Pith Number

pith:LEF5NNBQ

pith:2023:LEF5NNBQI6G2QVH4XNSDTH2YC3

not attested not anchored not stored refs pending

Haagerup property and group-invariant percolation

Chiranjib Mukherjee, Konstantin Recke

arxiv:2303.17429 v3 · 2023-03-30 · math.GR · math.OA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LEF5NNBQI6G2QVH4XNSDTH2YC3}

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.

Cited by

1 paper in Pith

Coarse embeddability, $L^1$-compression and Percolations on General Graphs

Receipt and verification

First computed	2026-06-25T01:17:42.243597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

590bd6b430478da854fcbb64399f5816c1b4fc5965364075257fae53b4e4ec3b

Aliases

arxiv: 2303.17429 · arxiv_version: 2303.17429v3 · doi: 10.48550/arxiv.2303.17429 · pith_short_12: LEF5NNBQI6G2 · pith_short_16: LEF5NNBQI6G2QVH4 · pith_short_8: LEF5NNBQ

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/LEF5NNBQI6G2QVH4XNSDTH2YC3 \
  | 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: 590bd6b430478da854fcbb64399f5816c1b4fc5965364075257fae53b4e4ec3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93765a269cbda5e2ddfe4a4fa3f66fdd73c483caa004e74e8643492a7a4bb344",
    "cross_cats_sorted": [
      "math.OA",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2023-03-30T14:51:32Z",
    "title_canon_sha256": "856345c920444083c882e158d091cbf4aad4bb634b1ad8bff773f8c8c7780085"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.17429",
    "kind": "arxiv",
    "version": 3
  }
}