Pith Number

pith:NAZMM2MJ

pith:2013:NAZMM2MJRBVD5NMRVCKZNJNPLO

not attested not anchored not stored refs pending

Sharp results for the Weyl product on modulation spaces

Elena Cordero, Joachim Toft, Patrik Wahlberg

arxiv:1311.1405 v3 · 2013-11-06 · 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{NAZMM2MJRBVD5NMRVCKZNJNPLO}

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	2026-05-18T01:16:19.228236Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6832c66989886a3eb591a89596a5af5b91933f0d62c59bb57b0ed1bda075e96b

Aliases

arxiv: 1311.1405 · arxiv_version: 1311.1405v3 · doi: 10.48550/arxiv.1311.1405 · pith_short_12: NAZMM2MJRBVD · pith_short_16: NAZMM2MJRBVD5NMR · pith_short_8: NAZMM2MJ

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/NAZMM2MJRBVD5NMRVCKZNJNPLO \
  | 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: 6832c66989886a3eb591a89596a5af5b91933f0d62c59bb57b0ed1bda075e96b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02b7e6fa76f321b7cd7a5d3f93fb95c4bcf75c976f1e3bc0315eb16be4be946d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-11-06T14:28:34Z",
    "title_canon_sha256": "a62d87a2670f1466080b0009bbf67560b5977b7f8599aea59d82ed31ec0e0ef1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1405",
    "kind": "arxiv",
    "version": 3
  }
}