Pith Number

pith:3N5RUXSW

pith:2004:3N5RUXSW6IF44TUWNPUEGUBRML

not attested not anchored not stored refs pending

A densest compact planar packing with two sizes of discs

Tom Kennedy

arxiv:math/0412418 v1 · 2004-12-21 · 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{3N5RUXSW6IF44TUWNPUEGUBRML}

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.

Cited by

1 paper in Pith

On Dense Tetrahedra in Binary Sphere Packings

Receipt and verification

First computed	2026-07-04T14:39:28.857187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db7b1a5e56f20bce4e966be843503162e4c4b44b475324d25b74136b8a62fb02

Aliases

arxiv: math/0412418 · arxiv_version: math/0412418v1 · doi: 10.48550/arxiv.math/0412418 · pith_short_12: 3N5RUXSW6IF4 · pith_short_16: 3N5RUXSW6IF44TUW · pith_short_8: 3N5RUXSW

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/3N5RUXSW6IF44TUWNPUEGUBRML \
  | 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: db7b1a5e56f20bce4e966be843503162e4c4b44b475324d25b74136b8a62fb02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c5448dd70321abbfa76518a0b99cd63c23f3414bcc247bfbe2062251edb98c8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "2004-12-21T05:01:05Z",
    "title_canon_sha256": "aa75a136f65d84ffd5553e3139637ecf3a0b8925a5a687225209e48568e57c1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412418",
    "kind": "arxiv",
    "version": 1
  }
}