Pith Number

pith:GUIRD7ZX

pith:2015:GUIRD7ZX3MZWH7LY2KIXXMKGHC

not attested not anchored not stored refs pending

Improved Cheeger's Inequality and Analysis of Local Graph Partitioning using Vertex Expansion and Expansion Profile

Lap Chi Lau, Tsz Chiu Kwok, Yin Tat Lee

arxiv:1504.00686 v1 · 2015-04-02 · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GUIRD7ZX3MZWH7LY2KIXXMKGHC}

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	2026-05-18T02:19:42.155208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

351111ff37db3363fd78d2917bb146389a82d11b9bc1c6c68fb78ddb4f8571b5

Aliases

arxiv: 1504.00686 · arxiv_version: 1504.00686v1 · doi: 10.48550/arxiv.1504.00686 · pith_short_12: GUIRD7ZX3MZW · pith_short_16: GUIRD7ZX3MZWH7LY · pith_short_8: GUIRD7ZX

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/GUIRD7ZX3MZWH7LY2KIXXMKGHC \
  | 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: 351111ff37db3363fd78d2917bb146389a82d11b9bc1c6c68fb78ddb4f8571b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e0a55e4cd6094d24e826a3e3ac1ef9d50b9da7c81e11291ac750854131ae2d13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2015-04-02T20:45:39Z",
    "title_canon_sha256": "2ac1d999c5745f57f5c206887510f397a3001d8e4576baded64696789973a691"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00686",
    "kind": "arxiv",
    "version": 1
  }
}