Pith Number

pith:6YF4WU4H

pith:2012:6YF4WU4H5245ASUYWK77UKOGOD

not attested not anchored not stored refs pending

Finite-dimensional approximation properties for uniform Roe algebras

Hiroki Sako

arxiv:1212.5900 v4 · 2012-12-24 · math.OA · 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{6YF4WU4H5245ASUYWK77UKOGOD}

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

Quasi-local Algebras and Asymptotic Expanders

Receipt and verification

First computed	2026-07-05T00:55:00.824176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f60bcb5387eeb9d04a98b2bffa29c670e76db97dc813c87064f98e4e2ed47beb

Aliases

arxiv: 1212.5900 · arxiv_version: 1212.5900v4 · doi: 10.48550/arxiv.1212.5900 · pith_short_12: 6YF4WU4H5245 · pith_short_16: 6YF4WU4H5245ASUY · pith_short_8: 6YF4WU4H

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/6YF4WU4H5245ASUYWK77UKOGOD \
  | 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: f60bcb5387eeb9d04a98b2bffa29c670e76db97dc813c87064f98e4e2ed47beb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "810fdff96fdadda70f1c5277ea94303ddf399dd542323026cf01e4124b062a64",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-12-24T12:14:11Z",
    "title_canon_sha256": "655fc045628a3b652a441186e563ddfa431ea46aaf41224beb15162bd2582987"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5900",
    "kind": "arxiv",
    "version": 4
  }
}