Pith Number

pith:HJVH5PFF

pith:2015:HJVH5PFFMMQMM3X4N2QTHSNR4I

not attested not anchored not stored refs pending

Gaussian estimates with best constants for higher-order Schr\"odinger operators with Kato potentials

Gerassimos Barbatis

arxiv:1511.08711 v3 · 2015-11-27 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HJVH5PFFMMQMM3X4N2QTHSNR4I}

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	2026-05-18T01:18:25.107916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a6a7ebca56320c66efc6ea133c9b1e2098a431250432dd6e76d33ec5b4707d5

Aliases

arxiv: 1511.08711 · arxiv_version: 1511.08711v3 · doi: 10.48550/arxiv.1511.08711 · pith_short_12: HJVH5PFFMMQM · pith_short_16: HJVH5PFFMMQMM3X4 · pith_short_8: HJVH5PFF

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/HJVH5PFFMMQMM3X4N2QTHSNR4I \
  | 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: 3a6a7ebca56320c66efc6ea133c9b1e2098a431250432dd6e76d33ec5b4707d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dee7c11c396c0d3f125d76cfd2205e903df4cf5c5656fbea3bf6fcd52e6de978",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-27T15:40:31Z",
    "title_canon_sha256": "4ecfd010a51f2f051efe4bcfa96578fad791bfed074b314e74b54e4b80571223"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08711",
    "kind": "arxiv",
    "version": 3
  }
}