Pith Number

pith:Y4D3RNB6

pith:2010:Y4D3RNB6XOUSMR2QHZ2AKFABIT

not attested not anchored not stored refs pending

On a Fourth Order Lichnerowicz Type Equation Involving The Paneitz-Branson Operator

Ali Maalaoui

arxiv:1012.4505 v3 · 2010-12-20 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y4D3RNB6XOUSMR2QHZ2AKFABIT}

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	2026-05-18T02:23:06.775514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c707b8b43ebba92647503e7405140144f9dd6749053d2cd6646afdb77ad94802

Aliases

arxiv: 1012.4505 · arxiv_version: 1012.4505v3 · doi: 10.48550/arxiv.1012.4505 · pith_short_12: Y4D3RNB6XOUS · pith_short_16: Y4D3RNB6XOUSMR2Q · pith_short_8: Y4D3RNB6

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/Y4D3RNB6XOUSMR2QHZ2AKFABIT \
  | 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: c707b8b43ebba92647503e7405140144f9dd6749053d2cd6646afdb77ad94802

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1cf878436e3de520706faaceaac889936ba3e94dac6e4b6e94cd8e710c82c19d",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-20T23:34:52Z",
    "title_canon_sha256": "8542184167943cb332b849612cea5dc22729549f63d49122656bafba111c121f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4505",
    "kind": "arxiv",
    "version": 3
  }
}