Pith Number

pith:OIY5GXZ7

pith:2011:OIY5GXZ7N6U772ZLNNZ53G4QB7

not attested not anchored not stored refs pending

On upper bounds on stable commutator lengths in mapping class groups

Naoyuki Monden

arxiv:1106.0422 v2 · 2011-06-02 · 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{OIY5GXZ7N6U772ZLNNZ53G4QB7}

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	2026-05-18T04:20:49.336434Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7231d35f3f6fa9ffeb2b6b73dd9b900ffe932c69bf12855b92c92ed58a104012

Aliases

arxiv: 1106.0422 · arxiv_version: 1106.0422v2 · doi: 10.48550/arxiv.1106.0422 · pith_short_12: OIY5GXZ7N6U7 · pith_short_16: OIY5GXZ7N6U772ZL · pith_short_8: OIY5GXZ7

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/OIY5GXZ7N6U772ZLNNZ53G4QB7 \
  | 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: 7231d35f3f6fa9ffeb2b6b73dd9b900ffe932c69bf12855b92c92ed58a104012

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4612b30477e5d0b402f564ab963809bb186ba272f6cb025551952a9a40120ca7",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-06-02T13:04:53Z",
    "title_canon_sha256": "4cf4123f1d6cc1b69eecf1660768049407a9879316cc37b704dc2aa1d65ea742"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0422",
    "kind": "arxiv",
    "version": 2
  }
}