Pith Number

pith:4MXB7B3A

pith:2007:4MXB7B3AYWKYFKD3YVPXUOJKKE

not attested not anchored not stored refs pending

A note on percolation on Z^d: isoperimetric profile via exponential cluster repulsion

Gabor Pete

arxiv:math/0702474 v5 · 2007-02-16 · 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{4MXB7B3AYWKYFKD3YVPXUOJKKE}

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	2026-05-18T01:09:12.017461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e32e1f8760c59582a87bc55f7a392a5129ff5b45fcb2a728458d1a8b26913fe0

Aliases

arxiv: math/0702474 · arxiv_version: math/0702474v5 · doi: 10.48550/arxiv.math/0702474 · pith_short_12: 4MXB7B3AYWKY · pith_short_16: 4MXB7B3AYWKYFKD3 · pith_short_8: 4MXB7B3A

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/4MXB7B3AYWKYFKD3YVPXUOJKKE \
  | 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: e32e1f8760c59582a87bc55f7a392a5129ff5b45fcb2a728458d1a8b26913fe0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ddef5316e28725c404dd6ce0df49a30f02890b60823da6b4f46f69e84e7b1c1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2007-02-16T06:32:01Z",
    "title_canon_sha256": "196e4cbc0782bd427e9b535ac8eda5429d9d6a288d1686266de62c12006caefc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0702474",
    "kind": "arxiv",
    "version": 5
  }
}