Pith Number

pith:4BVC5PGM

pith:1999:4BVC5PGM653XTEIY3QRB775HXL

not attested not anchored not stored refs pending

Values of Brownian intersection exponents I: Half-plane exponents

Gregory F. Lawler, Oded Schramm, Wendelin Werner

arxiv:math/9911084 v2 · 1999-11-12 · math.PR · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4BVC5PGM653XTEIY3QRB775HXL}

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

Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity

Receipt and verification

First computed	2026-07-04T15:16:41.130976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e06a2ebcccf777799118dc221fffa7bad1fd34cf61661b4ce85d5483d69b58b1

Aliases

arxiv: math/9911084 · arxiv_version: math/9911084v2 · doi: 10.48550/arxiv.math/9911084 · pith_short_12: 4BVC5PGM653X · pith_short_16: 4BVC5PGM653XTEIY · pith_short_8: 4BVC5PGM

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/4BVC5PGM653XTEIY3QRB775HXL \
  | 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: e06a2ebcccf777799118dc221fffa7bad1fd34cf61661b4ce85d5483d69b58b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac092586e13f9594207fd09eac6bc83e5b7869cb1b5476c44ad4e9da2f400504",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-11-12T15:52:00Z",
    "title_canon_sha256": "01fda25909c6b4284b7a6b0c9e3b585252315e5900896a5424dfa7daa268f059"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9911084",
    "kind": "arxiv",
    "version": 2
  }
}