Pith Number

pith:HASYBRZQ

pith:2016:HASYBRZQKZMHRSPIIBI3RFJ2PT

not attested not anchored not stored refs pending

On Sharpness of the Local Kato Smoothing Property of Dispersive Wave Equations

Bingyu Zhang, Emmanuel Trelat, Ning Zhong, Shu-Ming Sun

arxiv:1603.08271 v1 · 2016-03-28 · 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{HASYBRZQKZMHRSPIIBI3RFJ2PT}

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	2026-05-18T01:18:12.676298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

382580c730565878c9e84051b8953a7ce04f02213fd83e33c04d377713d526ba

Aliases

arxiv: 1603.08271 · arxiv_version: 1603.08271v1 · doi: 10.48550/arxiv.1603.08271 · pith_short_12: HASYBRZQKZMH · pith_short_16: HASYBRZQKZMHRSPI · pith_short_8: HASYBRZQ

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/HASYBRZQKZMHRSPIIBI3RFJ2PT \
  | 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: 382580c730565878c9e84051b8953a7ce04f02213fd83e33c04d377713d526ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccfc5d1198595fc0e4af52dda8029d27bf7425bc7a4f1f456c0b2da7f25485b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-03-28T00:21:50Z",
    "title_canon_sha256": "0761a8598c6e34dbd851e89b5d75bca6c34aa9c1a47d4f6294d59c82a29002a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.08271",
    "kind": "arxiv",
    "version": 1
  }
}