Pith Number

pith:APK665OS

pith:2011:APK665OS4GBBYCJS76ZAQT26TD

not attested not anchored not stored refs pending

The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$

A. A. Balinsky, T. Umeda, W. D. Evans

arxiv:1101.3129 v1 · 2011-01-17 · math.SP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{APK665OS4GBBYCJS76ZAQT26TD}

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	2026-05-18T04:31:30.448399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03d5ef75d2e1821c0932ffb2084f5e98cb3bfe142dc05ab3deddaa56b54be7fa

Aliases

arxiv: 1101.3129 · arxiv_version: 1101.3129v1 · doi: 10.48550/arxiv.1101.3129 · pith_short_12: APK665OS4GBB · pith_short_16: APK665OS4GBBYCJS · pith_short_8: APK665OS

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/APK665OS4GBBYCJS76ZAQT26TD \
  | 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: 03d5ef75d2e1821c0932ffb2084f5e98cb3bfe142dc05ab3deddaa56b54be7fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bad9a850ce6c51171576ba1f52fe7644b4b2ac912c21e6a7e36f1c6068fac66",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-01-17T06:38:46Z",
    "title_canon_sha256": "9d7df40fe7819d1ed8da18dabcad531cc38c2c64ff488c0b3ca490a32052bea6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3129",
    "kind": "arxiv",
    "version": 1
  }
}