Pith Number

pith:B4DQJX2P

pith:2016:B4DQJX2PRDA4NSP35Y3VUAXCKW

not attested not anchored not stored refs pending

The Weyl product on quasi-Banach modulation spaces

Joachim Toft, Patrik Wahlberg, Yuanyuan Chen

arxiv:1605.00318 v3 · 2016-05-01 · 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{B4DQJX2PRDA4NSP35Y3VUAXCKW}

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	2026-05-18T00:26:13.080053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f0704df4f88c1c6c9fbee375a02e255ab56b8e0b4a1766cfce54ad701f32fed

Aliases

arxiv: 1605.00318 · arxiv_version: 1605.00318v3 · doi: 10.48550/arxiv.1605.00318 · pith_short_12: B4DQJX2PRDA4 · pith_short_16: B4DQJX2PRDA4NSP3 · pith_short_8: B4DQJX2P

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/B4DQJX2PRDA4NSP35Y3VUAXCKW \
  | 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: 0f0704df4f88c1c6c9fbee375a02e255ab56b8e0b4a1766cfce54ad701f32fed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9074c56fdca19463816c43a93511625906969e74a1f287e360f79c7875b8b131",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-05-01T23:02:04Z",
    "title_canon_sha256": "2b3b78221751299b8813b368f5240354c04f257f0645fc8dbe95600ebfa9890d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.00318",
    "kind": "arxiv",
    "version": 3
  }
}