Pith Number

pith:JF5MQ6PH

pith:2013:JF5MQ6PHNUS226A4C3MEPZSFLC

not attested not anchored not stored refs pending

Two weight norm inequalities for the bilinear fractional integrals

Kangwei Li, Wenchang Sun

arxiv:1312.7707 v2 · 2013-12-30 · 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{JF5MQ6PHNUS226A4C3MEPZSFLC}

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	2026-05-18T00:39:14.081998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

497ac879e76d25ad781c16d847e64558bacf51f577252eff9c665e83ddc34ec2

Aliases

arxiv: 1312.7707 · arxiv_version: 1312.7707v2 · doi: 10.48550/arxiv.1312.7707 · pith_short_12: JF5MQ6PHNUS2 · pith_short_16: JF5MQ6PHNUS226A4 · pith_short_8: JF5MQ6PH

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/JF5MQ6PHNUS226A4C3MEPZSFLC \
  | 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: 497ac879e76d25ad781c16d847e64558bacf51f577252eff9c665e83ddc34ec2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "724a386e80e203e949a939793d01742ff1d51ff8456a9ded1e85647a818ff92b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-12-30T13:21:40Z",
    "title_canon_sha256": "363bc00c142342f09d3fd0b524ea1be10a35131036a159ffe235b141941804c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7707",
    "kind": "arxiv",
    "version": 2
  }
}