Pith Number

pith:IW5XCCTL

pith:1999:IW5XCCTLR2YP5VHV4E5B3FS4UY

not attested not anchored not stored refs pending

Percolation in the Hyperbolic Plane

Itai Benjamini, Oded Schramm

arxiv:math/9912233 v3 · 1999-12-30 · math.PR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IW5XCCTLR2YP5VHV4E5B3FS4UY}

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	2026-07-04T15:21:40.153595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45bb710a6b8eb0fed4f5e13a1d965ca63b407142d24cb48da110071877e9b01b

Aliases

arxiv: math/9912233 · arxiv_version: math/9912233v3 · doi: 10.48550/arxiv.math/9912233 · pith_short_12: IW5XCCTLR2YP · pith_short_16: IW5XCCTLR2YP5VHV · pith_short_8: IW5XCCTL

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/IW5XCCTLR2YP5VHV4E5B3FS4UY \
  | 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: 45bb710a6b8eb0fed4f5e13a1d965ca63b407142d24cb48da110071877e9b01b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcd31e921c3859425e8155744f4ffabefb37ad396700b77d8792d52ef734394e",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-12-30T18:56:37Z",
    "title_canon_sha256": "fc634a98960cf0ce7add6fad287c855fd8c393aa634fd132b7ee6c53d35d4783"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9912233",
    "kind": "arxiv",
    "version": 3
  }
}