Pith Number

pith:3RDVEID7

pith:2015:3RDVEID7RDM435BWEXTRYIXNWE

not attested not anchored not stored refs pending

A class of II_1 factors with exactly two group measure space decompositions

Anna Sofie Krogager, Stefaan Vaes

arxiv:1512.06677 v2 · 2015-12-21 · 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{3RDVEID7RDM435BWEXTRYIXNWE}

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	2026-05-18T00:42:39.597712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc4752207f88d9cdf43625e71c22edb13013f55eabaa984383ece4153d6941d5

Aliases

arxiv: 1512.06677 · arxiv_version: 1512.06677v2 · doi: 10.48550/arxiv.1512.06677 · pith_short_12: 3RDVEID7RDM4 · pith_short_16: 3RDVEID7RDM435BW · pith_short_8: 3RDVEID7

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/3RDVEID7RDM435BWEXTRYIXNWE \
  | 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: dc4752207f88d9cdf43625e71c22edb13013f55eabaa984383ece4153d6941d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65c880bee6d162998932793aab62671372b7063a9ff75c45f08f7a8ed6071487",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-12-21T16:06:22Z",
    "title_canon_sha256": "70a54dcb8aaad7bce0f6a9e1b7e9bf7f3075bd92d29a39ee6d3b0d920c2a4a0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06677",
    "kind": "arxiv",
    "version": 2
  }
}