Pith Number

pith:DE2MNZTB

pith:2015:DE2MNZTBQFPFADAVP3XGSKBVHE

not attested not anchored not stored refs pending

Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators

Ting Yang, Yan-Xia Ren, Zhen-Qing Chen

arxiv:1501.02023 v2 · 2015-01-09 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DE2MNZTBQFPFADAVP3XGSKBVHE}

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	2026-05-18T01:18:23.495122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1934c6e661815e500c157eee692835390167cdb2f7243b6966bc46d427c0e932

Aliases

arxiv: 1501.02023 · arxiv_version: 1501.02023v2 · doi: 10.48550/arxiv.1501.02023 · pith_short_12: DE2MNZTBQFPF · pith_short_16: DE2MNZTBQFPFADAV · pith_short_8: DE2MNZTB

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/DE2MNZTBQFPFADAVP3XGSKBVHE \
  | 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: 1934c6e661815e500c157eee692835390167cdb2f7243b6966bc46d427c0e932

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a7104f488fb189f743bb49a5a02b06a524ec042c84d462aa37df24be01d2ead",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-01-09T03:05:32Z",
    "title_canon_sha256": "65fcfeed95f2154072c47c6a6a19954a287ccf1b0ffe66efe182d778192b2280"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.02023",
    "kind": "arxiv",
    "version": 2
  }
}