Pith Number

pith:P3IULSCC

pith:2016:P3IULSCCUW4PPFWE7TPWYB7FFU

not attested not anchored not stored refs pending

Krein's trace formula for unitary operators and operator Lipschitz functions (English translation)

Aleksei Aleksandrov, Vladimir Peller

arxiv:1611.01630 v1 · 2016-11-05 · math.FA · math.CA · math.CV · 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{P3IULSCCUW4PPFWE7TPWYB7FFU}

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	2026-05-18T01:00:04.829389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ed145c842a5b8f796c4fcdf6c07e52d37761cf2b3eb4d0922428d2ef359ec79

Aliases

arxiv: 1611.01630 · arxiv_version: 1611.01630v1 · doi: 10.48550/arxiv.1611.01630 · pith_short_12: P3IULSCCUW4P · pith_short_16: P3IULSCCUW4PPFWE · pith_short_8: P3IULSCC

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/P3IULSCCUW4PPFWE7TPWYB7FFU \
  | 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: 7ed145c842a5b8f796c4fcdf6c07e52d37761cf2b3eb4d0922428d2ef359ec79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "005726d9a9d273743684072ea48092f3fd56d518387acc779d7c1a2f90d4a84b",
    "cross_cats_sorted": [
      "math.CA",
      "math.CV",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-11-05T11:07:15Z",
    "title_canon_sha256": "ad735f4c266608431ac6cb9591cffd535b318a7c13d650ef118239d86df795ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.01630",
    "kind": "arxiv",
    "version": 1
  }
}