Pith Number

pith:7GLM35YI

pith:2014:7GLM35YIQMOY4SAEMIY7WB2IX4

not attested not anchored not stored refs pending

A lower bound for the number of negative eigenvalues of Schr\"{o}dinger operators

Alexander Grigor'yan, Nikolai Nadirashvili, Yannick Sire

arxiv:1406.0317 v1 · 2014-06-02 · 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{7GLM35YIQMOY4SAEMIY7WB2IX4}

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	2026-05-18T02:50:41.168881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f996cdf708831d8e48046231fb0748bf26a0ac8da976f7e48c98283079d7866f

Aliases

arxiv: 1406.0317 · arxiv_version: 1406.0317v1 · doi: 10.48550/arxiv.1406.0317 · pith_short_12: 7GLM35YIQMOY · pith_short_16: 7GLM35YIQMOY4SAE · pith_short_8: 7GLM35YI

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/7GLM35YIQMOY4SAEMIY7WB2IX4 \
  | 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: f996cdf708831d8e48046231fb0748bf26a0ac8da976f7e48c98283079d7866f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0028feddf8fd67410b27a82da76ca13f3352e034a29a5795b620468f05a0de88",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-06-02T10:31:11Z",
    "title_canon_sha256": "c4957fd0e0413a574941e4154821775a36b59a6865c81cbe3e749f40da29fbb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.0317",
    "kind": "arxiv",
    "version": 1
  }
}