Pith Number

pith:VRI55VIK

pith:2025:VRI55VIKBWPNEMRGC5VDRNY6WF

not attested not anchored not stored refs pending

Uniqueness and dimension for the geodesic of the critical long-range percolation metric

Jian Ding, Lu-Jing Huang, Zherui Fan

arxiv:2506.10511 v1 · 2025-06-12 · 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{VRI55VIKBWPNEMRGC5VDRNY6WF}

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	2026-07-05T11:20:25.306197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac51ded50a0d9ed23226176a38b71eb14b597e7c83532f02a677842cfa16cb9a

Aliases

arxiv: 2506.10511 · arxiv_version: 2506.10511v1 · doi: 10.48550/arxiv.2506.10511 · pith_short_12: VRI55VIKBWPN · pith_short_16: VRI55VIKBWPNEMRG · pith_short_8: VRI55VIK

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/VRI55VIKBWPNEMRGC5VDRNY6WF \
  | 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: ac51ded50a0d9ed23226176a38b71eb14b597e7c83532f02a677842cfa16cb9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d5ec783deb005ea39006f7873faeb183659a2ead0105baef3da1ccffac98daf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-06-12T09:19:33Z",
    "title_canon_sha256": "6c4044fc4ed7f27334a82fbf8e35f829915e68df3c35da705be093473f40d6b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.10511",
    "kind": "arxiv",
    "version": 1
  }
}