Pith Number

pith:Y55YV5UP

pith:2011:Y55YV5UPE7NRNAE4MGAUZWIXIQ

not attested not anchored not stored refs pending

Groupoid-theoretical methods in the mapping class groups of surfaces

Nariya Kawazumi, Yusuke Kuno

arxiv:1109.6479 v3 · 2011-09-29 · 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{Y55YV5UPE7NRNAE4MGAUZWIXIQ}

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	2026-05-18T03:42:44.731638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c77b8af68f27db16809c61814cd917440c046838514f629f861c1b3a852c022c

Aliases

arxiv: 1109.6479 · arxiv_version: 1109.6479v3 · doi: 10.48550/arxiv.1109.6479 · pith_short_12: Y55YV5UPE7NR · pith_short_16: Y55YV5UPE7NRNAE4 · pith_short_8: Y55YV5UP

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/Y55YV5UPE7NRNAE4MGAUZWIXIQ \
  | 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: c77b8af68f27db16809c61814cd917440c046838514f629f861c1b3a852c022c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe8a95fbbeab6776339d5aff980294f646732a1b999e6138a6f2edb79e4cb112",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-09-29T11:15:23Z",
    "title_canon_sha256": "5a9f89ec7007e19bb414f46d86ed820276035e924c132303c1e0a42257be514e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6479",
    "kind": "arxiv",
    "version": 3
  }
}