Pith Number

pith:MDWCVA6J

pith:2018:MDWCVA6JLXZTPW4LU6QEPEHZ2O

not attested not anchored not stored refs pending

Existence and non-existence of minimizers for Poincar\'e-Sobolev inequalities

Crist\'obal Vallejos, Hanne Van Den Bosch, Rafael D. Benguria

arxiv:1810.05698 v1 · 2018-10-12 · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MDWCVA6JLXZTPW4LU6QEPEHZ2O}

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	2026-05-18T00:03:27.203222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60ec2a83c95df337db8ba7a04790f9d39885a3970ae189048cff41b78c3a1e99

Aliases

arxiv: 1810.05698 · arxiv_version: 1810.05698v1 · doi: 10.48550/arxiv.1810.05698 · pith_short_12: MDWCVA6JLXZT · pith_short_16: MDWCVA6JLXZTPW4L · pith_short_8: MDWCVA6J

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/MDWCVA6JLXZTPW4LU6QEPEHZ2O \
  | 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: 60ec2a83c95df337db8ba7a04790f9d39885a3970ae189048cff41b78c3a1e99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "464d3682746ca1038f792c5b577c43c66aa59ccd7202f892c046047a269e14dd",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2018-10-12T19:43:02Z",
    "title_canon_sha256": "2917dbd3f3155f2a0184a7b4e75513c61b1ccbb48db81dd005f489199c5fb75d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.05698",
    "kind": "arxiv",
    "version": 1
  }
}