Pith Number

pith:ZHJZHCJD

pith:2011:ZHJZHCJDIYI4UZT2373GBU3CEC

not attested not anchored not stored refs pending

Weak invariance principle for the local times of partial sums of Markov Chains

Michael Bromberg, Zemer Kosloff

arxiv:1103.5228 v3 · 2011-03-27 · 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{ZHJZHCJDIYI4UZT2373GBU3CEC}

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	2026-05-18T03:45:01.170326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9d39389234611ca667adff660d36220905afae0a39ed215575ac61f1a620f5c

Aliases

arxiv: 1103.5228 · arxiv_version: 1103.5228v3 · doi: 10.48550/arxiv.1103.5228 · pith_short_12: ZHJZHCJDIYI4 · pith_short_16: ZHJZHCJDIYI4UZT2 · pith_short_8: ZHJZHCJD

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/ZHJZHCJDIYI4UZT2373GBU3CEC \
  | 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: c9d39389234611ca667adff660d36220905afae0a39ed215575ac61f1a620f5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4f692907e595ea65d1552055b11bcddb316d4571c35f99c372a4255896f8760",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-27T15:54:10Z",
    "title_canon_sha256": "b7cbe9858c536fb33fb8b67c14d7b62b3b1bbee44ad435f77477179ad3253edd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.5228",
    "kind": "arxiv",
    "version": 3
  }
}