Pith Number

pith:XMRXPMJ6

pith:2014:XMRXPMJ6SR5QXVSCADCGSQASR4

not attested not anchored not stored refs pending

An algorithm to detect full irreducibility by bounding the volume of periodic free factors

Alexandra Pettet, Johanna Mangahas, Matt Clay

arxiv:1402.7342 v3 · 2014-02-28 · math.GR · 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{XMRXPMJ6SR5QXVSCADCGSQASR4}

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	2026-05-18T02:47:05.426885Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb2377b13e947b0bd64200c46940128f394d62dcc87c279ca15361ccc666d0ba

Aliases

arxiv: 1402.7342 · arxiv_version: 1402.7342v3 · doi: 10.48550/arxiv.1402.7342 · pith_short_12: XMRXPMJ6SR5Q · pith_short_16: XMRXPMJ6SR5QXVSC · pith_short_8: XMRXPMJ6

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/XMRXPMJ6SR5QXVSCADCGSQASR4 \
  | 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: bb2377b13e947b0bd64200c46940128f394d62dcc87c279ca15361ccc666d0ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d65c41a619ff06d5e2266e465fb00e0973f2532f9164fdf265c1efb14f029cf1",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-02-28T18:47:02Z",
    "title_canon_sha256": "6995cf31d27385f4a27d11c359b7130aeda9b83b5bf11d60b36684fe17f767a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.7342",
    "kind": "arxiv",
    "version": 3
  }
}