Pith Number

pith:UTOTZ6ZL

pith:2012:UTOTZ6ZLI7EHEE5ZWF7BNE27OX

not attested not anchored not stored refs pending

A Complete Representation Theorem for $G$-martingales

Jianfeng Zhang, Shige Peng, Yongsheng Song

arxiv:1201.2629 v2 · 2012-01-12 · 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{UTOTZ6ZLI7EHEE5ZWF7BNE27OX}

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	2026-05-18T03:35:54.309395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4dd3cfb2b47c87213b9b17e16935f75c75cfd1057464b08fe316f7e71f5e382

Aliases

arxiv: 1201.2629 · arxiv_version: 1201.2629v2 · doi: 10.48550/arxiv.1201.2629 · pith_short_12: UTOTZ6ZLI7EH · pith_short_16: UTOTZ6ZLI7EHEE5Z · pith_short_8: UTOTZ6ZL

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/UTOTZ6ZLI7EHEE5ZWF7BNE27OX \
  | 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: a4dd3cfb2b47c87213b9b17e16935f75c75cfd1057464b08fe316f7e71f5e382

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "685bc8aaa07326c54b32a756b6a174b7de01a8ea179ec63673639b9ff48676bc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-01-12T17:51:36Z",
    "title_canon_sha256": "ce1c3f26ede47ca5cbc13ec99fcd026e595409c42050f748d00a8e86f640c4de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2629",
    "kind": "arxiv",
    "version": 2
  }
}