Pith Number

pith:LYQNHZ63

pith:2013:LYQNHZ63U5R3VN64ALIAJG4BBD

not attested not anchored not stored refs pending

On biharmonic submanifolds in non-positively curved manifolds

Yong Luo

arxiv:1306.6069 v4 · 2013-06-25 · 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{LYQNHZ63U5R3VN64ALIAJG4BBD}

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	2026-05-18T02:50:51.839557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e20d3e7dba763bab7dc02d0049b8108e342c41364335de5c68a7d7730f0fcce

Aliases

arxiv: 1306.6069 · arxiv_version: 1306.6069v4 · doi: 10.48550/arxiv.1306.6069 · pith_short_12: LYQNHZ63U5R3 · pith_short_16: LYQNHZ63U5R3VN64 · pith_short_8: LYQNHZ63

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/LYQNHZ63U5R3VN64ALIAJG4BBD \
  | 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: 5e20d3e7dba763bab7dc02d0049b8108e342c41364335de5c68a7d7730f0fcce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f884f045ef36b240105a5d9bed73b94e8d934b669a7020fe49d6d1657bdc175",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-06-25T19:42:04Z",
    "title_canon_sha256": "597cbf84f5f84f38f9b90d342f69be60b04bac6593de8b6be972d02a7b34eeba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.6069",
    "kind": "arxiv",
    "version": 4
  }
}