Pith Number

pith:LLI6TKBJ

pith:2011:LLI6TKBJVTJ47CK55CVUCFC2HI

not attested not anchored not stored refs pending

Boundedness of bilinear multipliers whose symbols have a narrow support

Frederic Bernicot, Pierre Germain

arxiv:1102.1693 v1 · 2011-02-08 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LLI6TKBJVTJ47CK55CVUCFC2HI}

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	2026-05-18T04:29:52.715013Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ad1e9a829acd3cf895de8ab41145a3a18f38b6d7447116e8c202c067ed05307

Aliases

arxiv: 1102.1693 · arxiv_version: 1102.1693v1 · doi: 10.48550/arxiv.1102.1693 · pith_short_12: LLI6TKBJVTJ4 · pith_short_16: LLI6TKBJVTJ47CK5 · pith_short_8: LLI6TKBJ

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/LLI6TKBJVTJ47CK55CVUCFC2HI \
  | 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: 5ad1e9a829acd3cf895de8ab41145a3a18f38b6d7447116e8c202c067ed05307

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a081c9fec16d75c456eacf740c224d8ebf93c85652b911f760872f5631a67eca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-02-08T19:18:51Z",
    "title_canon_sha256": "22b0ae201b71fca8797131d4af9c914253373e1b4ef6abcb2d2935ca9c73a30f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1693",
    "kind": "arxiv",
    "version": 1
  }
}