Pith Number

pith:ZGG2I2PO

pith:2016:ZGG2I2PO2B3ADBOUPEZKYDAF2F

not attested not anchored not stored refs pending

Second-order Sobolev inequalities on a class of Riemannian manifolds with nonnegative Ricci curvature

Alexandru Krist\'aly, Ezequiel Barbosa

arxiv:1608.04061 v2 · 2016-08-14 · 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{ZGG2I2PO2B3ADBOUPEZKYDAF2F}

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	2026-05-18T00:33:59.881597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c98da469eed0760185d47932ac0c05d147f87c63cd0550ba9545ade83488c5a0

Aliases

arxiv: 1608.04061 · arxiv_version: 1608.04061v2 · doi: 10.48550/arxiv.1608.04061 · pith_short_12: ZGG2I2PO2B3A · pith_short_16: ZGG2I2PO2B3ADBOU · pith_short_8: ZGG2I2PO

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/ZGG2I2PO2B3ADBOUPEZKYDAF2F \
  | 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: c98da469eed0760185d47932ac0c05d147f87c63cd0550ba9545ade83488c5a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee657a1d002b6620a3c4b5c1dd5a65d862944309e9d103ce88586d9f4997dfeb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-08-14T05:29:56Z",
    "title_canon_sha256": "8571014e2b98ed8b2c377a1c2790af81b609965039bb50543e6a95054f39d5e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.04061",
    "kind": "arxiv",
    "version": 2
  }
}