Pith Number

pith:4JPAZA4B

pith:2019:4JPAZA4BK4XIMGLFZDXOKFTUC5

not attested not anchored not stored refs pending

Maximum principles for Laplacian and fractional Laplacian with critical integrability

Congming Li, Yingshu L\"u

arxiv:1905.01782 v2 · 2019-05-06 · math.FA · 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{4JPAZA4BK4XIMGLFZDXOKFTUC5}

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	2026-07-05T05:00:34.450728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e25e0c8381572e861965c8eee516741766f62c34e22b9de22ce72bb9e573a051

Aliases

arxiv: 1905.01782 · arxiv_version: 1905.01782v2 · doi: 10.48550/arxiv.1905.01782 · pith_short_12: 4JPAZA4BK4XI · pith_short_16: 4JPAZA4BK4XIMGLF · pith_short_8: 4JPAZA4B

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/4JPAZA4BK4XIMGLFZDXOKFTUC5 \
  | 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: e25e0c8381572e861965c8eee516741766f62c34e22b9de22ce72bb9e573a051

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b586fab6255392177f145eeb2511a838246db03c05e756da5853c84aa9f96d6",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-05-06T01:32:50Z",
    "title_canon_sha256": "5714a737a397c596191682db2437237516a0cfeb52982198f0be78f9a288b35b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.01782",
    "kind": "arxiv",
    "version": 2
  }
}