Pith Number

pith:NF5PEV2O

pith:2000:NF5PEV2OCEIJTSYXZTJQ3L42PU

not attested not anchored not stored refs pending

Action of the mapping class group on a complex of curves and a presentation for the mapping class group of a surface

Susumu Hirose

arxiv:math/0008185 v1 · 2000-08-24 · 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{NF5PEV2OCEIJTSYXZTJQ3L42PU}

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	2026-05-18T03:07:11.306518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

697af2574e111099cb17ccd30daf9a7d158e021f780c6f320b81bbb55a92b0e3

Aliases

arxiv: math/0008185 · arxiv_version: math/0008185v1 · doi: 10.48550/arxiv.math/0008185 · pith_short_12: NF5PEV2OCEIJ · pith_short_16: NF5PEV2OCEIJTSYX · pith_short_8: NF5PEV2O

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/NF5PEV2OCEIJTSYXZTJQ3L42PU \
  | 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: 697af2574e111099cb17ccd30daf9a7d158e021f780c6f320b81bbb55a92b0e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d483d46aa0e44761d92803e0435ff1ac4e363900e4784f8e0cb9fde38e3d4b3a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2000-08-24T07:42:26Z",
    "title_canon_sha256": "c6d2b4e7f67a2218927e7ab8ec49e52f8fe831151c8d3edac78cc6bde39cb2ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0008185",
    "kind": "arxiv",
    "version": 1
  }
}