Pith Number

pith:BDH5DBFJ

pith:2020:BDH5DBFJA4PSNC7D5V3LZRPEAB

not attested not anchored not stored refs pending

Computer proofs for Property (T), and SDP duality

Martin Nitsche

arxiv:2009.05134 v3 · 2020-09-10 · math.GR · 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{BDH5DBFJA4PSNC7D5V3LZRPEAB}

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

2 papers in Pith

Abelianizations of finite-index subgroups of the handlebody group

Invariant trace simplices and relative property (T)

Receipt and verification

First computed	2026-07-05T05:28:03.938116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08cfd184a9071f268be3ed76bcc5e4006da9ab495927dddda070ab08d3fe2a28

Aliases

arxiv: 2009.05134 · arxiv_version: 2009.05134v3 · doi: 10.48550/arxiv.2009.05134 · pith_short_12: BDH5DBFJA4PS · pith_short_16: BDH5DBFJA4PSNC7D · pith_short_8: BDH5DBFJ

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/BDH5DBFJA4PSNC7D5V3LZRPEAB \
  | 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: 08cfd184a9071f268be3ed76bcc5e4006da9ab495927dddda070ab08d3fe2a28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b85e6b769a54a90a1c5d829da77969f4304f3152f43e89adb6b3262e2f8c24f",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2020-09-10T20:11:31Z",
    "title_canon_sha256": "081bd86e77daabf0d2c0aeda7472e37c395b51cea8ad742b0b13c6358fd3f32e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.05134",
    "kind": "arxiv",
    "version": 3
  }
}