Pith Number

pith:3U3UQQKW

pith:2011:3U3UQQKW2VAH4JZIIYUYDG6UCO

not attested not anchored not stored refs pending

On the boundedness of certain bilinear Fourier integral operators

David J. Rule, Salvador Rodriguez-Lopez, Wolfgang Staubach

arxiv:1111.4653 v1 · 2011-11-20 · 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{3U3UQQKW2VAH4JZIIYUYDG6UCO}

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	2026-05-18T04:08:02.908539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd37484156d5407e27284629819bd413abbed6fcfdc618421973acc4dd6c0075

Aliases

arxiv: 1111.4653 · arxiv_version: 1111.4653v1 · doi: 10.48550/arxiv.1111.4653 · pith_short_12: 3U3UQQKW2VAH · pith_short_16: 3U3UQQKW2VAH4JZI · pith_short_8: 3U3UQQKW

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/3U3UQQKW2VAH4JZIIYUYDG6UCO \
  | 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: dd37484156d5407e27284629819bd413abbed6fcfdc618421973acc4dd6c0075

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "241747c8c0bf0e69997a79e1109abb0a119dbfa98d939861c6551e3bbdf3db5d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-20T17:39:56Z",
    "title_canon_sha256": "45ba6d4b6ee00dea522ad4d1e49f54fe9ec4a5a924a2324d0fd02b5eb37a6bf3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4653",
    "kind": "arxiv",
    "version": 1
  }
}