Pith Number

pith:W3ENRDSF

pith:2002:W3ENRDSF5JCRXH5YO2UJ3BPFQ4

not attested not anchored not stored refs pending

Equivariant Euler characteristics and K-homology Euler classes for proper cocompact G-manifolds

Jonathan Rosenberg, Wolfgang Lueck

arxiv:math/0208164 v2 · 2002-08-22 · math.KT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W3ENRDSF5JCRXH5YO2UJ3BPFQ4}

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	2026-05-18T02:38:00.588777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6c8d88e45ea451b9fb876a89d85e5870cd8078d77d26b2e071d2f5f4cbc9d31

Aliases

arxiv: math/0208164 · arxiv_version: math/0208164v2 · doi: 10.48550/arxiv.math/0208164 · pith_short_12: W3ENRDSF5JCR · pith_short_16: W3ENRDSF5JCRXH5Y · pith_short_8: W3ENRDSF

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/W3ENRDSF5JCRXH5YO2UJ3BPFQ4 \
  | 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: b6c8d88e45ea451b9fb876a89d85e5870cd8078d77d26b2e071d2f5f4cbc9d31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "742bb9e71518eb223ab61fc61cf7fcba6d0f8f71327da5e97667958ec991508f",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.KT",
    "submitted_at": "2002-08-22T15:15:30Z",
    "title_canon_sha256": "209442f957c276a8a6116e677df19f29bc07ce6cbb489c34eba3d2266c6bb467"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0208164",
    "kind": "arxiv",
    "version": 2
  }
}