Pith Number

pith:FPYABJ5V

pith:2022:FPYABJ5V2BOWSA32DK3IBYCIV3

not attested not anchored not stored refs pending

A sharp leading order asymptotic of the diameter of a long range percolation graph

Tianqi Wu

arxiv:2211.16500 v1 · 2022-11-29 · 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{FPYABJ5V2BOWSA32DK3IBYCIV3}

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	2026-07-05T05:20:27.608524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bf000a7b5d05d69037a1ab680e048aed46c4c45d182c03e2e0a99cdb291909f

Aliases

arxiv: 2211.16500 · arxiv_version: 2211.16500v1 · doi: 10.48550/arxiv.2211.16500 · pith_short_12: FPYABJ5V2BOW · pith_short_16: FPYABJ5V2BOWSA32 · pith_short_8: FPYABJ5V

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/FPYABJ5V2BOWSA32DK3IBYCIV3 \
  | 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: 2bf000a7b5d05d69037a1ab680e048aed46c4c45d182c03e2e0a99cdb291909f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "786575f6b838a160622c4791f488976df829f1d1d2dc46f4933506290abad565",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-11-29T18:59:41Z",
    "title_canon_sha256": "3c3e67d409598bbc114a1be664970cad807c82f2b1c9aefde530c2ea018bea11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.16500",
    "kind": "arxiv",
    "version": 1
  }
}