Pith Number

pith:2O7SSY2H

pith:2015:2O7SSY2HSAF5JAY7ZBPNPVJXWF

not attested not anchored not stored refs pending

CR Sub-Laplacian Comparison and Liouville-type Theorem in a Complete Noncompact Sasakian Manifold

Chien Lin, Jingzhi Tie, Shu-Cheng Chang, Ting-Jung Kuo

arxiv:1506.03270 v2 · 2015-06-10 · math.AP · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2O7SSY2HSAF5JAY7ZBPNPVJXWF}

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	2026-05-18T00:24:45.566177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3bf296347900bd4831fc85ed7d537b164cf43ad2d6e87b8c16debdaf16c1792

Aliases

arxiv: 1506.03270 · arxiv_version: 1506.03270v2 · doi: 10.48550/arxiv.1506.03270 · pith_short_12: 2O7SSY2HSAF5 · pith_short_16: 2O7SSY2HSAF5JAY7 · pith_short_8: 2O7SSY2H

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/2O7SSY2HSAF5JAY7ZBPNPVJXWF \
  | 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: d3bf296347900bd4831fc85ed7d537b164cf43ad2d6e87b8c16debdaf16c1792

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eabfbb9211ef4211681d36bd21ede8a2e6f08fa723b8d45051620393ae389588",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-06-10T12:17:44Z",
    "title_canon_sha256": "34ff06c5cd6e1fb047462bb2531b712585beacbf53d682481d974d88185c4695"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03270",
    "kind": "arxiv",
    "version": 2
  }
}