Pith Number

pith:U5XKZHAF

pith:2018:U5XKZHAF3LFKR6Q5K2DI3SVCLJ

not attested not anchored not stored refs pending

Spikes of the two-component elliptic system in $\bbr^4$ with Sobolev critical exponent

Wenming Zou, Yuanze Wu

arxiv:1804.00400 v1 · 2018-04-02 · 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{U5XKZHAF3LFKR6Q5K2DI3SVCLJ}

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	2026-05-18T00:19:37.343340Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a76eac9c05dacaa8fa1d56868dcaa25a7dec78788999f6d7f28fb38b80929cd9

Aliases

arxiv: 1804.00400 · arxiv_version: 1804.00400v1 · doi: 10.48550/arxiv.1804.00400 · pith_short_12: U5XKZHAF3LFK · pith_short_16: U5XKZHAF3LFKR6Q5 · pith_short_8: U5XKZHAF

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/U5XKZHAF3LFKR6Q5K2DI3SVCLJ \
  | 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: a76eac9c05dacaa8fa1d56868dcaa25a7dec78788999f6d7f28fb38b80929cd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb5529ac9bcbc6f2447b19846699712d8415a94c12c6bf28f74fc198c063a37a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-04-02T05:33:28Z",
    "title_canon_sha256": "582aee06266202179af9fb6fe4ba06dc93fe6df98c53eac1114edebcec029b36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.00400",
    "kind": "arxiv",
    "version": 1
  }
}