Pith Number

pith:4AQB6P47

pith:2016:4AQB6P47APKUN4IDZSZOPGUHM7

not attested not anchored not stored refs pending

Essential Spectrum of the Weighted Laplacian on Noncompact Manifolds and Applications

Adina Rocha

arxiv:1608.01539 v1 · 2016-08-04 · 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{4AQB6P47APKUN4IDZSZOPGUHM7}

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	2026-05-18T01:09:52.188847Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0201f3f9f03d546f103ccb2e79a8767fd15129ab27759fa64655a85988858b2

Aliases

arxiv: 1608.01539 · arxiv_version: 1608.01539v1 · doi: 10.48550/arxiv.1608.01539 · pith_short_12: 4AQB6P47APKU · pith_short_16: 4AQB6P47APKUN4ID · pith_short_8: 4AQB6P47

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/4AQB6P47APKUN4IDZSZOPGUHM7 \
  | 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: e0201f3f9f03d546f103ccb2e79a8767fd15129ab27759fa64655a85988858b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "34e322a936c7f3d38bc12f79b97a5929ed758ff0da18d856c4f658fa4683faea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-08-04T14:10:50Z",
    "title_canon_sha256": "2d74ed9db2751218bcd31935b820b834ad43c7067658d384ad51b3c4f81d1126"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.01539",
    "kind": "arxiv",
    "version": 1
  }
}