Pith Number

pith:I7M3ZBMH

pith:2000:I7M3ZBMH3WAGS6MH7MSIHWGDOD

not attested not anchored not stored refs pending

On the mixing time of simple random walk on the super critical percolation cluster

Elchanan Mossel, Itai Benjamini

arxiv:math/0011092 v3 · 2000-11-14 · 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{I7M3ZBMH3WAGS6MH7MSIHWGDOD}

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	2026-07-04T14:34:55.165640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47d9bc8587dd80697987fb2483d8c370e79b6259a45d70235077f0e93e9e511c

Aliases

arxiv: math/0011092 · arxiv_version: math/0011092v3 · doi: 10.48550/arxiv.math/0011092 · pith_short_12: I7M3ZBMH3WAG · pith_short_16: I7M3ZBMH3WAGS6MH · pith_short_8: I7M3ZBMH

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/I7M3ZBMH3WAGS6MH7MSIHWGDOD \
  | 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: 47d9bc8587dd80697987fb2483d8c370e79b6259a45d70235077f0e93e9e511c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90edb31a741af51a38a84b81265d51f10e596b2be64ca1e8db283dac273f2b3d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2000-11-14T21:11:14Z",
    "title_canon_sha256": "d64c5c9bf15614f7089038301bae47d5c9ca8214ef8113ca971ed885c3fd65bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0011092",
    "kind": "arxiv",
    "version": 3
  }
}