Pith Number

pith:LLLODYG6

pith:2013:LLLODYG633HK6YZWFKXQCMNTIQ

not attested not anchored not stored refs pending

Stability estimates for the lowest eigenvalue of a Schr\"odinger operator

Elliott H. Lieb, Eric A. Carlen, Rupert L. Frank

arxiv:1301.5032 v2 · 2013-01-21 · math.AP · math-ph · math.MP · 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{LLLODYG633HK6YZWFKXQCMNTIQ}

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	2026-05-18T03:25:46.125594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ad6e1e0dedeceaf63362aaf0131b34414db85a8269b3501fad3fb6454c27585

Aliases

arxiv: 1301.5032 · arxiv_version: 1301.5032v2 · doi: 10.48550/arxiv.1301.5032 · pith_short_12: LLLODYG633HK · pith_short_16: LLLODYG633HK6YZW · pith_short_8: LLLODYG6

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/LLLODYG633HK6YZWFKXQCMNTIQ \
  | 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: 5ad6e1e0dedeceaf63362aaf0131b34414db85a8269b3501fad3fb6454c27585

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff73e1082b8c1e00db7da3140c7ff7cccb3cdf4ee98cb74fb80d96ba4c1e3682",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-01-21T22:49:23Z",
    "title_canon_sha256": "1c8b027bfee3c43fad136ea3a9870fd74e38ab9112b86fefdac265eddf30c169"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.5032",
    "kind": "arxiv",
    "version": 2
  }
}