Pith Number

pith:2YBRUB3Y

pith:2012:2YBRUB3YQUFEL5335JWGXYFAM5

not attested not anchored not stored refs pending

A sharp multiplier theorem for Grushin operators in arbitrary dimensions

Alessio Martini, Detlef M\"uller

arxiv:1210.3564 v1 · 2012-10-12 · math.AP · 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{2YBRUB3YQUFEL5335JWGXYFAM5}

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	2026-05-18T02:30:23.012177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6031a0778850a45f77bea6c6be0a0676683e1451e88502604a03fcd96e88bde

Aliases

arxiv: 1210.3564 · arxiv_version: 1210.3564v1 · doi: 10.48550/arxiv.1210.3564 · pith_short_12: 2YBRUB3YQUFE · pith_short_16: 2YBRUB3YQUFEL533 · pith_short_8: 2YBRUB3Y

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/2YBRUB3YQUFEL5335JWGXYFAM5 \
  | 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: d6031a0778850a45f77bea6c6be0a0676683e1451e88502604a03fcd96e88bde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7e6a12aabc8cfce58f73cc2a19d201c5fa4ad9f840321408bd1e07ea053cc54",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-12T16:20:39Z",
    "title_canon_sha256": "4ccd3296309bfc5d22787aaa79aeeed329ad73286176b71564178d3b07ad4372"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.3564",
    "kind": "arxiv",
    "version": 1
  }
}