Pith Number

pith:NE5SSKJ6

pith:2016:NE5SSKJ6HNBJUTCWMMO6PICNGZ

not attested not anchored not stored refs pending

A lower bound for $p_c$ in range-$R$ bond percolation in two and three dimensions

Edwin Perkins, Spencer Frei

arxiv:1603.04130 v1 · 2016-03-14 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NE5SSKJ6HNBJUTCWMMO6PICNGZ}

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	2026-05-18T01:19:09.321012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

693b29293e3b429a4c56631de7a04d36470436d0209d9df747ba4e76825b47d5

Aliases

arxiv: 1603.04130 · arxiv_version: 1603.04130v1 · doi: 10.48550/arxiv.1603.04130 · pith_short_12: NE5SSKJ6HNBJ · pith_short_16: NE5SSKJ6HNBJUTCW · pith_short_8: NE5SSKJ6

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/NE5SSKJ6HNBJUTCWMMO6PICNGZ \
  | 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: 693b29293e3b429a4c56631de7a04d36470436d0209d9df747ba4e76825b47d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23f8f9e27143dc8e13f3ae7d602ff44b310e4118baa61310dc84d40304261470",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-03-14T04:08:47Z",
    "title_canon_sha256": "a441be1fee23bc1063c1696d22dad67d6178a53b71e437c08e84c1ac8cc64aba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.04130",
    "kind": "arxiv",
    "version": 1
  }
}