Pith Number

pith:7FCEXTK7

pith:2012:7FCEXTK7O5OD6ZIC3GKFANBMKT

not attested not anchored not stored refs pending

Martingale transform and L\'evy Processes on Lie Groups

David Applebaum, Rodrigo Ba\~nuelos

arxiv:1206.1560 v1 · 2012-06-07 · math.PR · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7FCEXTK7O5OD6ZIC3GKFANBMKT}

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	2026-05-18T03:54:04.804085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9444bcd5f775c3f6502d99450342c54c5777c7771c44dc81d0970e2d6ca51e9

Aliases

arxiv: 1206.1560 · arxiv_version: 1206.1560v1 · doi: 10.48550/arxiv.1206.1560 · pith_short_12: 7FCEXTK7O5OD · pith_short_16: 7FCEXTK7O5OD6ZIC · pith_short_8: 7FCEXTK7

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/7FCEXTK7O5OD6ZIC3GKFANBMKT \
  | 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: f9444bcd5f775c3f6502d99450342c54c5777c7771c44dc81d0970e2d6ca51e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eaba942cbf2a2bf947d0392e53aa827167fdb485728d485442ae9c15ebdd3606",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-07T17:40:14Z",
    "title_canon_sha256": "70a606b28a9f690e90971936ff57c2ef00e31b13dbe3a96c0f914dcb3823ba7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1560",
    "kind": "arxiv",
    "version": 1
  }
}