Pith Number

pith:BAVSZKGU

pith:2016:BAVSZKGUZC5CLLLJXLPEUXG5YI

not attested not anchored not stored refs pending

Two-term, asymptotically sharp estimates for eigenvalue means of the Laplacian

Evans M. Harrell II, Joachim Stubbe

arxiv:1607.02207 v1 · 2016-07-08 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BAVSZKGUZC5CLLLJXLPEUXG5YI}

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	2026-05-18T01:11:21.031043Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

082b2ca8d4c8ba25ad69bade4a5cddc2364aa2c206a4c1c2e69282da55cb2819

Aliases

arxiv: 1607.02207 · arxiv_version: 1607.02207v1 · doi: 10.48550/arxiv.1607.02207 · pith_short_12: BAVSZKGUZC5C · pith_short_16: BAVSZKGUZC5CLLLJ · pith_short_8: BAVSZKGU

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/BAVSZKGUZC5CLLLJXLPEUXG5YI \
  | 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: 082b2ca8d4c8ba25ad69bade4a5cddc2364aa2c206a4c1c2e69282da55cb2819

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1458f5c65a67871a243099fc9388fe95fbfb91863798de73a2b82ececcc2fd7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-07-08T01:03:10Z",
    "title_canon_sha256": "47a41ba824c9cdf4d7e0dff9e9bfea2337df6e4677d765d9e00da832ef9dc105"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02207",
    "kind": "arxiv",
    "version": 1
  }
}