Pith Number

pith:YFM44GOA

pith:2008:YFM44GOAXG6AYYZQKXVLSSJ2XA

not attested not anchored not stored refs pending

Bounds for the annealed return probability on large finite percolation clusters

Florian Sobieczky

arxiv:0812.0117 v5 · 2008-11-30 · 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{YFM44GOAXG6AYYZQKXVLSSJ2XA}

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	2026-05-18T00:42:13.945016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c159ce19c0b9bc0c633055eab9493ab810eb56dd605d43b4345280dbfa44ded5

Aliases

arxiv: 0812.0117 · arxiv_version: 0812.0117v5 · doi: 10.48550/arxiv.0812.0117 · pith_short_12: YFM44GOAXG6A · pith_short_16: YFM44GOAXG6AYYZQ · pith_short_8: YFM44GOA

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/YFM44GOAXG6AYYZQKXVLSSJ2XA \
  | 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: c159ce19c0b9bc0c633055eab9493ab810eb56dd605d43b4345280dbfa44ded5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77e89885fa119be668efb8db1eaaa18f12a8c8b92f71a4d2fcaa5150fa214309",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-11-30T02:50:28Z",
    "title_canon_sha256": "33420444104c17ede86d5081b6f14efb09f1d91c8bce7a14d060c118678b3b21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.0117",
    "kind": "arxiv",
    "version": 5
  }
}