Pith Number

pith:AHFUTHFW

pith:2017:AHFUTHFWAG5DP3N76AJSNWQUYY

not attested not anchored not stored refs pending

A sharp version of the H\"ormander multiplier theorem

Lenka Slav\'ikov\'a, Loukas Grafakos

arxiv:1706.06507 v1 · 2017-06-20 · 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{AHFUTHFWAG5DP3N76AJSNWQUYY}

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	2026-05-18T00:42:03.075657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01cb499cb601ba37edbff01326da14c62db4ac0be830ca28f8dcffab6a9e1fe1

Aliases

arxiv: 1706.06507 · arxiv_version: 1706.06507v1 · doi: 10.48550/arxiv.1706.06507 · pith_short_12: AHFUTHFWAG5D · pith_short_16: AHFUTHFWAG5DP3N7 · pith_short_8: AHFUTHFW

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/AHFUTHFWAG5DP3N76AJSNWQUYY \
  | 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: 01cb499cb601ba37edbff01326da14c62db4ac0be830ca28f8dcffab6a9e1fe1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7afa282811b509960d88e1bce77c3085b8e41ca17da930d80ef7a4387da4dfc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-06-20T15:12:11Z",
    "title_canon_sha256": "3e60e7874b9055ed86ff6cb5a20b7da1d29060bbc58e49dc7c3a63621b6002b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.06507",
    "kind": "arxiv",
    "version": 1
  }
}