Pith Number

pith:J67PK27R

pith:2015:J67PK27RTBVBUGUVRVKNBR67Z3

not attested not anchored not stored refs pending

Survey on approximating L^2-invariants by their classical counterparts: Betti numbers, torsion invariants and homological growth

Wolfgang Lueck

arxiv:1501.07446 v2 · 2015-01-29 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J67PK27RTBVBUGUVRVKNBR67Z3}

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	2026-05-18T01:03:06.591684Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fbef56bf1986a1a1a958d54d0c7dfcefffd86d2ead9634460300f4fd0b4dd65

Aliases

arxiv: 1501.07446 · arxiv_version: 1501.07446v2 · doi: 10.48550/arxiv.1501.07446 · pith_short_12: J67PK27RTBVB · pith_short_16: J67PK27RTBVBUGUV · pith_short_8: J67PK27R

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/J67PK27RTBVBUGUVRVKNBR67Z3 \
  | 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: 4fbef56bf1986a1a1a958d54d0c7dfcefffd86d2ead9634460300f4fd0b4dd65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f3f1051d7e7cd2103c2f2fd3d4f4f49c118b0582dde1e5ec664693dd5143f19",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-01-29T13:19:57Z",
    "title_canon_sha256": "29079608e00db0ced0d51456facd785287e140733dd3d7c6e2f49d757c1e0158"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.07446",
    "kind": "arxiv",
    "version": 2
  }
}