Pith Number

pith:YJ3DNC6E

pith:2024:YJ3DNC6E6OOYME4GCFBVYBKGUW

not attested not anchored not stored refs pending

Optimality and uniqueness of the $D_4$ root system

David de Laat, Nando M. Leijenhorst, Willem H. H. de Muinck Keizer

arxiv:2404.18794 v2 · 2024-04-29 · math.MG · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YJ3DNC6E6OOYME4GCFBVYBKGUW}

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

Variations on five-dimensional sphere packings

Receipt and verification

First computed	2026-07-05T08:23:21.698459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c276368bc4f39d86138611435c0546a5b27822c4577ec8b38412e51df1f9eaf9

Aliases

arxiv: 2404.18794 · arxiv_version: 2404.18794v2 · doi: 10.48550/arxiv.2404.18794 · pith_short_12: YJ3DNC6E6OOY · pith_short_16: YJ3DNC6E6OOYME4G · pith_short_8: YJ3DNC6E

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/YJ3DNC6E6OOYME4GCFBVYBKGUW \
  | 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: c276368bc4f39d86138611435c0546a5b27822c4577ec8b38412e51df1f9eaf9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f87c0d2b6a38269a39152dd14ad32f883d2669a1507d40600eeb8b3eed3d4b52",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2024-04-29T15:27:50Z",
    "title_canon_sha256": "0a48ee6300d9a1cdf59d4c2c9de319641721e0b0171811de3be0bebf3f32d6f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.18794",
    "kind": "arxiv",
    "version": 2
  }
}