Pith Number

pith:AHZNF3I3

pith:2022:AHZNF3I3I5QUSIE5ZO6WJXNEF3

not attested not anchored not stored refs pending

A Mikhlin--H\"ormander multiplier theorem for the partial harmonic oscillator

Guixiang Xu, Xiaoyan Su, Ying Wang

arxiv:2208.02065 v1 · 2022-08-03 · 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{AHZNF3I3I5QUSIE5ZO6WJXNEF3}

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	2026-07-05T04:45:53.092352Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01f2d2ed1b476149209dcbbd64dda42ef98cbfb18150967cabbc58ff2eccc497

Aliases

arxiv: 2208.02065 · arxiv_version: 2208.02065v1 · doi: 10.48550/arxiv.2208.02065 · pith_short_12: AHZNF3I3I5QU · pith_short_16: AHZNF3I3I5QUSIE5 · pith_short_8: AHZNF3I3

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/AHZNF3I3I5QUSIE5ZO6WJXNEF3 \
  | 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: 01f2d2ed1b476149209dcbbd64dda42ef98cbfb18150967cabbc58ff2eccc497

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "463bf6e99f30fe099a276dbe5a61c9711d7e5f49a4682507db7c2e947cc349a9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-08-03T13:34:43Z",
    "title_canon_sha256": "8e25ee2beaef9837b7c97d65fb62f7a4d6f35b92d2205ec8c903b5f9b6051580"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2208.02065",
    "kind": "arxiv",
    "version": 1
  }
}