Pith Number

pith:2NB6GRMZ

pith:2010:2NB6GRMZ2LE4HBIKF3M56LJUET

not attested not anchored not stored refs pending

On the Hardy-Poincar\'e inequality with boundary singularities

Mouhamed Moustapha Fall

arxiv:1008.4785 v3 · 2010-08-27 · 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{2NB6GRMZ2LE4HBIKF3M56LJUET}

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	2026-05-18T04:22:40.316811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d343e34599d2c9c3850a2ed9df2d3424f38e32be0052b2f7ba6fcd733cdbdae8

Aliases

arxiv: 1008.4785 · arxiv_version: 1008.4785v3 · doi: 10.48550/arxiv.1008.4785 · pith_short_12: 2NB6GRMZ2LE4 · pith_short_16: 2NB6GRMZ2LE4HBIK · pith_short_8: 2NB6GRMZ

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/2NB6GRMZ2LE4HBIKF3M56LJUET \
  | 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: d343e34599d2c9c3850a2ed9df2d3424f38e32be0052b2f7ba6fcd733cdbdae8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13906fa1986c30f14a36ecf9ffa1c3d51929e037ea1ae12a9db5ea564dec8e2a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-08-27T18:57:42Z",
    "title_canon_sha256": "83d1f528b59e8e34d8158cd61b3a84c0548cb9bf42f9c6ba817593e9cc062474"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4785",
    "kind": "arxiv",
    "version": 3
  }
}