Pith Number

pith:K2C47D74

pith:2010:K2C47D74P7PD7USJRVOM2MYNCW

not attested not anchored not stored refs pending

Some properties on $G$-evaluation and its applications to $G$-martingale decomposition

Yongsheng Song

arxiv:1001.2802 v2 · 2010-01-17 · 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{K2C47D74P7PD7USJRVOM2MYNCW}

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	2026-05-18T02:09:43.520558Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5685cf8ffc7fde3fd2498d5ccd330d1591c217e66273de38d27958ef7f79ac37

Aliases

arxiv: 1001.2802 · arxiv_version: 1001.2802v2 · doi: 10.48550/arxiv.1001.2802 · pith_short_12: K2C47D74P7PD · pith_short_16: K2C47D74P7PD7USJ · pith_short_8: K2C47D74

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/K2C47D74P7PD7USJRVOM2MYNCW \
  | 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: 5685cf8ffc7fde3fd2498d5ccd330d1591c217e66273de38d27958ef7f79ac37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a661d3d2b959b0a5235d46aea36ce13f904c247bd06b2cacddbc8e16a04bfb23",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-01-17T03:49:08Z",
    "title_canon_sha256": "eb1e04e098372830e11b2646a8ab38b6aae7fd97043b3caa4dba26440b7d9453"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.2802",
    "kind": "arxiv",
    "version": 2
  }
}