Pith Number

pith:AS45ZS2J

pith:2011:AS45ZS2JXD4M6GNQHUBVFTPHV6

not attested not anchored not stored refs pending

$W^{m,p}$-Solution ($p\geq2$) of Linear Degenerate Backward Stochastic Partial Differential Equations in the Whole Space

Kai Du, Qi Zhang, Shanjian Tang

arxiv:1105.1428 v1 · 2011-05-07 · math.PR · 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{AS45ZS2JXD4M6GNQHUBVFTPHV6}

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	2026-05-18T04:22:39.456050Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04b9dccb49b8f8cf19b03d0352cde7af9d68405e15e14fe281983befdc521962

Aliases

arxiv: 1105.1428 · arxiv_version: 1105.1428v1 · doi: 10.48550/arxiv.1105.1428 · pith_short_12: AS45ZS2JXD4M · pith_short_16: AS45ZS2JXD4M6GNQ · pith_short_8: AS45ZS2J

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/AS45ZS2JXD4M6GNQHUBVFTPHV6 \
  | 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: 04b9dccb49b8f8cf19b03d0352cde7af9d68405e15e14fe281983befdc521962

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd1d14022c672d834d90a6f8ec0859986eb28e4425234c4175e5863d369f91db",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-05-07T09:00:37Z",
    "title_canon_sha256": "8a7d67c8a65691ee3b2a515d0191623b96e317506908f4e4305b76b66463fa43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1428",
    "kind": "arxiv",
    "version": 1
  }
}