Pith Number

pith:OPUGGUFE

pith:1998:OPUGGUFEF2HM6V2NIFMITNFR7B

not attested not anchored not stored refs pending

Novikov-Shubin invariants for arbitrary group actions and their positivity

Holger Reich (Duesseldorf), Thomas Schick (Goettingen), Wolfgang Lueck (Muenster)

arxiv:math/9809011 v2 · 1998-09-03 · 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{OPUGGUFEF2HM6V2NIFMITNFR7B}

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	2026-05-17T23:59:44.816560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73e86350a42e8ecf574d415889b4b1f84b27dc43e331adb6fd8692bdbd7bfd9f

Aliases

arxiv: math/9809011 · arxiv_version: math/9809011v2 · doi: 10.48550/arxiv.math/9809011 · pith_short_12: OPUGGUFEF2HM · pith_short_16: OPUGGUFEF2HM6V2N · pith_short_8: OPUGGUFE

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/OPUGGUFEF2HM6V2NIFMITNFR7B \
  | 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: 73e86350a42e8ecf574d415889b4b1f84b27dc43e331adb6fd8692bdbd7bfd9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0dc29e2c89e049dd054588bf2247f69d8b6e71e9f2b146511a386c8eaa2d2f07",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-09-03T07:51:16Z",
    "title_canon_sha256": "ee120fb6e37c8e2f4e6fd8aa052c369e9baac43e4ccf2a87669fb753e77b293d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9809011",
    "kind": "arxiv",
    "version": 2
  }
}