Pith Number

pith:4UFT3PV5

pith:2016:4UFT3PV5ENASFL5PYHYP2F6VZB

not attested not anchored not stored refs pending

On the number of cliques in graphs with a forbidden subdivision or immersion

Fan Wei, Jacob Fox

arxiv:1606.06810 v2 · 2016-06-22 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4UFT3PV5ENASFL5PYHYP2F6VZB}

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	2026-05-18T00:08:36.779697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e50b3dbebd234122afafc1f0fd17d5c87fa999ed32897ce6c486973b9d327ec9

Aliases

arxiv: 1606.06810 · arxiv_version: 1606.06810v2 · doi: 10.48550/arxiv.1606.06810 · pith_short_12: 4UFT3PV5ENAS · pith_short_16: 4UFT3PV5ENASFL5P · pith_short_8: 4UFT3PV5

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/4UFT3PV5ENASFL5PYHYP2F6VZB \
  | 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: e50b3dbebd234122afafc1f0fd17d5c87fa999ed32897ce6c486973b9d327ec9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16bd1de9a82f0e7dd9e01627e73e109e88903bf4e8ddf6a596132dfe6046ffb9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-22T03:25:17Z",
    "title_canon_sha256": "bf40629e62b2c12f5f35b7ff765701fc81231ac00370ff1066a56a60c5888a6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.06810",
    "kind": "arxiv",
    "version": 2
  }
}