Pith Number

pith:7NZ657HX

pith:2016:7NZ657HXW67OBN6B73DA6LMZLN

not attested not anchored not stored refs pending

The H\"ormander multiplier theorem, II: The bilinear local $L^2$ case

Danqing He, Loukas Grafakos, Petr Honz\'ik

arxiv:1607.02622 v1 · 2016-07-09 · 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{7NZ657HXW67OBN6B73DA6LMZLN}

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	2026-05-18T01:11:16.624477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb73eefcf7b7bee0b7c1fec60f2d995b5107e1bd802ce7c889b1fa57c100f5e4

Aliases

arxiv: 1607.02622 · arxiv_version: 1607.02622v1 · doi: 10.48550/arxiv.1607.02622 · pith_short_12: 7NZ657HXW67O · pith_short_16: 7NZ657HXW67OBN6B · pith_short_8: 7NZ657HX

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/7NZ657HXW67OBN6B73DA6LMZLN \
  | 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: fb73eefcf7b7bee0b7c1fec60f2d995b5107e1bd802ce7c889b1fa57c100f5e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cca01f246bca64cdb2663068c3c4e2df590983aa93f1205c2601056dfcacc42c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-07-09T15:07:59Z",
    "title_canon_sha256": "cdc696bf23457dd7044a89a6d57bd014ff577924fd74bf5ed1c8eba6401a231d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02622",
    "kind": "arxiv",
    "version": 1
  }
}