Pith Number

pith:3UW3BCV7

pith:2015:3UW3BCV7OKWR25LTCVPGSQIGFZ

not attested not anchored not stored refs pending

On Index Theory for Non-Fredholm Operators: A $(1+1)$-Dimensional Example

Alan Carey, Denis Potapov, Dima Zanin, Fedor Sukochev, Fritz Gesztesy, Galina Levitina

arxiv:1509.01356 v1 · 2015-09-04 · 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{3UW3BCV7OKWR25LTCVPGSQIGFZ}

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	2026-05-18T01:33:57.888109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd2db08abf72ad1d7573155e6941062e74af143c23a71e1cfc1370dc0d1ba87f

Aliases

arxiv: 1509.01356 · arxiv_version: 1509.01356v1 · doi: 10.48550/arxiv.1509.01356 · pith_short_12: 3UW3BCV7OKWR · pith_short_16: 3UW3BCV7OKWR25LT · pith_short_8: 3UW3BCV7

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/3UW3BCV7OKWR25LTCVPGSQIGFZ \
  | 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: dd2db08abf72ad1d7573155e6941062e74af143c23a71e1cfc1370dc0d1ba87f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aeae28eb21dc4a6f59f143bca14b183f85a7d75a5d5c04f067a9c69d2b06d387",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-09-04T07:51:04Z",
    "title_canon_sha256": "3eb38a326bfa784fb967353a87d2985db5a276e84b234e913da7674126692e70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01356",
    "kind": "arxiv",
    "version": 1
  }
}