Pith Number

pith:URS5ZQMX

pith:2012:URS5ZQMX6GPBBA3QDVGKZLZIMO

not attested not anchored not stored refs pending

Asymptotic Structure of Graphs with the Minimum Number of Triangles

Alexander Razborov, Oleg Pikhurko

arxiv:1204.2846 v2 · 2012-04-12 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{URS5ZQMX6GPBBA3QDVGKZLZIMO}

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	2026-05-18T01:15:15.646363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a465dcc197f19e1083701d4cacaf28639d06ee45b7b719759743245384625fd1

Aliases

arxiv: 1204.2846 · arxiv_version: 1204.2846v2 · doi: 10.48550/arxiv.1204.2846 · pith_short_12: URS5ZQMX6GPB · pith_short_16: URS5ZQMX6GPBBA3Q · pith_short_8: URS5ZQMX

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/URS5ZQMX6GPBBA3QDVGKZLZIMO \
  | 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: a465dcc197f19e1083701d4cacaf28639d06ee45b7b719759743245384625fd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d267ee1793d3de6d81e27e12bfea17a46ce8ce1a08407c911382e67af21715b1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-04-12T21:58:07Z",
    "title_canon_sha256": "f19642604616139494f8638ea12c0f94ff74bae0a7c6ce29f60f67d3c33ad1cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2846",
    "kind": "arxiv",
    "version": 2
  }
}