Pith Number

pith:WMUJNP6U

pith:2016:WMUJNP6UJ2E372PO4PURLRL44Y

not attested not anchored not stored refs pending

A non-variational system involving the critical Sobolev exponent. The radial case

Christophe Troestler, Francesca Gladiali, Massimo Grossi

arxiv:1603.05641 v1 · 2016-03-17 · 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{WMUJNP6UJ2E372PO4PURLRL44Y}

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	2026-05-18T01:18:55.947895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b32896bfd44e89bfe9eee3e915c57ce60d2beb2f31288b5b6c026ab8107c2016

Aliases

arxiv: 1603.05641 · arxiv_version: 1603.05641v1 · doi: 10.48550/arxiv.1603.05641 · pith_short_12: WMUJNP6UJ2E3 · pith_short_16: WMUJNP6UJ2E372PO · pith_short_8: WMUJNP6U

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/WMUJNP6UJ2E372PO4PURLRL44Y \
  | 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: b32896bfd44e89bfe9eee3e915c57ce60d2beb2f31288b5b6c026ab8107c2016

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0808ac15dbf9c5ebcf1c8d0db1bb4dcf2e433a04a50dafd41e2a4c66d61d9e17",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-03-17T19:47:49Z",
    "title_canon_sha256": "736d4d5e56a847107e0430826910317c956a90cf0e61cb9c5c853bcf4b91acd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.05641",
    "kind": "arxiv",
    "version": 1
  }
}