Pith Number

pith:NRO7OQZV

pith:2026:NRO7OQZV2MLBMKUW2TPYZ4ZNCG

not attested not anchored not stored refs pending

From hexagonal lattice to 3-12 lattice: self-avoiding walk, Ising model and percolation

Hao Wu, Junyu Mou

arxiv:2606.00945 v1 · 2026-05-31 · 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{NRO7OQZV2MLBMKUW2TPYZ4ZNCG}

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	2026-06-02T01:04:10.085385Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c5df74335d316162a96d4df8cf32d1191a9f79aa6445dacb9b7ff197b314318

Aliases

arxiv: 2606.00945 · arxiv_version: 2606.00945v1 · doi: 10.48550/arxiv.2606.00945 · pith_short_12: NRO7OQZV2MLB · pith_short_16: NRO7OQZV2MLBMKUW · pith_short_8: NRO7OQZV

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/NRO7OQZV2MLBMKUW2TPYZ4ZNCG \
  | 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: 6c5df74335d316162a96d4df8cf32d1191a9f79aa6445dacb9b7ff197b314318

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eed079a6ef403ddeb3dee08e8ed7c02fd08436abe6199c96d1d3e30034c74fd1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-31T01:20:50Z",
    "title_canon_sha256": "e25125db771ce67bcf3c6938c873f50de45f7dc136d5f0b3597042d6e1e1d72b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.00945",
    "kind": "arxiv",
    "version": 1
  }
}