Pith Number

pith:S3XTQCHM

pith:2009:S3XTQCHMOJ6COSMPAMVQQDTE2P

not attested not anchored not stored refs pending

Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs

Andrzej Rucinski, Svante Janson

arxiv:0905.0972 v1 · 2009-05-07 · 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{S3XTQCHMOJ6COSMPAMVQQDTE2P}

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	2026-05-18T02:13:46.875940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96ef3808ec727c27498f032b080e64d3ddc9c4b36d4f4162b78b6cd80f5d28a1

Aliases

arxiv: 0905.0972 · arxiv_version: 0905.0972v1 · doi: 10.48550/arxiv.0905.0972 · pith_short_12: S3XTQCHMOJ6C · pith_short_16: S3XTQCHMOJ6COSMP · pith_short_8: S3XTQCHM

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/S3XTQCHMOJ6COSMPAMVQQDTE2P \
  | 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: 96ef3808ec727c27498f032b080e64d3ddc9c4b36d4f4162b78b6cd80f5d28a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0deb83b14942a1bd88ec4004de5bcbaadd522d8255b980c3bc6459a81805f33",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-05-07T09:08:49Z",
    "title_canon_sha256": "cd87443fb7d3e9342d690c6d41c3c4636a78e52ae4ce833c730c66e735fc4163"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.0972",
    "kind": "arxiv",
    "version": 1
  }
}