Pith Number

pith:UBXZ6JXF

pith:2016:UBXZ6JXFMKQFMOTJQTK6VFUZS2

not attested not anchored not stored refs pending

On Contact Numbers of Finite Lattice Sphere Packings of 20-27 Balls

Istvan Szalkai

arxiv:1603.05390 v1 · 2016-03-17 · 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{UBXZ6JXFMKQFMOTJQTK6VFUZS2}

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	2026-05-18T01:18:56.459274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a06f9f26e562a0563a6984d5ea969996a3547fd4562720fc13ad7767139f3487

Aliases

arxiv: 1603.05390 · arxiv_version: 1603.05390v1 · doi: 10.48550/arxiv.1603.05390 · pith_short_12: UBXZ6JXFMKQF · pith_short_16: UBXZ6JXFMKQFMOTJ · pith_short_8: UBXZ6JXF

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/UBXZ6JXFMKQFMOTJQTK6VFUZS2 \
  | 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: a06f9f26e562a0563a6984d5ea969996a3547fd4562720fc13ad7767139f3487

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dda5d30cc14a8015875065fce5755516cd4a0a057cf4571a4829ea9e4b20710",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-03-17T08:38:00Z",
    "title_canon_sha256": "506adc93ffd63ef6741068961c6e1607a7f17241a39786b3d9c28e2024372f6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.05390",
    "kind": "arxiv",
    "version": 1
  }
}