Pith Number

pith:Y5CKPI7U

pith:2016:Y5CKPI7UQEQY52PWMMBVFVVBXJ

not attested not anchored not stored refs pending

Hyperbolic valued random variables and conditional expectation

Kailash Sharma, Romesh Kumar

arxiv:1611.06850 v2 · 2016-11-12 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5CKPI7UQEQY52PWMMBVFVVBXJ}

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	2026-05-18T00:47:56.630700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c744a7a3f481218ee9f6630352d6a1ba70cc54e598d0dc80fefdc253a4658d79

Aliases

arxiv: 1611.06850 · arxiv_version: 1611.06850v2 · doi: 10.48550/arxiv.1611.06850 · pith_short_12: Y5CKPI7UQEQY · pith_short_16: Y5CKPI7UQEQY52PW · pith_short_8: Y5CKPI7U

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/Y5CKPI7UQEQY52PWMMBVFVVBXJ \
  | 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: c744a7a3f481218ee9f6630352d6a1ba70cc54e598d0dc80fefdc253a4658d79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c03cf96995040cd2b2f7dfe174fe80aa2d9e96ce166ffeb90d9ea9888b2377c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-12T09:51:10Z",
    "title_canon_sha256": "1e6e9f5c6ce70c892980fa1d928952e1133417b2b29f595b05df8192ac20ac73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.06850",
    "kind": "arxiv",
    "version": 2
  }
}