Pith Number

pith:2DNI5Y3A

pith:2010:2DNI5Y3ABG5K2HPKHYCQX5HJZU

not attested not anchored not stored refs pending

The connectivity at infinity of a manifold and $L^{q,p}$-Sobolev inequalities

Alberto G. Setti, Marc Troyanov, Stefano Pigola

arxiv:1007.1761 v3 · 2010-07-11 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2DNI5Y3ABG5K2HPKHYCQX5HJZU}

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	2026-05-18T03:25:35.370908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0da8ee36009baad1dea3e050bf4e9cd0adbd1948252c8348aaa96271d9e51a5

Aliases

arxiv: 1007.1761 · arxiv_version: 1007.1761v3 · doi: 10.48550/arxiv.1007.1761 · pith_short_12: 2DNI5Y3ABG5K · pith_short_16: 2DNI5Y3ABG5K2HPK · pith_short_8: 2DNI5Y3A

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/2DNI5Y3ABG5K2HPKHYCQX5HJZU \
  | 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: d0da8ee36009baad1dea3e050bf4e9cd0adbd1948252c8348aaa96271d9e51a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "590db54b6305bffe795457c11e55aa02dd4010fc46294c152c330c07d9b7762d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-07-11T07:45:28Z",
    "title_canon_sha256": "1d21219d45dc1a01b49dd79307d1d0e8681aa0e8dab12d4c0b2452c67cd84dd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1761",
    "kind": "arxiv",
    "version": 3
  }
}