Pith Number

pith:KHYLHLDT

pith:2017:KHYLHLDTBR24RTEH7UI2DT4BIK

not attested not anchored not stored refs pending

An integral formula for the powered sum of the independent, identically and normally distributed random variables

Tamio Koyama

arxiv:1706.03989 v2 · 2017-06-13 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KHYLHLDTBR24RTEH7UI2DT4BIK}

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	2026-05-18T00:12:38.609908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51f0b3ac730c75c8cc87fd11a1cf814289456cbcb2e055ba461de61ef6f9b1c6

Aliases

arxiv: 1706.03989 · arxiv_version: 1706.03989v2 · doi: 10.48550/arxiv.1706.03989 · pith_short_12: KHYLHLDTBR24 · pith_short_16: KHYLHLDTBR24RTEH · pith_short_8: KHYLHLDT

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/KHYLHLDTBR24RTEH7UI2DT4BIK \
  | 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: 51f0b3ac730c75c8cc87fd11a1cf814289456cbcb2e055ba461de61ef6f9b1c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e391364f4a73d209455b3c72307b1d51c600c5ea324a5bcaaf73a91bfb9fbbcd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-06-13T10:33:18Z",
    "title_canon_sha256": "efb0ce054bfebbc9730604f9933d959e6e490181ef36da641f8acf208a2a08f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.03989",
    "kind": "arxiv",
    "version": 2
  }
}