Pith Number

pith:3OAWXK4U

pith:2011:3OAWXK4UWFGTRXKVMEKYYOO4IQ

not attested not anchored not stored refs pending

Sharp Moser-Trudinger inequalities for the Laplacian without boundary conditions

Carlo Morpurgo, Luigi Fontana

arxiv:1102.1924 v1 · 2011-02-09 · 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{3OAWXK4UWFGTRXKVMEKYYOO4IQ}

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	2026-05-18T04:29:44.007398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db816bab94b14d38dd5561158c39dc44007c653fbcf35bf72ac27db27c105958

Aliases

arxiv: 1102.1924 · arxiv_version: 1102.1924v1 · doi: 10.48550/arxiv.1102.1924 · pith_short_12: 3OAWXK4UWFGT · pith_short_16: 3OAWXK4UWFGTRXKV · pith_short_8: 3OAWXK4U

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/3OAWXK4UWFGTRXKVMEKYYOO4IQ \
  | 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: db816bab94b14d38dd5561158c39dc44007c653fbcf35bf72ac27db27c105958

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "250322c36e64ee40b549036cf449b383cf0534b5c71619f91c675abba9947952",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-02-09T18:13:16Z",
    "title_canon_sha256": "bd551cb0d2f65fab3aeedf1aaea2e1edff9ac64586e3c9107dd2cdea90eb423f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1924",
    "kind": "arxiv",
    "version": 1
  }
}