Pith Number

pith:WN7HBIF5

pith:2017:WN7HBIF5OBBNQO4D7HNA2WEMI3

not attested not anchored not stored refs pending

The geometrical origins of some distributions and the complete concentration of measure phenomenon for mean-values of functionals

Cheng-shi Liu

arxiv:1705.01327 v1 · 2017-05-03 · math.PR · math-ph · math.FA · math.MP · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WN7HBIF5OBBNQO4D7HNA2WEMI3}

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	2026-05-18T00:45:05.425169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b37e70a0bd7042d83b83f9da0d588c46fd033bc9e3fcb527cf4653ed6bf984ab

Aliases

arxiv: 1705.01327 · arxiv_version: 1705.01327v1 · doi: 10.48550/arxiv.1705.01327 · pith_short_12: WN7HBIF5OBBN · pith_short_16: WN7HBIF5OBBNQO4D · pith_short_8: WN7HBIF5

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/WN7HBIF5OBBNQO4D7HNA2WEMI3 \
  | 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: b37e70a0bd7042d83b83f9da0d588c46fd033bc9e3fcb527cf4653ed6bf984ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc6e6b380411d468952a26099b2bc582575df535154a4e7925ec28983ae30e7d",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-05-03T09:35:38Z",
    "title_canon_sha256": "d946306231a44ad3929083967111c52f41e795c42f021c9a2a1654847685faf1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.01327",
    "kind": "arxiv",
    "version": 1
  }
}