Pith Number

pith:4CMCMKBQ

pith:2017:4CMCMKBQPXGKBXKN76OEFA7SQZ

not attested not anchored not stored refs pending

Gradient and Stability Estimates of Heat Kernels for Fractional Powers of Elliptic Operator

Yaozhong Hu, Yong Chen, Zhi Wang

arxiv:1705.11182 v1 · 2017-05-31 · 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{4CMCMKBQPXGKBXKN76OEFA7SQZ}

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	2026-05-18T00:43:19.017748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0982628307dcca0dd4dff9c4283f2867fca420a93bc7b0c9fa5d2098d9bff00

Aliases

arxiv: 1705.11182 · arxiv_version: 1705.11182v1 · doi: 10.48550/arxiv.1705.11182 · pith_short_12: 4CMCMKBQPXGK · pith_short_16: 4CMCMKBQPXGKBXKN · pith_short_8: 4CMCMKBQ

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/4CMCMKBQPXGKBXKN76OEFA7SQZ \
  | 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: e0982628307dcca0dd4dff9c4283f2867fca420a93bc7b0c9fa5d2098d9bff00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18e6bbc39bfea5a252f5e43275bcb693a27c5090450f4847d252442fcf923111",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-05-31T17:04:47Z",
    "title_canon_sha256": "550a459610e8ca435ca449ba5580c936ec9ed80317d5ab8e504de1287f272c4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.11182",
    "kind": "arxiv",
    "version": 1
  }
}