Pith Number

pith:BK5RKF7S

pith:2010:BK5RKF7SC4NKXL2CDPKTR5G2ZO

not attested not anchored not stored refs pending

New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

Andrea Malchiodi, David Ruiz

arxiv:1007.3861 v2 · 2010-07-22 · 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{BK5RKF7SC4NKXL2CDPKTR5G2ZO}

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	2026-05-18T04:21:53.037026Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0abb1517f2171aabaf421bd538f4dacb95b8e2de0fa69e73b5f57190039101ca

Aliases

arxiv: 1007.3861 · arxiv_version: 1007.3861v2 · doi: 10.48550/arxiv.1007.3861 · pith_short_12: BK5RKF7SC4NK · pith_short_16: BK5RKF7SC4NKXL2C · pith_short_8: BK5RKF7S

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/BK5RKF7SC4NKXL2CDPKTR5G2ZO \
  | 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: 0abb1517f2171aabaf421bd538f4dacb95b8e2de0fa69e73b5f57190039101ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53299a5805c9a28d55ed6f08e83d31b1b1bca9ed6763e08cf3a87079e7b921bc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-07-22T11:45:39Z",
    "title_canon_sha256": "c870dd053631ed9a0cea84e19b6fe32fbab689bed49a9c925837b254f13d5ff7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.3861",
    "kind": "arxiv",
    "version": 2
  }
}