Pith Number

pith:H4X27SU7

pith:2012:H4X27SU75ZJONNOOT46SOF5N5W

not attested not anchored not stored refs pending

Spectral multiplier theorems of H\"ormander type on Hardy and Lebesgue spaces

Matthias Uhl, Peer Christian Kunstmann

arxiv:1209.0358 v1 · 2012-09-03 · 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{H4X27SU75ZJONNOOT46SOF5N5W}

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	2026-05-18T03:46:29.265791Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f2fafca9fee52e6b5ce9f3d2717adedb658443f41a076228c7256d91e6e1309

Aliases

arxiv: 1209.0358 · arxiv_version: 1209.0358v1 · doi: 10.48550/arxiv.1209.0358 · pith_short_12: H4X27SU75ZJO · pith_short_16: H4X27SU75ZJONNOO · pith_short_8: H4X27SU7

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/H4X27SU75ZJONNOOT46SOF5N5W \
  | 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: 3f2fafca9fee52e6b5ce9f3d2717adedb658443f41a076228c7256d91e6e1309

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7a560257fc8ff04114e02e1f6503c0776484160e820732b99344585451a45b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-09-03T13:58:05Z",
    "title_canon_sha256": "5e7a03829c11c411b175a9d9fbd001351fe0bc1f0d34f7f7c99c1882f52caefc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0358",
    "kind": "arxiv",
    "version": 1
  }
}