Pith Number

pith:7LLL3NZD

pith:2012:7LLL3NZDYOD4JRU3NVOSXR5ZWA

not attested not anchored not stored refs pending

Vertex Isoperimetric Inequalities for a Family of Graphs on Z^k

A. J. Radcliffe, Ellen Veomett

arxiv:1202.4204 v1 · 2012-02-20 · 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{7LLL3NZDYOD4JRU3NVOSXR5ZWA}

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	2026-05-18T04:01:52.040565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fad6bdb723c387c4c69b6d5d2bc7b9b033138a51389839685735f15aff67f57c

Aliases

arxiv: 1202.4204 · arxiv_version: 1202.4204v1 · doi: 10.48550/arxiv.1202.4204 · pith_short_12: 7LLL3NZDYOD4 · pith_short_16: 7LLL3NZDYOD4JRU3 · pith_short_8: 7LLL3NZD

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/7LLL3NZDYOD4JRU3NVOSXR5ZWA \
  | 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: fad6bdb723c387c4c69b6d5d2bc7b9b033138a51389839685735f15aff67f57c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bfda9a7fa2d860e083e97081433a292041d7a44ea19cd7f711bae39ac04c7cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-20T01:08:20Z",
    "title_canon_sha256": "33108bb463e9adee62c01c23f26be92586c9b943bdd9d30a77ff570710a4d523"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.4204",
    "kind": "arxiv",
    "version": 1
  }
}