Pith Number

pith:34DHBDNU

pith:2010:34DHBDNUENPJBWGDJSZ2B7WKY2

not attested not anchored not stored refs pending

The Range of Localization Operators and Lifting Theorems for Modulation and Bargmann-Fock Spaces

Joachim Toft, Karlheinz Gr\"ochenig

arxiv:1010.0513 v1 · 2010-10-04 · 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{34DHBDNUENPJBWGDJSZ2B7WKY2}

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	2026-05-18T02:47:31.853925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df06708db4235e90d8c34cb3a0fecac6aa28b9ddca9ca612ed9fcacabf66006a

Aliases

arxiv: 1010.0513 · arxiv_version: 1010.0513v1 · doi: 10.48550/arxiv.1010.0513 · pith_short_12: 34DHBDNUENPJ · pith_short_16: 34DHBDNUENPJBWGD · pith_short_8: 34DHBDNU

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/34DHBDNUENPJBWGDJSZ2B7WKY2 \
  | 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: df06708db4235e90d8c34cb3a0fecac6aa28b9ddca9ca612ed9fcacabf66006a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "342ed07acaad607a13737f8a33d762c7c27d305c7965345d746ed9bd19dfbeed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-10-04T09:21:14Z",
    "title_canon_sha256": "03c9e4ea2b0c3519bf9d1de52caa23a2ef3b1a4734a0780d83f71e73f1a893bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0513",
    "kind": "arxiv",
    "version": 1
  }
}