Pith Number

pith:GLLS4KUP

pith:2015:GLLS4KUPN6A7XIRGN227S6TAQO

not attested not anchored not stored refs pending

The Bochner-Type Formula and The First Eigenvalue of the sub-Laplacian on a Contact Riemannian Manifold

Feifan Wu, Wei Wang

arxiv:1501.06775 v1 · 2015-01-27 · math.DG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GLLS4KUPN6A7XIRGN227S6TAQO}

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	2026-05-18T02:28:32.677585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32d72e2a8f6f81fba2266eb5f97a6083af171077b4666b12ecc6211eeb3a7ba9

Aliases

arxiv: 1501.06775 · arxiv_version: 1501.06775v1 · doi: 10.48550/arxiv.1501.06775 · pith_short_12: GLLS4KUPN6A7 · pith_short_16: GLLS4KUPN6A7XIRG · pith_short_8: GLLS4KUP

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/GLLS4KUPN6A7XIRGN227S6TAQO \
  | 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: 32d72e2a8f6f81fba2266eb5f97a6083af171077b4666b12ecc6211eeb3a7ba9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62525a7317d5345353453b628914ec082fdee37c34faaba1622ce29cc1dcbe6b",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-01-27T14:25:44Z",
    "title_canon_sha256": "cff3e74bd5b9658fbd50a3383bafcd15efdb52a8b468ee52258b6ec534364aad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.06775",
    "kind": "arxiv",
    "version": 1
  }
}