Pith Number

pith:KVZK3YV3

pith:2010:KVZK3YV3NZKDKTGQHGPW4BF2HV

not attested not anchored not stored refs pending

Random G-expectations

Marcel Nutz

arxiv:1009.2168 v3 · 2010-09-11 · math.PR · math.OC · q-fin.RM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KVZK3YV3NZKDKTGQHGPW4BF2HV}

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	2026-05-18T03:14:08.910696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5572ade2bb6e54354cd0399f6e04ba3d45a541544cf3fefa02e8170cd8a2061f

Aliases

arxiv: 1009.2168 · arxiv_version: 1009.2168v3 · doi: 10.48550/arxiv.1009.2168 · pith_short_12: KVZK3YV3NZKD · pith_short_16: KVZK3YV3NZKDKTGQ · pith_short_8: KVZK3YV3

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/KVZK3YV3NZKDKTGQHGPW4BF2HV \
  | 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: 5572ade2bb6e54354cd0399f6e04ba3d45a541544cf3fefa02e8170cd8a2061f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7272c6577227ebb25c31ccae09b2581a4071cfffd56c3d334fb2b125aac27df4",
    "cross_cats_sorted": [
      "math.OC",
      "q-fin.RM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-09-11T13:44:53Z",
    "title_canon_sha256": "0cf2d50e3d18c2014dd1e98667690641bc05c27ce7e28308ac176a7ca083928d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2168",
    "kind": "arxiv",
    "version": 3
  }
}