Pith Number

pith:YGZ3JOW6

pith:2015:YGZ3JOW6MHI7AMUNPN2K2FOFQ5

not attested not anchored not stored refs pending

Saturation in random graphs

Benny Sudakov, D\'aniel Kor\'andi

arxiv:1510.09187 v2 · 2015-10-30 · 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{YGZ3JOW6MHI7AMUNPN2K2FOFQ5}

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	2026-05-18T01:17:11.513564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1b3b4bade61d1f0328d7b74ad15c587414ccd3dbd2cd4106c4cee102c45dfd0

Aliases

arxiv: 1510.09187 · arxiv_version: 1510.09187v2 · doi: 10.48550/arxiv.1510.09187 · pith_short_12: YGZ3JOW6MHI7 · pith_short_16: YGZ3JOW6MHI7AMUN · pith_short_8: YGZ3JOW6

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/YGZ3JOW6MHI7AMUNPN2K2FOFQ5 \
  | 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: c1b3b4bade61d1f0328d7b74ad15c587414ccd3dbd2cd4106c4cee102c45dfd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63c8aa5c644bb15b29c137005fe612d714763f8f1ffdea26497a268fd6107b3b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-10-30T18:34:59Z",
    "title_canon_sha256": "bc83515d87cb7dc82cf11f0629e214f6445cf401eb6148c4a2d9bc1f5459da19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.09187",
    "kind": "arxiv",
    "version": 2
  }
}