Pith Number

pith:QGKBVG6Z

pith:2014:QGKBVG6ZLMLXBFCXQTMAL5A7AB

not attested not anchored not stored refs pending

The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces

Renjin Jiang

arxiv:1405.0684 v2 · 2014-05-04 · math.MG · math.AP · 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{QGKBVG6ZLMLXBFCXQTMAL5A7AB}

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	2026-05-18T02:39:00.931715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81941a9bd95b1770945784d805f41f0055f5169a2edf7a4475f87aef507243a9

Aliases

arxiv: 1405.0684 · arxiv_version: 1405.0684v2 · doi: 10.48550/arxiv.1405.0684 · pith_short_12: QGKBVG6ZLMLX · pith_short_16: QGKBVG6ZLMLXBFCX · pith_short_8: QGKBVG6Z

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/QGKBVG6ZLMLXBFCXQTMAL5A7AB \
  | 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: 81941a9bd95b1770945784d805f41f0055f5169a2edf7a4475f87aef507243a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e4a93b463a92c256e70024e128918f69c0e1523fa061d2b11692c8d7b9abfe8",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2014-05-04T11:49:17Z",
    "title_canon_sha256": "9c97cba95a18becbff3f6b9976252860e490940c9996583768dc580de1cb5798"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.0684",
    "kind": "arxiv",
    "version": 2
  }
}