Pith Number

pith:332LPWZ6

pith:2018:332LPWZ6GHMIAJPMENAEWSKHOY

not attested not anchored not stored refs pending

Cheeger inequalities for graph limits

Abhishek Khetan, Mahan Mj

arxiv:1807.02225 v2 · 2018-07-06 · math.GT · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{332LPWZ6GHMIAJPMENAEWSKHOY}

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	2026-05-18T00:01:07.221834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

def4b7db3e31d88025ec23404b4947762165aaeca32ffc765cb2c31ead94ca77

Aliases

arxiv: 1807.02225 · arxiv_version: 1807.02225v2 · doi: 10.48550/arxiv.1807.02225 · pith_short_12: 332LPWZ6GHMI · pith_short_16: 332LPWZ6GHMIAJPM · pith_short_8: 332LPWZ6

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/332LPWZ6GHMIAJPMENAEWSKHOY \
  | 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: def4b7db3e31d88025ec23404b4947762165aaeca32ffc765cb2c31ead94ca77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "473e27bbf6cb8c81b7ec1499bbd4f063b40d6f83c9b380a316fe5bf7ac8848b6",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-07-06T02:43:04Z",
    "title_canon_sha256": "c01b86f46ea396abedd02f8821822793c3e34ca0ab9d17a3690def3b4bedbdeb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.02225",
    "kind": "arxiv",
    "version": 2
  }
}