Pith Number

pith:BUVP6JCT

pith:2010:BUVP6JCTHSL3HRP5PTZ6P6I54J

not attested not anchored not stored refs pending

Closed manifolds with transcendental L2-Betti numbers

Andrzej Zuk (Paris 7), Mika\"el Pichot (McGill University), Thomas Schick (Georg-August-Universit\"at G\"ottingen)

arxiv:1005.1147 v2 · 2010-05-07 · math.KT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BUVP6JCTHSL3HRP5PTZ6P6I54J}

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	2026-05-18T00:44:30.639469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d2aff24533c97b3c5fd7cf3e7f91de25dab63f52a4c1a227a03f21435058800

Aliases

arxiv: 1005.1147 · arxiv_version: 1005.1147v2 · doi: 10.48550/arxiv.1005.1147 · pith_short_12: BUVP6JCTHSL3 · pith_short_16: BUVP6JCTHSL3HRP5 · pith_short_8: BUVP6JCT

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/BUVP6JCTHSL3HRP5PTZ6P6I54J \
  | 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: 0d2aff24533c97b3c5fd7cf3e7f91de25dab63f52a4c1a227a03f21435058800

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1b709a9042ee8291715ca707ec51025399cb7832efd0db5679b321ac37ba9cc",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2010-05-07T08:02:57Z",
    "title_canon_sha256": "06b6d7441bc38779b66fc720a52fb9e30297e80cdcfd0ba45962f3c4d350e947"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.1147",
    "kind": "arxiv",
    "version": 2
  }
}