Pith Number

pith:E6BUDD7A

pith:2016:E6BUDD7AKR4N2B42PAS3W3MDJE

not attested not anchored not stored refs pending

The Brezis-Nirenberg problem for the curl-curl operator

Jaros{\l}aw Mederski

arxiv:1609.03989 v4 · 2016-09-13 · 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{E6BUDD7AKR4N2B42PAS3W3MDJE}

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	2026-05-18T00:24:22.813555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2783418fe05478dd079a7825bb6d83491cab7dd7103cbce78b33d88a20521ed8

Aliases

arxiv: 1609.03989 · arxiv_version: 1609.03989v4 · doi: 10.48550/arxiv.1609.03989 · pith_short_12: E6BUDD7AKR4N · pith_short_16: E6BUDD7AKR4N2B42 · pith_short_8: E6BUDD7A

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/E6BUDD7AKR4N2B42PAS3W3MDJE \
  | 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: 2783418fe05478dd079a7825bb6d83491cab7dd7103cbce78b33d88a20521ed8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8aa76565a61dbcb87aba00a431523002da8b510d0c290c8d72ebbb0df58f7c03",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-13T19:30:48Z",
    "title_canon_sha256": "349f9ba9f2954dff61d24751bc1cd692f685f79c676c86c24a17b5a0f1cebf36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03989",
    "kind": "arxiv",
    "version": 4
  }
}