Pith Number

pith:UXRSLRAZ

pith:2010:UXRSLRAZL5FYFKPUD5S2A2GJ7I

not attested not anchored not stored refs pending

A note on Hardy's inequalities with boundary singularities

Mouhamed Moustapha Fall

arxiv:1009.3158 v1 · 2010-09-16 · 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{UXRSLRAZL5FYFKPUD5S2A2GJ7I}

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	2026-05-18T04:40:46.888555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5e325c4195f4b82a9f41f65a068c9fa39d4083b91450e4b1f980f677100a7e0

Aliases

arxiv: 1009.3158 · arxiv_version: 1009.3158v1 · doi: 10.48550/arxiv.1009.3158 · pith_short_12: UXRSLRAZL5FY · pith_short_16: UXRSLRAZL5FYFKPU · pith_short_8: UXRSLRAZ

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/UXRSLRAZL5FYFKPUD5S2A2GJ7I \
  | 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: a5e325c4195f4b82a9f41f65a068c9fa39d4083b91450e4b1f980f677100a7e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "875e65c3e69144472e5579c2cf2e2953cbba8fbd8933348f6b1d598996978858",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-09-16T12:32:05Z",
    "title_canon_sha256": "fa7da0d41ecec8fe08269018a9e960323c93c74aadf1b62e08fe49a806562c4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3158",
    "kind": "arxiv",
    "version": 1
  }
}