Pith Number

pith:4BWH4CZQ

pith:1997:4BWH4CZQZINQ7AHJTC4VLG5OZT

not attested not anchored not stored refs pending

L^2-torsion of hyperbolic manifolds of finite volume

Thomas Schick, Wolfgang Lueck

arxiv:dg-ga/9707009 v2 · 1997-07-10 · dg-ga · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4BWH4CZQZINQ7AHJTC4VLG5OZT}

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	2026-05-17T23:59:45.092600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e06c7e0b30ca1b0f80e998b9559baeccd2ab400aa43f924df8a6c0b4b89f29a2

Aliases

arxiv: dg-ga/9707009 · arxiv_version: dg-ga/9707009v2 · doi: 10.48550/arxiv.dg-ga/9707009 · pith_short_12: 4BWH4CZQZINQ · pith_short_16: 4BWH4CZQZINQ7AHJ · pith_short_8: 4BWH4CZQ

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/4BWH4CZQZINQ7AHJTC4VLG5OZT \
  | 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: e06c7e0b30ca1b0f80e998b9559baeccd2ab400aa43f924df8a6c0b4b89f29a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5afd0a0f70a50f8a1eb8d44f7da99273e420a7ed05102616d62c7b570f86ceb4",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "dg-ga",
    "submitted_at": "1997-07-10T10:22:41Z",
    "title_canon_sha256": "bba80c1dae37c3fdce99b85cdfe1ae6a860b93d5c4b63787e12ecffeeffb577c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "dg-ga/9707009",
    "kind": "arxiv",
    "version": 2
  }
}