Pith Number

pith:P7V6M4BR

pith:2007:P7V6M4BRSREZ4LWWIZFOHMLEE7

not attested not anchored not stored refs pending

Long Range Percolation Mixing Time

Ariel Yadin, Itai Benjamini, Noam Berger

arxiv:math/0703872 v2 · 2007-03-29 · math.PR · math-ph · math.CO · 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{P7V6M4BRSREZ4LWWIZFOHMLEE7}

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	2026-07-04T15:41:21.740819Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7febe6703194499e2ed6464ae3b16427f5ba4d061cc36a04f5ada6541275331e

Aliases

arxiv: math/0703872 · arxiv_version: math/0703872v2 · doi: 10.48550/arxiv.math/0703872 · pith_short_12: P7V6M4BRSREZ · pith_short_16: P7V6M4BRSREZ4LWW · pith_short_8: P7V6M4BR

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/P7V6M4BRSREZ4LWWIZFOHMLEE7 \
  | 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: 7febe6703194499e2ed6464ae3b16427f5ba4d061cc36a04f5ada6541275331e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9b5288242992ff4a051a19ba348b49c21bbf0ba92770754b52f92539e022cd3",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2007-03-29T08:26:38Z",
    "title_canon_sha256": "cc3216ea0d67535d208b2a4220014f58ddebe33b091fe07215fc3e96eac00440"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703872",
    "kind": "arxiv",
    "version": 2
  }
}