Pith Number

pith:4XJNMALM

pith:2011:4XJNMALM2JNHUL4DKA2NPG26YY

not attested not anchored not stored refs pending

Riesz transforms and multipliers for the Grushin operator

K.Jotsaroop, P.K.Sanjay, S. Thangavelu

arxiv:1110.3227 v1 · 2011-10-14 · 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{4XJNMALM2JNHUL4DKA2NPG26YY}

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	2026-05-18T04:10:57.717074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5d2d6016cd25a7a2f835034d79b5ec615e276350f7f944a709b1528eee6dba4

Aliases

arxiv: 1110.3227 · arxiv_version: 1110.3227v1 · doi: 10.48550/arxiv.1110.3227 · pith_short_12: 4XJNMALM2JNH · pith_short_16: 4XJNMALM2JNHUL4D · pith_short_8: 4XJNMALM

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/4XJNMALM2JNHUL4DKA2NPG26YY \
  | 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: e5d2d6016cd25a7a2f835034d79b5ec615e276350f7f944a709b1528eee6dba4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e6890dce4e932b566cc07c8c8f051dd688b579eda88b8893bd966a5030c3a07",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-10-14T14:50:14Z",
    "title_canon_sha256": "c109d548674a866f0ca85027520f03dfd3ce327ebfce8d4252e47de92103bbb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3227",
    "kind": "arxiv",
    "version": 1
  }
}