Pith Number

pith:GZB2IW4D

pith:2015:GZB2IW4DQV3QH5HGXJCG2RWCCJ

not attested not anchored not stored refs pending

A weighted identity for stochastic partial differential operators and its applications

Xiaoyu Fu, Xu Liu

arxiv:1508.05066 v1 · 2015-08-20 · math.OC · 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{GZB2IW4DQV3QH5HGXJCG2RWCCJ}

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	2026-05-18T01:34:59.764468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3643a45b83857703f4e6ba446d46c2124f46cb1aa0900c1941165f1e9dd3ead7

Aliases

arxiv: 1508.05066 · arxiv_version: 1508.05066v1 · doi: 10.48550/arxiv.1508.05066 · pith_short_12: GZB2IW4DQV3Q · pith_short_16: GZB2IW4DQV3QH5HG · pith_short_8: GZB2IW4D

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/GZB2IW4DQV3QH5HGXJCG2RWCCJ \
  | 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: 3643a45b83857703f4e6ba446d46c2124f46cb1aa0900c1941165f1e9dd3ead7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e71d55575f76cb128a55e0d3972df8ad61b67873c580fb24253bb4270ca20e6",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-08-20T18:39:43Z",
    "title_canon_sha256": "e9c5056b2e68ea787c3f32c83eacf2bba7b6d2434a6c4e74bfd83a110ae2680d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05066",
    "kind": "arxiv",
    "version": 1
  }
}