Pith Number

pith:PG6XNG4S

pith:1999:PG6XNG4SQF7HRDTHQAZIWNZMAE

not attested not anchored not stored refs pending

Structure of the mapping class groups of surfaces: a survey and a prospect

Shigeyuki Morita

arxiv:math/9911258 v1 · 1999-11-21 · 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{PG6XNG4SQF7HRDTHQAZIWNZMAE}

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.

Cited by

1 paper in Pith

Calculating the second rational cohomology group of the Torelli group

Receipt and verification

First computed	2026-05-18T01:05:32.393276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79bd769b92817e788e6780328b372c010dca72788d2da77d4c342439d132b1df

Aliases

arxiv: math/9911258 · arxiv_version: math/9911258v1 · doi: 10.48550/arxiv.math/9911258 · pith_short_12: PG6XNG4SQF7H · pith_short_16: PG6XNG4SQF7HRDTH · pith_short_8: PG6XNG4S

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/PG6XNG4SQF7HRDTHQAZIWNZMAE \
  | 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: 79bd769b92817e788e6780328b372c010dca72788d2da77d4c342439d132b1df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b27448030d675b28c738bf5ca5f7d42810ecc914a88ab0f695e7524b08c507ec",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1999-11-21T00:00:00Z",
    "title_canon_sha256": "6ca6863d01522a3dbdb99f2668d78794add7a59e9ab3a187713d75e1ad70f015"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9911258",
    "kind": "arxiv",
    "version": 1
  }
}