Pith Number

pith:KECKF36H

pith:2010:KECKF36HLS7H6T5TZOCYJSCYJM

not attested not anchored not stored refs pending

Upper tails of self-intersection local times of random walks: survey of proof techniques

Wolfgang K\"onig

arxiv:1011.3125 v1 · 2010-11-13 · 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{KECKF36HLS7H6T5TZOCYJSCYJM}

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	2026-05-18T04:35:56.470468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5104a2efc75cbe7f4fb3cb8584c8584b168fb819f681302dbde3657b904637fb

Aliases

arxiv: 1011.3125 · arxiv_version: 1011.3125v1 · doi: 10.48550/arxiv.1011.3125 · pith_short_12: KECKF36HLS7H · pith_short_16: KECKF36HLS7H6T5T · pith_short_8: KECKF36H

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/KECKF36HLS7H6T5TZOCYJSCYJM \
  | 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: 5104a2efc75cbe7f4fb3cb8584c8584b168fb819f681302dbde3657b904637fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4cad3473f574eef4f2d261fe0946bddfd9aec15c1e066df8e69a7beea59e78c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-11-13T11:08:04Z",
    "title_canon_sha256": "72676cc837e93aa3cbf13de74de5482fdc4385c07ba91bc5e0a8facd2d44498c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.3125",
    "kind": "arxiv",
    "version": 1
  }
}