Pith Number

pith:PZPQC2HO

pith:2012:PZPQC2HONFCPLBVQLG2EOCU3VY

not attested not anchored not stored refs pending

Stable weighted minimal surfaces in manifolds with nonnegative Bakry-Emery Ricci tensor

Gang Liu

arxiv:1211.3770 v3 · 2012-11-15 · 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{PZPQC2HONFCPLBVQLG2EOCU3VY}

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	2026-05-18T03:40:15.659465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e5f0168ee6944f586b059b4470a9bae3ac391b32aa7b4d4f2cb0b98ec6ed325

Aliases

arxiv: 1211.3770 · arxiv_version: 1211.3770v3 · doi: 10.48550/arxiv.1211.3770 · pith_short_12: PZPQC2HONFCP · pith_short_16: PZPQC2HONFCPLBVQ · pith_short_8: PZPQC2HO

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/PZPQC2HONFCPLBVQLG2EOCU3VY \
  | 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: 7e5f0168ee6944f586b059b4470a9bae3ac391b32aa7b4d4f2cb0b98ec6ed325

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67d0f9062e667383c781a736366199beb5da9627ad867eb29a5f35dba0d57156",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-11-15T22:43:51Z",
    "title_canon_sha256": "9eeb558cf49eedf8a58920f596aa89000f369cf25028e23c03a99a1e385410d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3770",
    "kind": "arxiv",
    "version": 3
  }
}