Pith Number

pith:CLN5PYN2

pith:2025:CLN5PYN2RBLOBS2YMMPZPYGYKJ

not attested not anchored not stored refs pending

Stability, approximable quotients, and higher property (T)

Francesco Fournier-Facio

arxiv:2512.09180 v2 · 2025-12-09 · 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{CLN5PYN2RBLOBS2YMMPZPYGYKJ}

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	2026-06-09T02:08:35.934379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12dbd7e1ba8856e0cb58631f97e0d852613eb8e1e3104bd229a6ed524106a77e

Aliases

arxiv: 2512.09180 · arxiv_version: 2512.09180v2 · doi: 10.48550/arxiv.2512.09180 · pith_short_12: CLN5PYN2RBLO · pith_short_16: CLN5PYN2RBLOBS2Y · pith_short_8: CLN5PYN2

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/CLN5PYN2RBLOBS2YMMPZPYGYKJ \
  | 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: 12dbd7e1ba8856e0cb58631f97e0d852613eb8e1e3104bd229a6ed524106a77e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afc5ce66e3d109e6878595ac08d8cb1119b9a3d1e87132317d7bca2f4b9b2567",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-12-09T22:56:49Z",
    "title_canon_sha256": "5da373b08b993b9746616c1af3bc9a168426a9d0a231f76133f61773487b98b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.09180",
    "kind": "arxiv",
    "version": 2
  }
}