Pith Number

pith:ML3YEQVO

pith:2012:ML3YEQVOOFSJYPMWZB4NUNZG3Z

not attested not anchored not stored refs pending

$L^p$ spectral multipliers on the free group $N_{3,2}$

Alessio Martini, Detlef M\"uller

arxiv:1210.8090 v1 · 2012-10-30 · 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{ML3YEQVOOFSJYPMWZB4NUNZG3Z}

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	2026-05-18T03:08:59.658286Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62f78242ae71649c3d96c878da3726de54cbf8b46ed58caeea498dbe61cb4241

Aliases

arxiv: 1210.8090 · arxiv_version: 1210.8090v1 · doi: 10.48550/arxiv.1210.8090 · pith_short_12: ML3YEQVOOFSJ · pith_short_16: ML3YEQVOOFSJYPMW · pith_short_8: ML3YEQVO

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/ML3YEQVOOFSJYPMWZB4NUNZG3Z \
  | 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: 62f78242ae71649c3d96c878da3726de54cbf8b46ed58caeea498dbe61cb4241

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90d7e62dd69e46d0b679e1537e429659a2b1fb93f1a7aa905706eaaa7a77b0b4",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-30T17:26:02Z",
    "title_canon_sha256": "5169f325ea90b66ab2d33653f0acf24cfdedffee4aacd4c0e94dd51b9893cc96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.8090",
    "kind": "arxiv",
    "version": 1
  }
}