Pith Number

pith:7GN25ISU

pith:2012:7GN25ISUOZWQ5FEM2KFDDCFREV

not attested not anchored not stored refs pending

L\'evy processes, martingales, reversed martingales and orthogonal polynomials

Pawe{\l} J. Szab{\l}owski

arxiv:1212.3121 v5 · 2012-12-13 · 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{7GN25ISUOZWQ5FEM2KFDDCFREV}

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	2026-05-18T02:56:12.800322Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f99baea254766d0e948cd28a3188b12573e80a53bc6fc36bfc20c793c865d3d7

Aliases

arxiv: 1212.3121 · arxiv_version: 1212.3121v5 · doi: 10.48550/arxiv.1212.3121 · pith_short_12: 7GN25ISUOZWQ · pith_short_16: 7GN25ISUOZWQ5FEM · pith_short_8: 7GN25ISU

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/7GN25ISUOZWQ5FEM2KFDDCFREV \
  | 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: f99baea254766d0e948cd28a3188b12573e80a53bc6fc36bfc20c793c865d3d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee9b72977fe7693e25adff66998f38fb428b344ba5d23e16829a71cc9fae0c0c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-12-13T10:51:44Z",
    "title_canon_sha256": "f9785964387f73e7cec5190a49d7c28356280e1d513e5686ce5189798fc4c954"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3121",
    "kind": "arxiv",
    "version": 5
  }
}