Pith Number

pith:4EUMNPKG

pith:2011:4EUMNPKGSWMQCMA44RIFV2SOUA

not attested not anchored not stored refs pending

On covering expander graphs by Hamilton cycles

Michael Krivelevich, Roman Glebov, Tibor Szab\'o

arxiv:1111.3325 v1 · 2011-11-14 · 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{4EUMNPKGSWMQCMA44RIFV2SOUA}

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	2026-05-18T04:08:22.563272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e128c6bd46959901301ce4505aea4ea0245a5b8d9568b01c1704f1c429ad1a17

Aliases

arxiv: 1111.3325 · arxiv_version: 1111.3325v1 · doi: 10.48550/arxiv.1111.3325 · pith_short_12: 4EUMNPKGSWMQ · pith_short_16: 4EUMNPKGSWMQCMA4 · pith_short_8: 4EUMNPKG

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/4EUMNPKGSWMQCMA44RIFV2SOUA \
  | 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: e128c6bd46959901301ce4505aea4ea0245a5b8d9568b01c1704f1c429ad1a17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "430a2642e93de1e509cb11058b39cabf9788221e855635fa382a3e452e6e3af0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-11-14T19:06:14Z",
    "title_canon_sha256": "1e770230e4004302ba2be60d25d001f23eb3f8cf83c79bacb66d02802400447b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3325",
    "kind": "arxiv",
    "version": 1
  }
}