Pith Number

pith:CQNCZAY4

pith:2014:CQNCZAY4IHCEWZ7YAINNNRACJU

not attested not anchored not stored refs pending

On sharp lower bound of the spectral gap for a Schr\"odinger operator and some related results

Yue He

arxiv:1407.0526 v1 · 2014-07-02 · math.AP · math.DG · 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{CQNCZAY4IHCEWZ7YAINNNRACJU}

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	2026-05-18T02:48:26.669571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

141a2c831c41c44b67f8021ad6c4024d31f256b7b5a8ec4c6bff932db5f33580

Aliases

arxiv: 1407.0526 · arxiv_version: 1407.0526v1 · doi: 10.48550/arxiv.1407.0526 · pith_short_12: CQNCZAY4IHCE · pith_short_16: CQNCZAY4IHCEWZ7Y · pith_short_8: CQNCZAY4

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/CQNCZAY4IHCEWZ7YAINNNRACJU \
  | 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: 141a2c831c41c44b67f8021ad6c4024d31f256b7b5a8ec4c6bff932db5f33580

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99f296f12181fb3ead81e338af681f1993ed31b06ac2963a172f9b79cc6cccbc",
    "cross_cats_sorted": [
      "math.DG",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-07-02T11:44:18Z",
    "title_canon_sha256": "6e9553e4827ba9c78b37e81fb58146303fb114150f9c7949b418ffc98bfd8399"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.0526",
    "kind": "arxiv",
    "version": 1
  }
}