Pith Number

pith:VATD5NY7

pith:2025:VATD5NY7BHAMTRFSG3RS3NFN4E

not attested not anchored not stored refs pending

A continuum of non-measure equivalent groups

Adrian Ioana, Robin Tucker-Drob

arxiv:2512.04531 v2 · 2025-12-04 · math.GR · math.DS · 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{VATD5NY7BHAMTRFSG3RS3NFN4E}

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.

Cited by

1 paper in Pith

Kazhdan groups of dimension $16$ with prescribed second $\ell^2$-Betti number

Receipt and verification

First computed	2026-07-14T00:18:21.061272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8263eb71f09c0c9c4b236e32db4ade1212c059a6ad456a05b0e3743f0ab65c4

Aliases

arxiv: 2512.04531 · arxiv_version: 2512.04531v2 · doi: 10.48550/arxiv.2512.04531 · pith_short_12: VATD5NY7BHAM · pith_short_16: VATD5NY7BHAMTRFS · pith_short_8: VATD5NY7

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/VATD5NY7BHAMTRFSG3RS3NFN4E \
  | 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: a8263eb71f09c0c9c4b236e32db4ade1212c059a6ad456a05b0e3743f0ab65c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "297a4664951adc9f5163dfe4719519dee21e4cd2e29b0509b1240142f0be95cc",
    "cross_cats_sorted": [
      "math.DS",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-12-04T07:27:34Z",
    "title_canon_sha256": "ca9237cc76222d6677e0f862329656b6745f6d5665d4597eb0cbdc2aee772860"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.04531",
    "kind": "arxiv",
    "version": 2
  }
}