Pith Number

pith:UOO3UZ6G

pith:2012:UOO3UZ6GU3IFDIXAXQ7V2Z54TK

not attested not anchored not stored refs pending

A periodicity criterion and the section problem on the Mapping Class Group

Patrice Le Calvez

arxiv:1202.3106 v1 · 2012-02-14 · math.DS · 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{UOO3UZ6GU3IFDIXAXQ7V2Z54TK}

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	2026-05-18T04:02:24.117070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a39dba67c6a6d051a2e0bc3f5d67bc9aa73808c96a234c9b20db9d70d69d734a

Aliases

arxiv: 1202.3106 · arxiv_version: 1202.3106v1 · doi: 10.48550/arxiv.1202.3106 · pith_short_12: UOO3UZ6GU3IF · pith_short_16: UOO3UZ6GU3IFDIXA · pith_short_8: UOO3UZ6G

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/UOO3UZ6GU3IFDIXAXQ7V2Z54TK \
  | 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: a39dba67c6a6d051a2e0bc3f5d67bc9aa73808c96a234c9b20db9d70d69d734a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73655d951183311b59ac7a3b0ad3ce3f42c2cfe19280b347ce657c6c099a1fe0",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-02-14T17:55:37Z",
    "title_canon_sha256": "0e72e29a3bec61ae70ed91ed8bf16367011c171ce87df477beb185ba2915c2d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3106",
    "kind": "arxiv",
    "version": 1
  }
}