Pith Number

pith:U7A4O2AK

pith:2026:U7A4O2AKNCNHXT4X76R4XWPOU4

not attested not anchored not stored refs pending

Khinchin's and Chung's Laws of the Iterated Logarithm at Time Zero for the Linear Stochastic Fractional Diffusion Equation

Chang Liu, Ran Wang

arxiv:2608.04644 v1 · 2026-08-05 · 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{U7A4O2AKNCNHXT4X76R4XWPOU4}

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	2026-08-06T01:36:28.646582Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7c1c7680a689a7bcf97ffa3cbd9eea71bda176365c9154318cf4b7d1584c458

Aliases

arxiv: 2608.04644 · arxiv_version: 2608.04644v1 · doi: 10.48550/arxiv.2608.04644 · pith_short_12: U7A4O2AKNCNH · pith_short_16: U7A4O2AKNCNHXT4X · pith_short_8: U7A4O2AK

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/U7A4O2AKNCNHXT4X76R4XWPOU4 \
  | 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: a7c1c7680a689a7bcf97ffa3cbd9eea71bda176365c9154318cf4b7d1584c458

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1779fb447ef31b23ed666ff8662eeb5374beae1c9acea18be4b5e8807262b87d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-08-05T10:05:15Z",
    "title_canon_sha256": "6fb676d9e8dfc6b3dcc562d1838ca50d097feba9bbf64f513011bb6edef5eb7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04644",
    "kind": "arxiv",
    "version": 1
  }
}