Pith Number

pith:P3AQVG4I

pith:2016:P3AQVG4ISRWRKKTW4ADSLVAP6S

not attested not anchored not stored refs pending

The H\"ormander Multiplier Theorem III: The complete bilinear case via interpolation

Hanh Van Nguyen, Loukas Grafakos

arxiv:1607.02617 v3 · 2016-07-09 · math.AP · 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{P3AQVG4ISRWRKKTW4ADSLVAP6S}

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	2026-05-17T23:54:41.964804Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ec10a9b88946d152a76e00725d40ff4b73ce5cdfb382c72fc7251b76f90ab6b

Aliases

arxiv: 1607.02617 · arxiv_version: 1607.02617v3 · doi: 10.48550/arxiv.1607.02617 · pith_short_12: P3AQVG4ISRWR · pith_short_16: P3AQVG4ISRWRKKTW · pith_short_8: P3AQVG4I

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/P3AQVG4ISRWRKKTW4ADSLVAP6S \
  | 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: 7ec10a9b88946d152a76e00725d40ff4b73ce5cdfb382c72fc7251b76f90ab6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f856aa30d2d6311ff4c406c8c86d9571fbba66c3f57c789eea442c99b245dec5",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-07-09T14:41:31Z",
    "title_canon_sha256": "522e60366033ffddac02149f7cc18ec4b0dca772e730fcd3fcb3659dcf7cd1c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02617",
    "kind": "arxiv",
    "version": 3
  }
}