Pith Number

pith:UYHJYGO7

pith:2011:UYHJYGO75WPD64QCHSJ2IVITUM

not attested not anchored not stored refs pending

Martingale transforms and their projection operators on manifolds

Fabrice Baudoin, Rodrigo Ba\~nuelos

arxiv:1109.5751 v1 · 2011-09-27 · 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{UYHJYGO75WPD64QCHSJ2IVITUM}

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	2026-05-18T04:12:11.280452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a60e9c19dfed9e3f72023c93a45513a31a5f8a439a887f15de3a9b6ad63099f0

Aliases

arxiv: 1109.5751 · arxiv_version: 1109.5751v1 · doi: 10.48550/arxiv.1109.5751 · pith_short_12: UYHJYGO75WPD · pith_short_16: UYHJYGO75WPD64QC · pith_short_8: UYHJYGO7

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/UYHJYGO75WPD64QCHSJ2IVITUM \
  | 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: a60e9c19dfed9e3f72023c93a45513a31a5f8a439a887f15de3a9b6ad63099f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1415820b6a6816d4c59f6627bb33acdd0e43b84c99f896093f88eb1c681cf67",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-09-27T00:20:21Z",
    "title_canon_sha256": "bef185c6bda31c301d853983303d26c7e6c10f939ae226f668bca4b8db7d9412"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5751",
    "kind": "arxiv",
    "version": 1
  }
}