Pith Number

pith:63NJ5NNM

pith:2015:63NJ5NNMI74W6WOI5XSIPUT6A6

not attested not anchored not stored refs pending

The solution gap of the Brezis-Nirenberg problem on the hyperbolic space

Soledad Benguria

arxiv:1507.05318 v2 · 2015-07-19 · 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{63NJ5NNMI74W6WOI5XSIPUT6A6}

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	2026-05-18T01:22:37.752898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6da9eb5ac47f96f59c8ede487d27e07a5bcf9fef1a9b1bd353b69112c3ffc49

Aliases

arxiv: 1507.05318 · arxiv_version: 1507.05318v2 · doi: 10.48550/arxiv.1507.05318 · pith_short_12: 63NJ5NNMI74W · pith_short_16: 63NJ5NNMI74W6WOI · pith_short_8: 63NJ5NNM

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/63NJ5NNMI74W6WOI5XSIPUT6A6 \
  | 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: f6da9eb5ac47f96f59c8ede487d27e07a5bcf9fef1a9b1bd353b69112c3ffc49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74e89ab7bd80d0ee833faf72d5d3eae6401af7a090d0817763055854bd700787",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-07-19T18:45:17Z",
    "title_canon_sha256": "b9f831786e37dc2b932435da914a870f68ea12e64ab9274c58f46e0ea70ea28d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05318",
    "kind": "arxiv",
    "version": 2
  }
}