Pith Number

pith:5WB6EQU2

pith:2012:5WB6EQU2YFZZLNQWXLMQ2MXLU5

not attested not anchored not stored refs pending

Hardy inequalities on Riemannian manifolds and applications

Lorenzo D'Ambrosio, Serena Dipierro

arxiv:1210.5723 v2 · 2012-10-21 · 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{5WB6EQU2YFZZLNQWXLMQ2MXLU5}

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	2026-05-18T03:28:05.558832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed83e2429ac17395b616bad90d32eba767036fae499f3d697ce9b4236a233fdb

Aliases

arxiv: 1210.5723 · arxiv_version: 1210.5723v2 · doi: 10.48550/arxiv.1210.5723 · pith_short_12: 5WB6EQU2YFZZ · pith_short_16: 5WB6EQU2YFZZLNQW · pith_short_8: 5WB6EQU2

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/5WB6EQU2YFZZLNQWXLMQ2MXLU5 \
  | 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: ed83e2429ac17395b616bad90d32eba767036fae499f3d697ce9b4236a233fdb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1877e16d63aba4282f5f1e6aa7f0f8da96d1553581226e6bc3361628e92ace10",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-21T12:42:30Z",
    "title_canon_sha256": "d0da6e775a11574c1d7b4d35bd577ee94e7d37d9e6a4519bb075458a5d761014"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5723",
    "kind": "arxiv",
    "version": 2
  }
}