Pith Number

pith:56PP2BRT

pith:2012:56PP2BRTUWGFA7Q7LVTOP2SELO

not attested not anchored not stored refs pending

Martingale Problem under Nonlinear Expectations

Chen Pan, Shige Peng, Xin Guo

arxiv:1211.2869 v3 · 2012-11-13 · 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{56PP2BRTUWGFA7Q7LVTOP2SELO}

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	2026-05-18T02:55:18.644568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef9efd0633a58c507e1f5d66e7ea445b9320df01ad356b958cbf97e70d6d2ce3

Aliases

arxiv: 1211.2869 · arxiv_version: 1211.2869v3 · doi: 10.48550/arxiv.1211.2869 · pith_short_12: 56PP2BRTUWGF · pith_short_16: 56PP2BRTUWGFA7Q7 · pith_short_8: 56PP2BRT

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/56PP2BRTUWGFA7Q7LVTOP2SELO \
  | 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: ef9efd0633a58c507e1f5d66e7ea445b9320df01ad356b958cbf97e70d6d2ce3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ffd595ea602012206f7f4cb6a7ac7f312ea30b63cf174cb45e7ba677b6902b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-13T01:45:03Z",
    "title_canon_sha256": "487096db449521eb5e9cf7db9cfbcfb40ed20a7a7ac3a12cc118dba0dfc43c38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2869",
    "kind": "arxiv",
    "version": 3
  }
}