Pith Number

pith:W6YPZJXW

pith:2012:W6YPZJXWEWP5WAOICY3EVDPPY3

not attested not anchored not stored refs pending

The first $L^2$-Betti number and approximation in arbitrary characteristic

Mikhail Ershov, Wolfgang Lueck

arxiv:1206.0474 v3 · 2012-06-03 · 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{W6YPZJXWEWP5WAOICY3EVDPPY3}

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	2026-05-18T02:58:22.222124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7b0fca6f6259fdb01c816364a8defc6ec966539304925c7ab908e98019c6dba

Aliases

arxiv: 1206.0474 · arxiv_version: 1206.0474v3 · doi: 10.48550/arxiv.1206.0474 · pith_short_12: W6YPZJXWEWP5 · pith_short_16: W6YPZJXWEWP5WAOI · pith_short_8: W6YPZJXW

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/W6YPZJXWEWP5WAOICY3EVDPPY3 \
  | 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: b7b0fca6f6259fdb01c816364a8defc6ec966539304925c7ab908e98019c6dba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "246416d2f5bccfd76c2efc5130dedd8fb5077e7cb146ad73defd3c6a282ce560",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-06-03T18:24:05Z",
    "title_canon_sha256": "cfcbe8a832b27f9b11bd867f976c9e703014f5404d7ee1d899099531bdced289"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0474",
    "kind": "arxiv",
    "version": 3
  }
}