Pith Number

pith:WBJWQIVM

pith:2018:WBJWQIVMFXDD5HO3TQUC7JKGPI

not attested not anchored not stored refs pending

Schur's Lemma for Coupled Reducibility and Coupled Normality

Christian Jutten, Dana Lahat, Helene Shapiro

arxiv:1811.08467 v2 · 2018-11-20 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WBJWQIVMFXDD5HO3TQUC7JKGPI}

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	2026-05-17T23:59:31.953269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0536822ac2dc63e9ddb9c282fa5467a278d3b015a710fca19e43d2b46c3de0f

Aliases

arxiv: 1811.08467 · arxiv_version: 1811.08467v2 · doi: 10.48550/arxiv.1811.08467 · pith_short_12: WBJWQIVMFXDD · pith_short_16: WBJWQIVMFXDD5HO3 · pith_short_8: WBJWQIVM

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/WBJWQIVMFXDD5HO3TQUC7JKGPI \
  | 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: b0536822ac2dc63e9ddb9c282fa5467a278d3b015a710fca19e43d2b46c3de0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f2e5c74ad0aa21cce037723f56d9bc8fdde8ef57f339f274dbc026bd089264f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2018-11-20T19:56:34Z",
    "title_canon_sha256": "204491dfbc2222383e61936f0d0088e81b8edc5accfa500e6a34ad968d1752b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.08467",
    "kind": "arxiv",
    "version": 2
  }
}