Pith Number

pith:3XOT6YES

pith:2015:3XOT6YESCBWAMDCS2NCSJ5VZNH

not attested not anchored not stored refs pending

$L^p$ estimates for fractional schrodinger operators with kato class potentials

Ming Wang, Quan Zheng, Shanlin Huang, Zhiwen Duan

arxiv:1511.08041 v2 · 2015-11-25 · math.AP

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3XOT6YESCBWAMDCS2NCSJ5VZNH}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:13:48.538854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dddd3f6092106c060c52d34524f6b969df161891955b38c66057a0024f8afb27

Aliases

arxiv: 1511.08041 · arxiv_version: 1511.08041v2 · doi: 10.48550/arxiv.1511.08041 · pith_short_12: 3XOT6YESCBWA · pith_short_16: 3XOT6YESCBWAMDCS · pith_short_8: 3XOT6YES

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/3XOT6YESCBWAMDCS2NCSJ5VZNH \
  | 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: dddd3f6092106c060c52d34524f6b969df161891955b38c66057a0024f8afb27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4c72528bf9ace654a06938e1f1c29faf4f3e3a2d7bbe97708c3fd8b2434c87e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-25T12:53:34Z",
    "title_canon_sha256": "0d91c98cdcb432d86a4a3725569025c0a7d0186a371b76a9e81a5ab7875cdb59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08041",
    "kind": "arxiv",
    "version": 2
  }
}