Pith Number

pith:QPO2NJNB

pith:2017:QPO2NJNBTUZWZNKM22P3YKZEWL

not attested not anchored not stored refs pending

Vanishing of $\ell^2$-Betti numbers of locally compact groups as an invariant of coarse equivalence

Michael Schr\"odl, Roman Sauer

arxiv:1702.01685 v3 · 2017-02-06 · math.AT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QPO2NJNBTUZWZNKM22P3YKZEWL}

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	2026-05-18T00:01:30.659834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83dda6a5a19d336cb54cd69fbc2b24b2d4be0d61b551444c9a5a78a881e14337

Aliases

arxiv: 1702.01685 · arxiv_version: 1702.01685v3 · doi: 10.48550/arxiv.1702.01685 · pith_short_12: QPO2NJNBTUZW · pith_short_16: QPO2NJNBTUZWZNKM · pith_short_8: QPO2NJNB

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/QPO2NJNBTUZWZNKM22P3YKZEWL \
  | 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: 83dda6a5a19d336cb54cd69fbc2b24b2d4be0d61b551444c9a5a78a881e14337

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0067fdff48cfdfeb3a5c16ba0162d48ad5e94a33672d4e8aca5d8795cb4f780",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2017-02-06T16:22:54Z",
    "title_canon_sha256": "50e3fc8539453357813b14d2fecfc8ecc7c43516862984899914f55193b5f2f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.01685",
    "kind": "arxiv",
    "version": 3
  }
}