Pith Number

pith:U4K72FHU

pith:2016:U4K72FHUPVPACQC4EBHFWIMI5R

not attested not anchored not stored refs pending

On the number of cliques in graphs with a forbidden minor

Fan Wei, Jacob Fox

arxiv:1603.07056 v1 · 2016-03-23 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U4K72FHUPVPACQC4EBHFWIMI5R}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:18:24.595773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a715fd14f47d5e01405c204e5b2188ec7c05868804db47796909d4555fa5a676

Aliases

arxiv: 1603.07056 · arxiv_version: 1603.07056v1 · doi: 10.48550/arxiv.1603.07056 · pith_short_12: U4K72FHUPVPA · pith_short_16: U4K72FHUPVPACQC4 · pith_short_8: U4K72FHU

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/U4K72FHUPVPACQC4EBHFWIMI5R \
  | 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: a715fd14f47d5e01405c204e5b2188ec7c05868804db47796909d4555fa5a676

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "616ce24fcf4dcc93d0b2e42ddcb318910de359f68ef04e35f35e3b45b3eea3d5",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-03-23T02:56:56Z",
    "title_canon_sha256": "bc5eb96265bda0e954f6dd4d5a6e9021f3d5bf975f5ff643815d412d9ef36eda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.07056",
    "kind": "arxiv",
    "version": 1
  }
}