Pith Number

pith:VNUZDGQK

pith:2026:VNUZDGQKRY3QZWDXKUAZVVRZ67

not attested not anchored not stored refs pending

Range convergence and sharp one-arm asymptotics for the critical percolation cluster in high dimensions

A. Fribegh, D. Croydon, M. Cabezas, N. Kawamoto

arxiv:2607.24561 v1 · 2026-07-27 · 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{VNUZDGQKRY3QZWDXKUAZVVRZ67}

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	2026-07-28T02:24:10.366772Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab69919a0a8e370cd87755019ad639f7f8d4d2fdcb20888e8d93af042a2c9e3d

Aliases

arxiv: 2607.24561 · arxiv_version: 2607.24561v1 · doi: 10.48550/arxiv.2607.24561 · pith_short_12: VNUZDGQKRY3Q · pith_short_16: VNUZDGQKRY3QZWDX · pith_short_8: VNUZDGQK

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/VNUZDGQKRY3QZWDXKUAZVVRZ67 \
  | 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: ab69919a0a8e370cd87755019ad639f7f8d4d2fdcb20888e8d93af042a2c9e3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8773bb641bd0b41b905d33f4a506f58a0dfaacf6f9963da11f0e2c664c0dbca",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-27T15:31:28Z",
    "title_canon_sha256": "8d32ecd7f8e48aaaed3c8b52c8f83ff1ca0cd4a9e7f9043b8cee0672f2b621f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24561",
    "kind": "arxiv",
    "version": 1
  }
}