Pith Number

pith:GUQGBIJW

pith:2000:GUQGBIJWJJSOSLWUGX5LSDDHUQ

not attested not anchored not stored refs pending

Homology cylinders: an enlargement of the mapping class group

Jerome Levine

arxiv:math/0010247 v2 · 2000-10-26 · math.GT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GUQGBIJWJJSOSLWUGX5LSDDHUQ}

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	2026-05-18T02:41:33.391944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

352060a1364a64e92ed435fab90c67a4018fd0a683e8d0cf60b9baff9ac04bdb

Aliases

arxiv: math/0010247 · arxiv_version: math/0010247v2 · doi: 10.48550/arxiv.math/0010247 · pith_short_12: GUQGBIJWJJSO · pith_short_16: GUQGBIJWJJSOSLWU · pith_short_8: GUQGBIJW

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/GUQGBIJWJJSOSLWUGX5LSDDHUQ \
  | 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: 352060a1364a64e92ed435fab90c67a4018fd0a683e8d0cf60b9baff9ac04bdb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb4ed29202ded4f3fb72678e636fb63addb405d32f0eb9291ec0419a351fa555",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2000-10-26T14:44:06Z",
    "title_canon_sha256": "de448d502581c2db3ace1d30ee36b990f6421a5e5d6a008be429334337edd5b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0010247",
    "kind": "arxiv",
    "version": 2
  }
}