Pith Number

pith:MNUDMWNT

pith:1999:MNUDMWNTBZM5BVUVXWYUPKOZZP

not attested not anchored not stored refs pending

On the effect of adding epsilon-Bernoulli percolation to everywhere percolating subgraphs of Z^d

Itai Benjamini, Oded Schramm, Olle H\"aggstr\"om

arxiv:math/9906002 v1 · 1999-06-01 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MNUDMWNTBZM5BVUVXWYUPKOZZP}

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	2026-07-04T16:15:07.403661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63683659b30e59d0d695bdb147a9d9cbd85e08cb8ad6c5864a32381fba23f595

Aliases

arxiv: math/9906002 · arxiv_version: math/9906002v1 · doi: 10.48550/arxiv.math/9906002 · pith_short_12: MNUDMWNTBZM5 · pith_short_16: MNUDMWNTBZM5BVUV · pith_short_8: MNUDMWNT

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/MNUDMWNTBZM5BVUVXWYUPKOZZP \
  | 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: 63683659b30e59d0d695bdb147a9d9cbd85e08cb8ad6c5864a32381fba23f595

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce4940254eafd90bf184cfcad25f147254b68f531457e0c17766ba94a22f3f59",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-06-01T10:42:50Z",
    "title_canon_sha256": "936bb5d8d5c8dde0b98ee89050b17538cdeca6ff7c03dfa7576e2740a88a9303"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9906002",
    "kind": "arxiv",
    "version": 1
  }
}