Pith Number

pith:MQRFQJ2K

pith:2018:MQRFQJ2KCLHJ4ZPAE43LEOJZ4L

not attested not anchored not stored refs pending

Minimum tree-stretch of Hamming graphs and higher-dimensional grids

Lan Lin, Yixun Lin

arxiv:1807.08252 v1 · 2018-07-22 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MQRFQJ2KCLHJ4ZPAE43LEOJZ4L}

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	2026-05-18T00:10:08.740158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

642258274a12ce9e65e02736b23939e2d615c33987dca8b9ad5b3fe62470dc9c

Aliases

arxiv: 1807.08252 · arxiv_version: 1807.08252v1 · doi: 10.48550/arxiv.1807.08252 · pith_short_12: MQRFQJ2KCLHJ · pith_short_16: MQRFQJ2KCLHJ4ZPA · pith_short_8: MQRFQJ2K

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/MQRFQJ2KCLHJ4ZPAE43LEOJZ4L \
  | 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: 642258274a12ce9e65e02736b23939e2d615c33987dca8b9ad5b3fe62470dc9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "951d93b0f428bcb1ee53c2df7536f1de875ec1e3cf548f57329813672e1df165",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-07-22T07:33:32Z",
    "title_canon_sha256": "8a6253f7c1ad057c33e87c6c6f28341c8793f4328b059639299011df82971b6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.08252",
    "kind": "arxiv",
    "version": 1
  }
}