Pith Number

pith:ZXZG57NC

pith:2010:ZXZG57NC277LVLQFM7KFQOIEBM

not attested not anchored not stored refs pending

Finitely additive equivalent martingale measures

Luca Pratelli, Patrizia Berti, Pietro Rigo

arxiv:1012.2811 v1 · 2010-12-13 · 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{ZXZG57NC277LVLQFM7KFQOIEBM}

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	2026-05-18T04:33:27.701937Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdf26efda2d7febaae0567d45839040b3237dec6fd79f3b03669c66dd712eb59

Aliases

arxiv: 1012.2811 · arxiv_version: 1012.2811v1 · doi: 10.48550/arxiv.1012.2811 · pith_short_12: ZXZG57NC277L · pith_short_16: ZXZG57NC277LVLQF · pith_short_8: ZXZG57NC

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/ZXZG57NC277LVLQFM7KFQOIEBM \
  | 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: cdf26efda2d7febaae0567d45839040b3237dec6fd79f3b03669c66dd712eb59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3d594a5b1f1d95773560a961b5272c210dc7b4d9cbc61c0dc05780a67858b74",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-13T17:40:06Z",
    "title_canon_sha256": "ec0ae97599190572b884368d73877579504f27d171b47e987f6d8e35b8fbccc8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2811",
    "kind": "arxiv",
    "version": 1
  }
}