Pith Number

pith:XFC7J532

pith:2022:XFC7J532636TDM2NR7OUOEXZVG

not attested not anchored not stored refs pending

Critical cluster volumes in hierarchical percolation

Tom Hutchcroft

arxiv:2211.05686 v1 · 2022-11-10 · 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{XFC7J532636TDM2NR7OUOEXZVG}

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.

Cited by

1 paper in Pith

Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models

Receipt and verification

First computed	2026-07-05T05:15:06.915850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b945f4f77af6fd31b34d8fdd4712f9a9a10426ab164af5d40aa4a82cfa22be51

Aliases

arxiv: 2211.05686 · arxiv_version: 2211.05686v1 · doi: 10.48550/arxiv.2211.05686 · pith_short_12: XFC7J532636T · pith_short_16: XFC7J532636TDM2N · pith_short_8: XFC7J532

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/XFC7J532636TDM2NR7OUOEXZVG \
  | 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: b945f4f77af6fd31b34d8fdd4712f9a9a10426ab164af5d40aa4a82cfa22be51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "988cabfa1545545c45845378c698e36f27ddc469cd94d4bbca9b8251d808a8ac",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-11-10T16:47:01Z",
    "title_canon_sha256": "958137cc9993fc9a9de474eb5c8ea7d37ad0187968ac1db45bd379f9a71e3062"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.05686",
    "kind": "arxiv",
    "version": 1
  }
}