Pith Number

pith:37UMPT7X

pith:2011:37UMPT7XCNTZFAMWE5Y3UUHQJI

not attested not anchored not stored refs pending

Numerical schemes for $G$--Expectations

Yan Dolinsky

arxiv:1109.3430 v1 · 2011-09-15 · 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{37UMPT7XCNTZFAMWE5Y3UUHQJI}

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	2026-05-18T04:12:56.765782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfe8c7cff713679281962771ba50f04a0fa7defa7041f1f8897d1b13e152a4c8

Aliases

arxiv: 1109.3430 · arxiv_version: 1109.3430v1 · doi: 10.48550/arxiv.1109.3430 · pith_short_12: 37UMPT7XCNTZ · pith_short_16: 37UMPT7XCNTZFAMW · pith_short_8: 37UMPT7X

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/37UMPT7XCNTZFAMWE5Y3UUHQJI \
  | 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: dfe8c7cff713679281962771ba50f04a0fa7defa7041f1f8897d1b13e152a4c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8855f7e66646f9a33ea365f1eea94b8b0eb0055c33f9728ad5ef07885e0d384",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-15T19:06:29Z",
    "title_canon_sha256": "0d5dd47d850f049241a8c7a526b7ec809b767203c4b53d791aa0cf95507187df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3430",
    "kind": "arxiv",
    "version": 1
  }
}