Pith Number

pith:PYQIFUDH

pith:2008:PYQIFUDHMOQMDMZKNE5EFZKWS4

not attested not anchored not stored refs pending

A combinatorial proof of the Removal Lemma for Groups

Daniel Kr\'al', Llu\'is Vena, Oriol Serra

arxiv:0804.4847 v1 · 2008-04-30 · 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{PYQIFUDHMOQMDMZKNE5EFZKWS4}

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	2026-07-04T15:11:15.975138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e2082d06763a0c1b32a693a42e55697061e49c6008cb3f524686bef07900e63

Aliases

arxiv: 0804.4847 · arxiv_version: 0804.4847v1 · doi: 10.48550/arxiv.0804.4847 · pith_short_12: PYQIFUDHMOQM · pith_short_16: PYQIFUDHMOQMDMZK · pith_short_8: PYQIFUDH

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/PYQIFUDHMOQMDMZKNE5EFZKWS4 \
  | 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: 7e2082d06763a0c1b32a693a42e55697061e49c6008cb3f524686bef07900e63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e15603968d51b744f7e7af3f7b7c84eb4bf02e2f1573c97c446d536d5edd0434",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-04-30T15:33:41Z",
    "title_canon_sha256": "36ed725a74ebeea1440d4b4ee35919efdd7cf01b61cf377adfc5128d5558ddf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.4847",
    "kind": "arxiv",
    "version": 1
  }
}