Pith Number

pith:N3NGQGN7

pith:2025:N3NGQGN7PEGTK6X3LXZLWVARMZ

not attested not anchored not stored refs pending

Characterizing the limiting critical Potts measures on locally regular-tree-like expander graphs

Hang Du, Yanxin Zhou

arxiv:2505.24283 v1 · 2025-05-30 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N3NGQGN7PEGTK6X3LXZLWVARMZ}

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	2026-07-05T11:12:45.916122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6eda6819bf790d357afb5df2bb54116650f9052829ee00c987562e1307358208

Aliases

arxiv: 2505.24283 · arxiv_version: 2505.24283v1 · doi: 10.48550/arxiv.2505.24283 · pith_short_12: N3NGQGN7PEGT · pith_short_16: N3NGQGN7PEGTK6X3 · pith_short_8: N3NGQGN7

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/N3NGQGN7PEGTK6X3LXZLWVARMZ \
  | 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: 6eda6819bf790d357afb5df2bb54116650f9052829ee00c987562e1307358208

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5684fe49dd571f9e1f9fe61008d5ed4ae65fed3c34c9c0d2497249e6b147e62c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-05-30T07:00:04Z",
    "title_canon_sha256": "b94493c3124021f37949597cb8eaf30d3b756dc7e352b702de2cba5dbcc248aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.24283",
    "kind": "arxiv",
    "version": 1
  }
}