Pith Number

pith:QMPCW6EM

pith:2013:QMPCW6EMVOAUHPS3NQVPKWLIDH

not attested not anchored not stored refs pending

The Haagerup property is stable under graph products

Dennis Dreesen, Yago Antol\'in

arxiv:1305.6748 v3 · 2013-05-29 · math.GR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QMPCW6EMVOAUHPS3NQVPKWLIDH}

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	2026-05-18T02:58:23.552714Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

831e2b788cab8143be5b6c2af5596819c4408ec8e95fb772e2a8aa4a275a571b

Aliases

arxiv: 1305.6748 · arxiv_version: 1305.6748v3 · doi: 10.48550/arxiv.1305.6748 · pith_short_12: QMPCW6EMVOAU · pith_short_16: QMPCW6EMVOAUHPS3 · pith_short_8: QMPCW6EM

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/QMPCW6EMVOAUHPS3NQVPKWLIDH \
  | 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: 831e2b788cab8143be5b6c2af5596819c4408ec8e95fb772e2a8aa4a275a571b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44eb5066051549af115a7c4665f87785c6ff18cfe1747cba7c2bca2912bff765",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-05-29T10:12:33Z",
    "title_canon_sha256": "8fa49611ef43580a4e9737ee64a35ff8475118ed6e47d32595103d7985b7d267"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6748",
    "kind": "arxiv",
    "version": 3
  }
}