Pith Number

pith:47FGYW5D

pith:2019:47FGYW5D3LFH23Y34CWVVVDMRI

not attested not anchored not stored refs pending

On a trace formula for functions of noncommuting operators

A.B. Aleksandrov, D.S. Potapov, V.V. Peller

arxiv:1901.09495 v1 · 2019-01-28 · 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{47FGYW5D3LFH23Y34CWVVVDMRI}

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	2026-05-17T23:55:24.620648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7ca6c5ba3daca7d6f1be0ad5ad46c8a2adef72a292c507cf03f6fc8161649fb

Aliases

arxiv: 1901.09495 · arxiv_version: 1901.09495v1 · doi: 10.48550/arxiv.1901.09495 · pith_short_12: 47FGYW5D3LFH · pith_short_16: 47FGYW5D3LFH23Y3 · pith_short_8: 47FGYW5D

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/47FGYW5D3LFH23Y34CWVVVDMRI \
  | 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: e7ca6c5ba3daca7d6f1be0ad5ad46c8a2adef72a292c507cf03f6fc8161649fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92fd8af7fd9000b90c1d593199e83999b0fd304c9b437b20c4f03e574c8330bc",
    "cross_cats_sorted": [
      "math.CA",
      "math.CV",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-01-28T03:09:44Z",
    "title_canon_sha256": "17d8dfe916675852a90fee741da5dca5f860a4765776d8a4bb0099fa967a4a13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.09495",
    "kind": "arxiv",
    "version": 1
  }
}