Pith Number

pith:ZMUZDMEC

pith:2015:ZMUZDMECAYDDEKFLQ7S7DTJXA7

not attested not anchored not stored refs pending

Limit theorems for random walks

Alexander Bendikov, Bartosz Trojan, Wojciech Cygan

arxiv:1504.01759 v3 · 2015-04-07 · 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{ZMUZDMECAYDDEKFLQ7S7DTJXA7}

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	2026-05-18T00:50:23.162255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb2991b08206063228ab87e5f1cd3707e12fc8748170c44ee8595f8a7f1144c3

Aliases

arxiv: 1504.01759 · arxiv_version: 1504.01759v3 · doi: 10.48550/arxiv.1504.01759 · pith_short_12: ZMUZDMECAYDD · pith_short_16: ZMUZDMECAYDDEKFL · pith_short_8: ZMUZDMEC

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/ZMUZDMECAYDDEKFLQ7S7DTJXA7 \
  | 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: cb2991b08206063228ab87e5f1cd3707e12fc8748170c44ee8595f8a7f1144c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86c7c7c29222bff99d23786d3b4c9b01e88972752a13b9281103e9e1a58c2f5e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-04-07T21:30:14Z",
    "title_canon_sha256": "e3014de2ad13345c2335ff7ab47f16c01b0866402cf6fafacf962031ee7c553a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01759",
    "kind": "arxiv",
    "version": 3
  }
}