Pith Number

pith:XRDRBY5B

pith:2018:XRDRBY5B3Z2N6J5D3HKFW5IVVQ

not attested not anchored not stored refs pending

A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds

Volker Branding, Yong Luo

arxiv:1806.11441 v2 · 2018-06-28 · 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{XRDRBY5B3Z2N6J5D3HKFW5IVVQ}

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	2026-05-18T00:10:48.724779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc4710e3a1de74df27a3d9d45b7515ac38fed2b85553c88d8797e74edfb8c396

Aliases

arxiv: 1806.11441 · arxiv_version: 1806.11441v2 · doi: 10.48550/arxiv.1806.11441 · pith_short_12: XRDRBY5B3Z2N · pith_short_16: XRDRBY5B3Z2N6J5D · pith_short_8: XRDRBY5B

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/XRDRBY5B3Z2N6J5D3HKFW5IVVQ \
  | 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: bc4710e3a1de74df27a3d9d45b7515ac38fed2b85553c88d8797e74edfb8c396

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42f5b2818def2ebef842635e5800aded0e341eee1c835dd9bfe20d9d55587985",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-06-28T08:09:24Z",
    "title_canon_sha256": "a42e85b2c6dcfe67eec3b51b64e4524e8a458ade9545584ccf4eda12a76c41eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.11441",
    "kind": "arxiv",
    "version": 2
  }
}