Pith Number

pith:BOOPYIIV

pith:2013:BOOPYIIVI4IR54P5YMSLGN5YZB

not attested not anchored not stored refs pending

Commutators of small rank and reducibility of operator semigroups

Alexey I. Popov, Ali Jafarian, Heydar Radjavi, Mehdi Radjabalipour

arxiv:1306.1972 v1 · 2013-06-09 · math.FA · math.GR · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BOOPYIIVI4IR54P5YMSLGN5YZB}

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	2026-05-18T03:21:11.403056Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b9cfc211547111ef1fdc324b337b8c8734dcba1ac31aa27ebf1eeb44bbf9993

Aliases

arxiv: 1306.1972 · arxiv_version: 1306.1972v1 · doi: 10.48550/arxiv.1306.1972 · pith_short_12: BOOPYIIVI4IR · pith_short_16: BOOPYIIVI4IR54P5 · pith_short_8: BOOPYIIV

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/BOOPYIIVI4IR54P5YMSLGN5YZB \
  | 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: 0b9cfc211547111ef1fdc324b337b8c8734dcba1ac31aa27ebf1eeb44bbf9993

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c809fd6057096e37812c85513d97cae7bb8fc01c1cda4dcf2129bd43c032c0f8",
    "cross_cats_sorted": [
      "math.GR",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-06-09T01:51:30Z",
    "title_canon_sha256": "8649c6b3835930563cb43b8fc2385ddafc36f81d7043294d7fb2afe163241d48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1972",
    "kind": "arxiv",
    "version": 1
  }
}