Pith Number

pith:FY3LFNPJ

pith:2017:FY3LFNPJBYSUNRGQ6EYCMJ6XR3

not attested not anchored not stored refs pending

Growth of the eigensolutions of Laplacians on Riemannian manifolds II: positivity of the initial energy

Wencai Liu

arxiv:1709.02916 v3 · 2017-09-09 · 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{FY3LFNPJBYSUNRGQ6EYCMJ6XR3}

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	2026-05-18T00:07:23.794943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e36b2b5e90e2546c4d0f1302627d78ece45930c66575fd6e0c242ae2546fc2f

Aliases

arxiv: 1709.02916 · arxiv_version: 1709.02916v3 · doi: 10.48550/arxiv.1709.02916 · pith_short_12: FY3LFNPJBYSU · pith_short_16: FY3LFNPJBYSUNRGQ · pith_short_8: FY3LFNPJ

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/FY3LFNPJBYSUNRGQ6EYCMJ6XR3 \
  | 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: 2e36b2b5e90e2546c4d0f1302627d78ece45930c66575fd6e0c242ae2546fc2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c20bf8faa3c44e2be7c7f9dc92e5f2f212e7f68eac0e76a8c07857f7ba3e103a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-09-09T05:56:36Z",
    "title_canon_sha256": "208d3f2187c1625ce696c438d8f8178fa28d64807c554e0ad182fdcca3148902"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.02916",
    "kind": "arxiv",
    "version": 3
  }
}