Pith Number

pith:GYEFGD4A

pith:2011:GYEFGD4AJSKJFQUSBZG27YRFXW

not attested not anchored not stored refs pending

Martingale approach to subexponential asymptotics for random walks

Denis Denisov, Vitali Wachtel

arxiv:1111.6810 v1 · 2011-11-29 · 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{GYEFGD4AJSKJFQUSBZG27YRFXW}

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	2026-05-18T04:07:28.517920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3608530f804c9492c2920e4dafe225bdaec37c426ea903de148e2439ca090cc2

Aliases

arxiv: 1111.6810 · arxiv_version: 1111.6810v1 · doi: 10.48550/arxiv.1111.6810 · pith_short_12: GYEFGD4AJSKJ · pith_short_16: GYEFGD4AJSKJFQUS · pith_short_8: GYEFGD4A

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/GYEFGD4AJSKJFQUSBZG27YRFXW \
  | 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: 3608530f804c9492c2920e4dafe225bdaec37c426ea903de148e2439ca090cc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcd66cb7e5ccd3f85f0ae8ba20275c320005606e4448dfde44f04a1a112a095f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-11-29T13:37:39Z",
    "title_canon_sha256": "183698b90273ee126903397e3d3cc3a1e17ed9e40245e34bae10603bfe2449ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6810",
    "kind": "arxiv",
    "version": 1
  }
}