Pith Number

pith:PBBPVAC6

pith:2004:PBBPVAC65K274V6S5QRGHSQEJM

not attested not anchored not stored refs pending

K- and L-theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by Z/4

Wolfgang Lueck

arxiv:math/0412156 v2 · 2004-12-08 · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PBBPVAC65K274V6S5QRGHSQEJM}

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	2026-05-18T02:37:59.854055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7842fa805eeab5fe57d2ec2263ca044b12f1805fcfe6f07c670dd16786a071e8

Aliases

arxiv: math/0412156 · arxiv_version: math/0412156v2 · doi: 10.48550/arxiv.math/0412156 · pith_short_12: PBBPVAC65K27 · pith_short_16: PBBPVAC65K274V6S · pith_short_8: PBBPVAC6

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/PBBPVAC65K274V6S5QRGHSQEJM \
  | 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: 7842fa805eeab5fe57d2ec2263ca044b12f1805fcfe6f07c670dd16786a071e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab1116bbd458d8f12dda37da81e43a2e749c0d8cc7b636d2a290576fa519ff5a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.KT",
    "submitted_at": "2004-12-08T07:42:28Z",
    "title_canon_sha256": "aee0e64b597cad29f89d35eaeddda4cdc782ed4cd42f6ac0efa1243565a8d17a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412156",
    "kind": "arxiv",
    "version": 2
  }
}