": 3
  }
}