Pith Number

pith:DBKHE7AB

pith:2018:DBKHE7ABA5VWC5FVN2STYHD65C

not attested not anchored not stored refs pending

The invariance principle and the large deviation for the biased random walk on $\mathbb{Z}^d$

Kainan Xiang, Longmin Wang, Vladas Sidoravicius, Yuelin Liu

arxiv:1811.03858 v1 · 2018-11-09 · 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{DBKHE7ABA5VWC5FVN2STYHD65C}

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	2026-05-18T00:01:11.781437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1854727c01076b6174b56ea53c1c7ee88316f9bf775a8f1eb7aaf0715cfba961

Aliases

arxiv: 1811.03858 · arxiv_version: 1811.03858v1 · doi: 10.48550/arxiv.1811.03858 · pith_short_12: DBKHE7ABA5VW · pith_short_16: DBKHE7ABA5VWC5FV · pith_short_8: DBKHE7AB

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/DBKHE7ABA5VWC5FVN2STYHD65C \
  | 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: 1854727c01076b6174b56ea53c1c7ee88316f9bf775a8f1eb7aaf0715cfba961

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "092ca58d272ed03c1736f46102c9878054d7946e9c5f8d5f341f7a5ac4cfc9dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-11-09T10:54:20Z",
    "title_canon_sha256": "bf7a3413a05b815bb08ad141eca7d430776bfbab68f4df6d1a077e8e7c0c1a28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.03858",
    "kind": "arxiv",
    "version": 1
  }
}