Pith Number

pith:33HKAXX7

pith:2015:33HKAXX7VGGWGYU77RWNZD6VP6

not attested not anchored not stored refs pending

On the Hardy-Littlewood-Sobolev type systems

Congming Li, Genggeng Huang, Ze Cheng

arxiv:1509.06822 v2 · 2015-09-23 · 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{33HKAXX7VGGWGYU77RWNZD6VP6}

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	2026-05-18T01:30:33.967695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

decea05effa98d63629ffc6cdc8fd57f98f6dcbb47778c4fd03e43349b68fe41

Aliases

arxiv: 1509.06822 · arxiv_version: 1509.06822v2 · doi: 10.48550/arxiv.1509.06822 · pith_short_12: 33HKAXX7VGGW · pith_short_16: 33HKAXX7VGGWGYU7 · pith_short_8: 33HKAXX7

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/33HKAXX7VGGWGYU77RWNZD6VP6 \
  | 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: decea05effa98d63629ffc6cdc8fd57f98f6dcbb47778c4fd03e43349b68fe41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "469f016a4a04570969b05960a2605e6c817a858fef5e050c0b00fdda06648661",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-23T01:54:32Z",
    "title_canon_sha256": "9d487e8dbb48c1abbe2c7ee4064e5c0624135a325d36f87c71f9e835fbb82ddf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06822",
    "kind": "arxiv",
    "version": 2
  }
}