Pith Number

pith:7YQFCVTP

pith:2000:7YQFCVTP4YUYWCGEXQBCH6A3M4

not attested not anchored not stored refs pending

Bounded cohomology of subgroups of mapping class groups

Koji Fujiwara, Mladen Bestvina

arxiv:math/0012115 v2 · 2000-12-14 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7YQFCVTP4YUYWCGEXQBCH6A3M4}

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	2026-05-18T02:38:00.915629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe2051566fe6298b08c4bc0223f81b671c5f6802a5a4b1369bd251be683afef8

Aliases

arxiv: math/0012115 · arxiv_version: math/0012115v2 · doi: 10.48550/arxiv.math/0012115 · pith_short_12: 7YQFCVTP4YUY · pith_short_16: 7YQFCVTP4YUYWCGE · pith_short_8: 7YQFCVTP

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/7YQFCVTP4YUYWCGEXQBCH6A3M4 \
  | 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: fe2051566fe6298b08c4bc0223f81b671c5f6802a5a4b1369bd251be683afef8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f14878b80378d8271af568c3e17a725a5a6f7f15899f6fd6b2a202c1b23d1f6",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2000-12-14T18:13:13Z",
    "title_canon_sha256": "b36748a4c855445aacca7c8bb67847e74e414037b346da467dd756f91f72f262"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012115",
    "kind": "arxiv",
    "version": 2
  }
}