Pith Number

pith:TYH4M6MW

pith:2017:TYH4M6MWU6DMN6AYVGRZAK2XEI

not attested not anchored not stored refs pending

Lectures on the mean values of functionals -- An elementary introduction to infinite-dimensional probability

Cheng-shi Liu

arxiv:1705.03584 v1 · 2017-05-10 · math.PR · math-ph · math.FA · math.MP · math.ST · physics.comp-ph · 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{TYH4M6MWU6DMN6AYVGRZAK2XEI}

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	2026-05-18T00:44:43.554811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e0fc67996a786c6f818a9a3902b572224827b8f262240a1d92a6e3ef7a415bd

Aliases

arxiv: 1705.03584 · arxiv_version: 1705.03584v1 · doi: 10.48550/arxiv.1705.03584 · pith_short_12: TYH4M6MWU6DM · pith_short_16: TYH4M6MWU6DMN6AY · pith_short_8: TYH4M6MW

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/TYH4M6MWU6DMN6AYVGRZAK2XEI \
  | 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: 9e0fc67996a786c6f818a9a3902b572224827b8f262240a1d92a6e3ef7a415bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e373d6f7ba5107b9ae77d78bb57c791b2e88b8cd093d14b8ab151d5abcec2560",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "math.ST",
      "physics.comp-ph",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-05-10T02:21:03Z",
    "title_canon_sha256": "c61036a10d401b8dd0cd21d9b73d61285365595dce2802f5bda1184a8fc243a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.03584",
    "kind": "arxiv",
    "version": 1
  }
}