Pith Number

pith:DOOZJXYD

pith:2019:DOOZJXYDTDPH5TEFAYTEVQNZO6

not attested not anchored not stored refs pending

On the top-dimensional $\ell^2$-Betti numbers

Camille No\^us, Damien Gaboriau (UMPA-ENSL)

arxiv:1909.01633 v4 · 2019-09-04 · 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{DOOZJXYDTDPH5TEFAYTEVQNZO6}

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	2026-07-05T04:34:43.556816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b9d94df0398de7ecc8506264ac1b97784b924d5d2e978f97fa3592826932d86

Aliases

arxiv: 1909.01633 · arxiv_version: 1909.01633v4 · doi: 10.48550/arxiv.1909.01633 · pith_short_12: DOOZJXYDTDPH · pith_short_16: DOOZJXYDTDPH5TEF · pith_short_8: DOOZJXYD

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/DOOZJXYDTDPH5TEFAYTEVQNZO6 \
  | 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: 1b9d94df0398de7ecc8506264ac1b97784b924d5d2e978f97fa3592826932d86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb32d7188ef0c0850e0a391052225dbc72d80ca5c16e2cef7bf5080e9fe4c1a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-09-04T09:05:32Z",
    "title_canon_sha256": "0f663a79a4f4d50b7948b89e573ffcb287fd56d3c797f9c1a6d2ccc6c6248e9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.01633",
    "kind": "arxiv",
    "version": 4
  }
}