Pith Number

pith:4WF4NNBY

pith:2019:4WF4NNBYVH7Z7X2J4I2XFOT7WO

not attested not anchored not stored refs pending

Representing some II$_1$ factors in $L^2(\Lambda \backslash G)$

Lauren C. Ruth

arxiv:1907.07641 v1 · 2019-07-17 · math.OA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4WF4NNBYVH7Z7X2J4I2XFOT7WO}

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	2026-05-17T23:40:21.466941Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e58bc6b438a9ff9fdf49e23572ba7fb3907c8917e095a2e3790dfc6c78416c74

Aliases

arxiv: 1907.07641 · arxiv_version: 1907.07641v1 · doi: 10.48550/arxiv.1907.07641 · pith_short_12: 4WF4NNBYVH7Z · pith_short_16: 4WF4NNBYVH7Z7X2J · pith_short_8: 4WF4NNBY

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/4WF4NNBYVH7Z7X2J4I2XFOT7WO \
  | 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: e58bc6b438a9ff9fdf49e23572ba7fb3907c8917e095a2e3790dfc6c78416c74

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e78d57bd2972193838ef83f29fff578abec5b6d8d643cda3060fa98f098b8f90",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2019-07-17T17:04:06Z",
    "title_canon_sha256": "03e426a84004e853398f1cd8302293d922365453d6e947e5bce019d8909ffc51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.07641",
    "kind": "arxiv",
    "version": 1
  }
}