Pith Number

pith:PL6VK36H

pith:2018:PL6VK36HY4BT2U33Q4IWYPDYPN

not attested not anchored not stored refs pending

Gundy-Varopoulos martingale transforms and their projection operators on manifolds and vector bundles

Fabrice Baudoin, Li Chen, Rodrigo Ba\~nuelos

arxiv:1802.02410 v1 · 2018-02-07 · math.FA · 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{PL6VK36HY4BT2U33Q4IWYPDYPN}

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	2026-05-18T00:24:08.392577Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7afd556fc7c7033d537b87116c3c787b4b74ee237e30db2547c82a664e2dc21b

Aliases

arxiv: 1802.02410 · arxiv_version: 1802.02410v1 · doi: 10.48550/arxiv.1802.02410 · pith_short_12: PL6VK36HY4BT · pith_short_16: PL6VK36HY4BT2U33 · pith_short_8: PL6VK36H

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/PL6VK36HY4BT2U33Q4IWYPDYPN \
  | 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: 7afd556fc7c7033d537b87116c3c787b4b74ee237e30db2547c82a664e2dc21b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de81816828302b9cda8f9d759369ec11671ad81810b6c4660fa1e43a3475dc89",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-02-07T13:21:26Z",
    "title_canon_sha256": "17294376b157c761ead1f77cfc59c5380494d4d55fc3afbff1e0c78b38f3665d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.02410",
    "kind": "arxiv",
    "version": 1
  }
}