Pith Number

pith:ENVLT3JT

pith:2019:ENVLT3JTHIZL5PU6TPKSXIR4KX

not attested not anchored not stored refs pending

Large number of bubble solutions for a perturbed fractional Laplacian equation

Chunhua Wang, Suting Wei

arxiv:1908.03386 v1 · 2019-08-09 · math.AP · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ENVLT3JTHIZL5PU6TPKSXIR4KX}

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	2026-07-05T04:06:12.583855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

236ab9ed333a32bebe9e9bd52ba23c55ce415ccb957f2c272f19d78fd30abe57

Aliases

arxiv: 1908.03386 · arxiv_version: 1908.03386v1 · doi: 10.48550/arxiv.1908.03386 · pith_short_12: ENVLT3JTHIZL · pith_short_16: ENVLT3JTHIZL5PU6 · pith_short_8: ENVLT3JT

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/ENVLT3JTHIZL5PU6TPKSXIR4KX \
  | 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: 236ab9ed333a32bebe9e9bd52ba23c55ce415ccb957f2c272f19d78fd30abe57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12407170d3e825e01867a21730a57b952fe052629c1e44a25edb7562a4cbb31c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-09T09:42:15Z",
    "title_canon_sha256": "b52b77c12a63d8d9eaf31f2a4fa15be35a909fc79d7fc5a8c7b21b085dd3f35a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03386",
    "kind": "arxiv",
    "version": 1
  }
}