Pith Number

pith:XF2B4U6D

pith:2015:XF2B4U6D4YXTZ74PX6SBYXNIV5

not attested not anchored not stored refs pending

Law of the Iterated Logarithm for some Markov operators

Hanna Wojew\'odka, Katarzyna Horbacz, Sander C. Hille, Tomasz Szarek

arxiv:1506.07371 v2 · 2015-06-24 · 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{XF2B4U6D4YXTZ74PX6SBYXNIV5}

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	2026-05-18T01:18:44.507249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9741e53c3e62f3cff8fbfa41c5da8af4accc94a3b914c750e6777b90bf2c7d1

Aliases

arxiv: 1506.07371 · arxiv_version: 1506.07371v2 · doi: 10.48550/arxiv.1506.07371 · pith_short_12: XF2B4U6D4YXT · pith_short_16: XF2B4U6D4YXTZ74P · pith_short_8: XF2B4U6D

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/XF2B4U6D4YXTZ74PX6SBYXNIV5 \
  | 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: b9741e53c3e62f3cff8fbfa41c5da8af4accc94a3b914c750e6777b90bf2c7d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23a4d931e7dc841b21295a1c35fa827467fe2496b754f49103b8ee632df2d7ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-24T14:08:26Z",
    "title_canon_sha256": "51967e694a0637bfe3f92f2c84b31f193a00585684a9ff8df815fe3046e2e8d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.07371",
    "kind": "arxiv",
    "version": 2
  }
}