Pith Number

pith:IXHO5SHV

pith:2011:IXHO5SHVY5FMCLLGADXMG5H6EB

not attested not anchored not stored refs pending

General laws of large numbers under sublinear expectations

Feng Hu

arxiv:1104.5296 v2 · 2011-04-28 · 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{IXHO5SHVY5FMCLLGADXMG5H6EB}

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	2026-05-18T04:02:39.633087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45ceeec8f5c74ac12d6600eec374fe20457fe76a2a1bfc1439dd7e1ff5493ed9

Aliases

arxiv: 1104.5296 · arxiv_version: 1104.5296v2 · doi: 10.48550/arxiv.1104.5296 · pith_short_12: IXHO5SHVY5FM · pith_short_16: IXHO5SHVY5FMCLLG · pith_short_8: IXHO5SHV

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/IXHO5SHVY5FMCLLGADXMG5H6EB \
  | 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: 45ceeec8f5c74ac12d6600eec374fe20457fe76a2a1bfc1439dd7e1ff5493ed9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12cdaef5d700b378478c6eaadaa2b7b21eed8ca36716fca7a5275756d7111948",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-04-28T05:03:16Z",
    "title_canon_sha256": "15dde143ee0b4c1a15c6a04338b85416aff10813520b99171d2f0abb7af59fd9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.5296",
    "kind": "arxiv",
    "version": 2
  }
}