Pith Number

pith:Y2XMG47N

pith:2015:Y2XMG47NZS372GIWGAL7BRGPOP

not attested not anchored not stored refs pending

Tur\'an's Theorem for random graphs

Bobby DeMarco, Jeff Kahn

arxiv:1501.01340 v1 · 2015-01-07 · 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{Y2XMG47NZS372GIWGAL7BRGPOP}

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	2026-05-18T02:29:54.474073Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6aec373edccb7fd19163017f0c4cf73c48b6a7e149ef605f83d550d284734c7

Aliases

arxiv: 1501.01340 · arxiv_version: 1501.01340v1 · doi: 10.48550/arxiv.1501.01340 · pith_short_12: Y2XMG47NZS37 · pith_short_16: Y2XMG47NZS372GIW · pith_short_8: Y2XMG47N

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/Y2XMG47NZS372GIWGAL7BRGPOP \
  | 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: c6aec373edccb7fd19163017f0c4cf73c48b6a7e149ef605f83d550d284734c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7efd0708d95e23a67871117315b43cd34c878e109156cfb4ca61b000083edce6",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-01-07T00:46:17Z",
    "title_canon_sha256": "2691a375b3375c49b6c5b2e64fff36fa0ca6fb1b13cc81c85543233ab6fa5c15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.01340",
    "kind": "arxiv",
    "version": 1
  }
}