Pith Number

pith:MSNWYZWW

pith:2014:MSNWYZWWIFDNTWKAJZVB24FFY6

not attested not anchored not stored refs pending

$G$-martingale representation in the $G$-L'evy setting

Krzysztof Paczka

arxiv:1404.2121 v1 · 2014-04-08 · 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{MSNWYZWWIFDNTWKAJZVB24FFY6}

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	2026-05-18T02:54:38.496113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

649b6c66d64146d9d9404e6a1d70a5c793978f1248ba38d1183be75cfeaefe20

Aliases

arxiv: 1404.2121 · arxiv_version: 1404.2121v1 · doi: 10.48550/arxiv.1404.2121 · pith_short_12: MSNWYZWWIFDN · pith_short_16: MSNWYZWWIFDNTWKA · pith_short_8: MSNWYZWW

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/MSNWYZWWIFDNTWKAJZVB24FFY6 \
  | 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: 649b6c66d64146d9d9404e6a1d70a5c793978f1248ba38d1183be75cfeaefe20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3de9156c634c8493c329a88c0e4e0e7f10b630c20b9adb94406acdfbac16d5a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-04-08T13:28:20Z",
    "title_canon_sha256": "59d0a9944bf4de414895df90973d76eee2b2da503a0182648bc47bd38f247153"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.2121",
    "kind": "arxiv",
    "version": 1
  }
}