Pith Number

pith:325SY4NL

pith:2011:325SY4NLM2PRDJH5B43P34DZJG

not attested not anchored not stored refs pending

Upper bounds for the maximum of a random walk with negative drift

Johannes Kugler, Vitali Wachtel

arxiv:1107.5400 v1 · 2011-07-27 · 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{325SY4NLM2PRDJH5B43P34DZJG}

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	2026-05-18T04:16:52.109784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

debb2c71ab669f11a4fd0f36fdf07949b08e8198e86cfa8f5da4eb8dc1cc837c

Aliases

arxiv: 1107.5400 · arxiv_version: 1107.5400v1 · doi: 10.48550/arxiv.1107.5400 · pith_short_12: 325SY4NLM2PR · pith_short_16: 325SY4NLM2PRDJH5 · pith_short_8: 325SY4NL

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/325SY4NLM2PRDJH5B43P34DZJG \
  | 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: debb2c71ab669f11a4fd0f36fdf07949b08e8198e86cfa8f5da4eb8dc1cc837c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f0bc584f37d20e7d8b087c5be4c3ad78fb593c8bc6b4895eeb5cbf68212c91c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-27T07:46:22Z",
    "title_canon_sha256": "64f2c122040ab33d78bff30568ed0bc12ab5445f61e7a619d229abcd8bb14a91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5400",
    "kind": "arxiv",
    "version": 1
  }
}