Pith Number

pith:4KLEO6ZT

pith:2011:4KLEO6ZTTPJRCX2ML6ZWWJVUHV

not attested not anchored not stored refs pending

Approximation of Fourier Integral Operators by Gabor multipliers

Elena Cordero, Fabio Nicola, Karlheinz Gr\"ochenig

arxiv:1107.2050 v1 · 2011-07-11 · math.FA · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4KLEO6ZTTPJRCX2ML6ZWWJVUHV}

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	2026-05-18T02:47:31.817073Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e296477b339bd3115f4c5fb36b26b43d5fcdef7cc01c029a1ca4a5420055656e

Aliases

arxiv: 1107.2050 · arxiv_version: 1107.2050v1 · doi: 10.48550/arxiv.1107.2050 · pith_short_12: 4KLEO6ZTTPJR · pith_short_16: 4KLEO6ZTTPJRCX2M · pith_short_8: 4KLEO6ZT

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/4KLEO6ZTTPJRCX2ML6ZWWJVUHV \
  | 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: e296477b339bd3115f4c5fb36b26b43d5fcdef7cc01c029a1ca4a5420055656e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ed6fd30d124240c4c62507e2f9b8c52190a519c99e6b9284ba81c69e877b1ae",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-07-11T15:02:55Z",
    "title_canon_sha256": "b634b465c60c649e9fc588a4a041fc4f05dc0169576a3bcb79218618549983da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2050",
    "kind": "arxiv",
    "version": 1
  }
}