Pith Number

pith:H4D4Q2JA

pith:2018:H4D4Q2JAAUKK5RBVBAPO5GYQHK

not attested not anchored not stored refs pending

Complementary asymptotically sharp estimates for eigenvalue means of Laplacians

Evans M. Harrell II, Joachim Stubbe, Luigi Provenzano

arxiv:1806.10366 v2 · 2018-06-27 · 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{H4D4Q2JAAUKK5RBVBAPO5GYQHK}

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	2026-05-17T23:48:22.610065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f07c869200514aec435081eee9b103abed10507edbaded09fe5355e18182120

Aliases

arxiv: 1806.10366 · arxiv_version: 1806.10366v2 · doi: 10.48550/arxiv.1806.10366 · pith_short_12: H4D4Q2JAAUKK · pith_short_16: H4D4Q2JAAUKK5RBV · pith_short_8: H4D4Q2JA

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/H4D4Q2JAAUKK5RBVBAPO5GYQHK \
  | 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: 3f07c869200514aec435081eee9b103abed10507edbaded09fe5355e18182120

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23f725945dd3f78cbe9ee35199c5a8e63d6d27c2e5c93bca2deb9b495abee986",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-06-27T09:32:37Z",
    "title_canon_sha256": "d1618875b2638b34303144530bc48b5273eabcd2bbcd6ef8a29260f92e136224"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.10366",
    "kind": "arxiv",
    "version": 2
  }
}