Pith Number

pith:4RKH2EUW

pith:2010:4RKH2EUWUYNSVREMVJO2FUCRPK

not attested not anchored not stored refs pending

Uniqueness of the representation for $G$-martingales with finite variation

Yongsheng Song

arxiv:1012.1913 v2 · 2010-12-09 · 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{4RKH2EUWUYNSVREMVJO2FUCRPK}

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	2026-05-18T04:32:11.337457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4547d1296a61b2ac48caa5da2d0517a86b0a1a80f884b04941d13a77a4d00ce

Aliases

arxiv: 1012.1913 · arxiv_version: 1012.1913v2 · doi: 10.48550/arxiv.1012.1913 · pith_short_12: 4RKH2EUWUYNS · pith_short_16: 4RKH2EUWUYNSVREM · pith_short_8: 4RKH2EUW

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/4RKH2EUWUYNSVREMVJO2FUCRPK \
  | 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: e4547d1296a61b2ac48caa5da2d0517a86b0a1a80f884b04941d13a77a4d00ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4745526c428eaf6eb7c2b542c6acc1cd0ff1fc99f01b218a974454ffa592890c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-09T02:58:51Z",
    "title_canon_sha256": "3ab52e937ee316771354052976e38c4b07a48bd290494bade313887643776f18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1913",
    "kind": "arxiv",
    "version": 2
  }
}