Pith Number

pith:BEL6KWIB

pith:2012:BEL6KWIBRTDOOTO7SDJCAOLRVJ

not attested not anchored not stored refs pending

The fractional Riesz transform and an exponential potential

Alexander Volberg, Benjamin Jaye, Fedor Nazarov

arxiv:1204.2135 v2 · 2012-04-10 · math.AP · math.CA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BEL6KWIBRTDOOTO7SDJCAOLRVJ}

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	2026-05-18T03:43:42.179069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0917e559018cc6e74ddf90d2203971aa6480751f97123fbdae0f9f4b63339d23

Aliases

arxiv: 1204.2135 · arxiv_version: 1204.2135v2 · doi: 10.48550/arxiv.1204.2135 · pith_short_12: BEL6KWIBRTDO · pith_short_16: BEL6KWIBRTDOOTO7 · pith_short_8: BEL6KWIB

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/BEL6KWIBRTDOOTO7SDJCAOLRVJ \
  | 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: 0917e559018cc6e74ddf90d2203971aa6480751f97123fbdae0f9f4b63339d23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19997a987bb5fd9f5492b9920219d34a35fdcec487846ba1921c67c956fe62b2",
    "cross_cats_sorted": [
      "math.CA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-04-10T13:09:19Z",
    "title_canon_sha256": "e1027ab5851727c940979c8cd21514d0a6665b2f2616b320b15190db177bea6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2135",
    "kind": "arxiv",
    "version": 2
  }
}