Pith Number

pith:7VFKSY26

pith:2011:7VFKSY26QDPEUR7SLOMQC2GGYS

not attested not anchored not stored refs pending

On the tree-depth of Random Graphs

Guillem Perarnau, Oriol Serra

arxiv:1104.2132 v2 · 2011-04-12 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7VFKSY26QDPEUR7SLOMQC2GGYS}

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	2026-05-18T04:02:15.158647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd4aa9635e80de4a47f25b990168c6c4bc5a110d8b749e09a2a52f0b3023a310

Aliases

arxiv: 1104.2132 · arxiv_version: 1104.2132v2 · doi: 10.48550/arxiv.1104.2132 · pith_short_12: 7VFKSY26QDPE · pith_short_16: 7VFKSY26QDPEUR7S · pith_short_8: 7VFKSY26

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/7VFKSY26QDPEUR7SLOMQC2GGYS \
  | 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: fd4aa9635e80de4a47f25b990168c6c4bc5a110d8b749e09a2a52f0b3023a310

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a7c6351ef4e3a19091bcf2b1a6ad777e5dfdcef07e7682dcd0b72de7b6260bb",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-04-12T08:10:32Z",
    "title_canon_sha256": "0ca0dc3ef56b26c05118868e3636e57fd0b630fed117b5af5efdc12898dc2f2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2132",
    "kind": "arxiv",
    "version": 2
  }
}