Pith Number

pith:LK7WFGPJ

pith:2018:LK7WFGPJM32D7QGN7UJAQUGUR6

not attested not anchored not stored refs pending

Percolation on the product graph of a regular tree and a line does not satisfy the triangle condition at the uniqueness threshold

Kohei Yamamoto

arxiv:1811.01477 v1 · 2018-11-05 · 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{LK7WFGPJM32D7QGN7UJAQUGUR6}

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	2026-05-18T00:01:34.200835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5abf6299e966f43fc0cdfd120850d48f8198dfa72c1e7e81e9bab42219904a96

Aliases

arxiv: 1811.01477 · arxiv_version: 1811.01477v1 · doi: 10.48550/arxiv.1811.01477 · pith_short_12: LK7WFGPJM32D · pith_short_16: LK7WFGPJM32D7QGN · pith_short_8: LK7WFGPJ

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/LK7WFGPJM32D7QGN7UJAQUGUR6 \
  | 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: 5abf6299e966f43fc0cdfd120850d48f8198dfa72c1e7e81e9bab42219904a96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d24816bb918634bd8b8d9fec18f67798c2a2fd367214305f39729b5bec04fb9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-11-05T01:45:56Z",
    "title_canon_sha256": "6b70d2a5e25eec15e441868f89a0710021df9a71e899c457b13af731313b702a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.01477",
    "kind": "arxiv",
    "version": 1
  }
}