Pith Number

pith:VJLZGNWD

pith:2011:VJLZGNWDPTEMWISFXITSS7C2MZ

not attested not anchored not stored refs pending

Splitting theorems on complete manifolds with Bakry-\'Emery curvature

Jia-Yong Wu

arxiv:1112.6302 v1 · 2011-12-29 · 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{VJLZGNWDPTEMWISFXITSS7C2MZ}

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	2026-05-18T04:05:36.283518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa579336c37cc8cb2245ba27297c5a6656143be3fef1d4e99233f53ea071abf4

Aliases

arxiv: 1112.6302 · arxiv_version: 1112.6302v1 · doi: 10.48550/arxiv.1112.6302 · pith_short_12: VJLZGNWDPTEM · pith_short_16: VJLZGNWDPTEMWISF · pith_short_8: VJLZGNWD

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/VJLZGNWDPTEMWISFXITSS7C2MZ \
  | 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: aa579336c37cc8cb2245ba27297c5a6656143be3fef1d4e99233f53ea071abf4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4e19bdaa99f109082ec537834d7aab674460729230cede407999fc2eee3bfd1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-12-29T13:15:39Z",
    "title_canon_sha256": "6444e50b368973685df7b0e27fb9447461fdca0929880c571407906c0a1eed1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.6302",
    "kind": "arxiv",
    "version": 1
  }
}