Pith Number

pith:WYWUKGPB

pith:2015:WYWUKGPBRRFY6E6VOPME2VRVJV

not attested not anchored not stored refs pending

Cohomology and $L^2$-Betti numbers for subfactors and quasi-regular inclusions

Dimitri Shlyakhtenko, Sorin Popa, Stefaan Vaes

arxiv:1511.07329 v3 · 2015-11-23 · math.OA · math.CT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WYWUKGPBRRFY6E6VOPME2VRVJV}

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	2026-05-18T00:17:35.869354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b62d4519e18c4b8f13d573d84d56354d4f9cd17dd74090942259b6f4c119934f

Aliases

arxiv: 1511.07329 · arxiv_version: 1511.07329v3 · doi: 10.48550/arxiv.1511.07329 · pith_short_12: WYWUKGPBRRFY · pith_short_16: WYWUKGPBRRFY6E6V · pith_short_8: WYWUKGPB

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/WYWUKGPBRRFY6E6VOPME2VRVJV \
  | 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: b62d4519e18c4b8f13d573d84d56354d4f9cd17dd74090942259b6f4c119934f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "114a8ddb87c277164c5a69321db3c536d43a173bed94b89a00f0c42a67da2be5",
    "cross_cats_sorted": [
      "math.CT",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-11-23T17:33:06Z",
    "title_canon_sha256": "ab9230d06be6f7ca5403018da09398dd342a3b7a061b51b7c7a8c25f02ecab51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07329",
    "kind": "arxiv",
    "version": 3
  }
}