Pith Number

pith:WYU7SO6D

pith:2015:WYU7SO6D4FZO4G32BKAFSDFTNF

not attested not anchored not stored refs pending

The normal closure of a power of a half-twist has infinite index in the mapping class group of a punctured sphere

Charalampos Stylianakis

arxiv:1511.02912 v1 · 2015-11-09 · math.GR · math.GT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WYU7SO6D4FZO4G32BKAFSDFTNF}

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	2026-05-18T01:27:17.459816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b629f93bc3e172ee1b7a0a80590cb369693e86470499504fc028a9d1c85bd861

Aliases

arxiv: 1511.02912 · arxiv_version: 1511.02912v1 · doi: 10.48550/arxiv.1511.02912 · pith_short_12: WYU7SO6D4FZO · pith_short_16: WYU7SO6D4FZO4G32 · pith_short_8: WYU7SO6D

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/WYU7SO6D4FZO4G32BKAFSDFTNF \
  | 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: b629f93bc3e172ee1b7a0a80590cb369693e86470499504fc028a9d1c85bd861

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7479b9e2f03fb88e62d4aa8f1db1d08d48c295d6318d3ab455257b992fb83469",
    "cross_cats_sorted": [
      "math.GT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-11-09T22:15:32Z",
    "title_canon_sha256": "abb4c7801f811d68ee07ffaf430194df34599f59cbb66347bced035b1f9af682"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02912",
    "kind": "arxiv",
    "version": 1
  }
}