Pith Number

pith:GHPG5TWP

pith:2021:GHPG5TWPU2AIRULMUSB3HE6S76

not attested not anchored not stored refs pending

Positive normalized solutions to nonlinear elliptic systems in $\R^4$ with critical Sobolev exponent

Wenming Zou, Xiaolong Yang, Xiao Luo

arxiv:2107.08708 v1 · 2021-07-19 · 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{GHPG5TWPU2AIRULMUSB3HE6S76}

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	2026-07-05T02:58:51.909640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31de6ececfa68088d16ca483b393d2ff9ab280f46d9cfb52f39e3ca9e87d3ecd

Aliases

arxiv: 2107.08708 · arxiv_version: 2107.08708v1 · doi: 10.48550/arxiv.2107.08708 · pith_short_12: GHPG5TWPU2AI · pith_short_16: GHPG5TWPU2AIRULM · pith_short_8: GHPG5TWP

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/GHPG5TWPU2AIRULMUSB3HE6S76 \
  | 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: 31de6ececfa68088d16ca483b393d2ff9ab280f46d9cfb52f39e3ca9e87d3ecd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ac981073e9adcdaed5c6a505dcc871d2a1a42e0ae5d6aa30394de7c1d2ca6d1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-07-19T09:31:52Z",
    "title_canon_sha256": "57c0fcca95f8c119ca82564b287ee8ba3561bd7f48077aeb134221bdc37423bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.08708",
    "kind": "arxiv",
    "version": 1
  }
}