Pith Number

pith:QDTQXGUT

pith:2016:QDTQXGUTUNLG6ZT2ALMYQPJABZ

not attested not anchored not stored refs pending

Regularity of the optimal sets for some spectral functionals

Bozhidar Velichkov, Dario Mazzoleni, Susanna Terracini

arxiv:1609.01231 v3 · 2016-09-05 · math.AP · math.FA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QDTQXGUTUNLG6ZT2ALMYQPJABZ}

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	2026-05-18T00:52:25.369442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80e70b9a93a3566f667a02d9883d200e5563d5d1c913ccba01f80f16724aac83

Aliases

arxiv: 1609.01231 · arxiv_version: 1609.01231v3 · doi: 10.48550/arxiv.1609.01231 · pith_short_12: QDTQXGUTUNLG · pith_short_16: QDTQXGUTUNLG6ZT2 · pith_short_8: QDTQXGUT

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/QDTQXGUTUNLG6ZT2ALMYQPJABZ \
  | 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: 80e70b9a93a3566f667a02d9883d200e5563d5d1c913ccba01f80f16724aac83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0dd712f538fd4970ae4658ad207d00fae0d507847562466e9cc33bf7ee53db10",
    "cross_cats_sorted": [
      "math.FA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-05T17:35:51Z",
    "title_canon_sha256": "c1c3b80b06089446c79e1ac4c84d0d3309d5a18c5782b25153c0a956eed96be4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.01231",
    "kind": "arxiv",
    "version": 3
  }
}