Pith Number

pith:IRPOLZGW

pith:2012:IRPOLZGW2IUIQU3IN4EDOHMFMB

not attested not anchored not stored refs pending

The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions

Alexander Volberg, Fedor Nazarov, Xavier Tolsa

arxiv:1212.5431 v2 · 2012-12-21 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IRPOLZGW2IUIQU3IN4EDOHMFMB}

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	2026-05-18T03:05:28.315993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

445ee5e4d6d2288853686f08371d856049408c4cccea13f271f1a3dcd6088f70

Aliases

arxiv: 1212.5431 · arxiv_version: 1212.5431v2 · doi: 10.48550/arxiv.1212.5431 · pith_short_12: IRPOLZGW2IUI · pith_short_16: IRPOLZGW2IUIQU3I · pith_short_8: IRPOLZGW

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/IRPOLZGW2IUIQU3IN4EDOHMFMB \
  | 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: 445ee5e4d6d2288853686f08371d856049408c4cccea13f271f1a3dcd6088f70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d58e5f09229ac2cca589c711ea7d1e7e6e28d093e152ff1ff0f68f64e39e6e78",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-12-21T13:43:30Z",
    "title_canon_sha256": "7c36bcb92b340efae8e046f7dbbf69babf6897f8fea71e5198c56a68c159e0cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5431",
    "kind": "arxiv",
    "version": 2
  }
}