Pith Number

pith:5SNJ3HNO

pith:2010:5SNJ3HNOXJ7ZJFK6PNMK7OX4VF

not attested not anchored not stored refs pending

Bandwidth theorem for random graphs

Benny Sudakov, Choongbum Lee, Hao Huang

arxiv:1005.1947 v2 · 2010-05-11 · 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{5SNJ3HNOXJ7ZJFK6PNMK7OX4VF}

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	2026-05-18T02:24:08.216487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec9a9d9daeba7f94955e7b58afbafca9620d947aea93b2614e3aca845e08c1b7

Aliases

arxiv: 1005.1947 · arxiv_version: 1005.1947v2 · doi: 10.48550/arxiv.1005.1947 · pith_short_12: 5SNJ3HNOXJ7Z · pith_short_16: 5SNJ3HNOXJ7ZJFK6 · pith_short_8: 5SNJ3HNO

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/5SNJ3HNOXJ7ZJFK6PNMK7OX4VF \
  | 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: ec9a9d9daeba7f94955e7b58afbafca9620d947aea93b2614e3aca845e08c1b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "216f445194ef53cdd9b191897c2041fec7e27d41dd5133d980cf6617b980b92d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-05-11T20:41:47Z",
    "title_canon_sha256": "37bd75373ee0244becf361063266fba0a2fdbf17f4879a3d414a88c231475671"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.1947",
    "kind": "arxiv",
    "version": 2
  }
}