Pith Number

pith:UFLPKMZT

pith:2016:UFLPKMZTMJJH3LJ5W2EB3SEX3N

not attested not anchored not stored refs pending

The distribution of minimum-weight cliques and other subgraphs in graphs with random edge weights

Alan Frieze, Gregory Sorkin, Wesley Pegden

arxiv:1606.04925 v2 · 2016-06-15 · math.PR · 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{UFLPKMZTMJJH3LJ5W2EB3SEX3N}

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	2026-05-18T00:41:01.944923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a156f5333362527dad3db6881dc897db51778e3e5b4f3a7748da1210c9a21486

Aliases

arxiv: 1606.04925 · arxiv_version: 1606.04925v2 · doi: 10.48550/arxiv.1606.04925 · pith_short_12: UFLPKMZTMJJH · pith_short_16: UFLPKMZTMJJH3LJ5 · pith_short_8: UFLPKMZT

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/UFLPKMZTMJJH3LJ5W2EB3SEX3N \
  | 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: a156f5333362527dad3db6881dc897db51778e3e5b4f3a7748da1210c9a21486

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72113cfdb181ea0b652b0dd30034c5e21bb75b948cb1503b3402eac2a1f2a5f0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-06-15T19:34:27Z",
    "title_canon_sha256": "1cf924a6e5af1aa1cf16edabee72160dd96c6bc21022de10a8cb2faa7a4bbb28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.04925",
    "kind": "arxiv",
    "version": 2
  }
}