Pith Number

pith:JTMWRMMW

pith:2010:JTMWRMMWLKFIYXKLNTQTUWMEVX

not attested not anchored not stored refs pending

Krein-like extensions and the lower boundedness problem for elliptic operators

Gerd Grubb

arxiv:1002.4549 v3 · 2010-02-24 · math.AP · 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{JTMWRMMWLKFIYXKLNTQTUWMEVX}

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	2026-05-18T02:38:46.521426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4cd968b1965a8a8c5d4b6ce13a5984adcd89e935da8abe6a9dfb3549d4db0ffb

Aliases

arxiv: 1002.4549 · arxiv_version: 1002.4549v3 · doi: 10.48550/arxiv.1002.4549 · pith_short_12: JTMWRMMWLKFI · pith_short_16: JTMWRMMWLKFIYXKL · pith_short_8: JTMWRMMW

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/JTMWRMMWLKFIYXKLNTQTUWMEVX \
  | 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: 4cd968b1965a8a8c5d4b6ce13a5984adcd89e935da8abe6a9dfb3549d4db0ffb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "712fee271eddcfa8ceadfc4f3b75cde900c8eaf619267581071b43bc4f7af90a",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-02-24T14:20:28Z",
    "title_canon_sha256": "a0ae7f7424ee1a70f60e6b35686451c50319148da1f1a6569ae9a8509fb51a43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.4549",
    "kind": "arxiv",
    "version": 3
  }
}