Pith Number

pith:AOHAQLAI

pith:2024:AOHAQLAIX6E6X2DHSUYK5FNPCG

not attested not anchored not stored refs pending

The Planar Lattice Two-Neighbor Graph Percolates

Benedikt Jahnel (WIAS), Beno\^it Henry (IMT Nord Europe), David Coupier (IMT Nord Europe), Jonas K\"oppl (WIAS)

arxiv:2412.20781 v1 · 2024-12-30 · 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{AOHAQLAIX6E6X2DHSUYK5FNPCG}

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	2026-07-05T09:55:22.156355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

038e082c08bf89ebe8679530ae95af11b6c9b0a019764df2480ab344ff943167

Aliases

arxiv: 2412.20781 · arxiv_version: 2412.20781v1 · doi: 10.48550/arxiv.2412.20781 · pith_short_12: AOHAQLAIX6E6 · pith_short_16: AOHAQLAIX6E6X2DH · pith_short_8: AOHAQLAI

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/AOHAQLAIX6E6X2DHSUYK5FNPCG \
  | 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: 038e082c08bf89ebe8679530ae95af11b6c9b0a019764df2480ab344ff943167

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "425fc5d5b17ff5c7c722ed7474f163b40cb9dd147bf1bd70317774bdc58c3f4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-12-30T07:59:18Z",
    "title_canon_sha256": "a5ef3a44a0ccdcf7af2215b9b696aa47ceb6c6789553730bfa3f1773e8114899"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.20781",
    "kind": "arxiv",
    "version": 1
  }
}