Pith Number

pith:WG42DXXB

pith:2014:WG42DXXBCEQSZDW4I3637FEYLQ

not attested not anchored not stored refs pending

New Lower Bound for the Optimal Ball Packing Density in Hyperbolic 4-space

Jen\H{o} Szirmai, Robert Thijs Kozma

arxiv:1401.6084 v3 · 2014-01-23 · 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{WG42DXXBCEQSZDW4I3637FEYLQ}

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	2026-05-18T02:44:40.280108Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1b9a1dee111212c8edc46fdbf94985c01562fc55801ee3ea08b7455d3af77c4

Aliases

arxiv: 1401.6084 · arxiv_version: 1401.6084v3 · doi: 10.48550/arxiv.1401.6084 · pith_short_12: WG42DXXBCEQS · pith_short_16: WG42DXXBCEQSZDW4 · pith_short_8: WG42DXXB

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/WG42DXXBCEQSZDW4I3637FEYLQ \
  | 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: b1b9a1dee111212c8edc46fdbf94985c01562fc55801ee3ea08b7455d3af77c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cc80e198fbf76243dcaa1f769b07734fdd3e73ef0ccb50cb3d4a784f3c38793",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2014-01-23T18:23:29Z",
    "title_canon_sha256": "99d727b31046517b0b61070c7f97e3c5821acb166b91e0a51c21ebc2a1ca8049"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.6084",
    "kind": "arxiv",
    "version": 3
  }
}