Pith Number

pith:IGQIV4VE

pith:2010:IGQIV4VEOAZELCLEB2656NOW67

not attested not anchored not stored refs pending

Upper bound on the packing density of regular tetrahedra and octahedra

Simon Gravel, Veit Elser, Yoav Kallus

arxiv:1008.2830 v1 · 2010-08-17 · math.MG · cond-mat.soft · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IGQIV4VEOAZELCLEB2656NOW67}

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	2026-05-18T04:35:04.653765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41a08af2a470324589640ebddf35d6f7c35eadea3acb90c99c2f8d6f1ad24c4d

Aliases

arxiv: 1008.2830 · arxiv_version: 1008.2830v1 · doi: 10.48550/arxiv.1008.2830 · pith_short_12: IGQIV4VEOAZE · pith_short_16: IGQIV4VEOAZELCLE · pith_short_8: IGQIV4VE

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/IGQIV4VEOAZELCLEB2656NOW67 \
  | 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: 41a08af2a470324589640ebddf35d6f7c35eadea3acb90c99c2f8d6f1ad24c4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f3620941c7a4245a8bc8fceca64df8efd74566457bc263345d52d329a613cb4",
    "cross_cats_sorted": [
      "cond-mat.soft",
      "cond-mat.stat-mech"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-08-17T06:33:15Z",
    "title_canon_sha256": "a50b4b6dd8c0f3421c3d32a15eb1cf88f127a7ce4a977e40062f3ce63ecae0c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.2830",
    "kind": "arxiv",
    "version": 1
  }
}