Pith Number

pith:G7SGV2WA

pith:2016:G7SGV2WABCNVAAQGK4O6O6YAUJ

not attested not anchored not stored refs pending

Box spaces of the free group that neither contain expanders nor embed into a Hilbert space

Ana Khukhro, Thiebout Delabie

arxiv:1611.08451 v2 · 2016-11-25 · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G7SGV2WABCNVAAQGK4O6O6YAUJ}

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	2026-05-18T00:17:02.026996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37e46aeac0089b500206571de77b00a27f2b4cd956f0455dcc5bd6e3b93e36c4

Aliases

arxiv: 1611.08451 · arxiv_version: 1611.08451v2 · doi: 10.48550/arxiv.1611.08451 · pith_short_12: G7SGV2WABCNV · pith_short_16: G7SGV2WABCNVAAQG · pith_short_8: G7SGV2WA

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/G7SGV2WABCNVAAQGK4O6O6YAUJ \
  | 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: 37e46aeac0089b500206571de77b00a27f2b4cd956f0455dcc5bd6e3b93e36c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe2c8cee4dcdf72533c82817dcd57f1f6f960e8f27f7816effbd5d51eaa64bee",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-11-25T13:30:27Z",
    "title_canon_sha256": "1d810d794a8839e6ad51bcd23f993fdaadec0690fa8edbb5cd9d62c8c4c77479"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.08451",
    "kind": "arxiv",
    "version": 2
  }
}