Pith Number

pith:TDPC5TLA

pith:2014:TDPC5TLAUNFB44A6RGV3PXGSV5

not attested not anchored not stored refs pending

Density bounds for outer parallel domains of unit ball packings

Karoly Bezdek, Zsolt Langi

arxiv:1409.4508 v2 · 2014-09-16 · 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{TDPC5TLAUNFB44A6RGV3PXGSV5}

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	2026-05-18T01:26:18.942571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98de2ecd60a34a1e701e89abb7dcd2af5570524abd95aa4acfa99d9bfbab994e

Aliases

arxiv: 1409.4508 · arxiv_version: 1409.4508v2 · doi: 10.48550/arxiv.1409.4508 · pith_short_12: TDPC5TLAUNFB · pith_short_16: TDPC5TLAUNFB44A6 · pith_short_8: TDPC5TLA

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/TDPC5TLAUNFB44A6RGV3PXGSV5 \
  | 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: 98de2ecd60a34a1e701e89abb7dcd2af5570524abd95aa4acfa99d9bfbab994e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8aa8cdb91d7a6429a38c9413350f081088ca72aef9080402c595886985cb6c23",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2014-09-16T05:24:32Z",
    "title_canon_sha256": "c4d2a07643573308a9757bbf6134be520353a30062cee21eaa8c89f3192265d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.4508",
    "kind": "arxiv",
    "version": 2
  }
}