Pith Number

pith:WWF6OQML

pith:2013:WWF6OQML63W4WYU5ILI2LDJF2S

not attested not anchored not stored refs pending

On the $L^p$-estimates for Beurling-Ahlfors and Riesz transforms on Riemannian manifolds

Xiang-Dong Li

arxiv:1304.1168 v2 · 2013-04-03 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WWF6OQML63W4WYU5ILI2LDJF2S}

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	2026-05-18T03:28:18.989483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b58be7418bf6edcb629d42d1a58d25d481ff73b7b09dc37bdda621646a1ad05e

Aliases

arxiv: 1304.1168 · arxiv_version: 1304.1168v2 · doi: 10.48550/arxiv.1304.1168 · pith_short_12: WWF6OQML63W4 · pith_short_16: WWF6OQML63W4WYU5 · pith_short_8: WWF6OQML

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/WWF6OQML63W4WYU5ILI2LDJF2S \
  | 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: b58be7418bf6edcb629d42d1a58d25d481ff73b7b09dc37bdda621646a1ad05e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46bbdb51fed42dfcd68f00180ca20793d4a8a40afa2bfc15ce30f22763e54250",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-04-03T20:03:14Z",
    "title_canon_sha256": "e1fbbfb48b9645a42d5488bc6e1822fc05fbbd1f09e75d28a5748525f854d96e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.1168",
    "kind": "arxiv",
    "version": 2
  }
}