Pith Number

pith:7R3ZWDIE

pith:2013:7R3ZWDIEYQHLFOUIBO2AQC6ICL

not attested not anchored not stored refs pending

Subgroup decomposition in $\text{Out}(F_n)$, Part IV: Relatively irreducible subgroups

Lee Mosher, Michael Handel

arxiv:1306.4711 v4 · 2013-06-19 · 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{7R3ZWDIEYQHLFOUIBO2AQC6ICL}

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	2026-05-18T01:26:19.175381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc779b0d04c40eb2ba880bb4080bc812e45e3e101321b883a54d073791699433

Aliases

arxiv: 1306.4711 · arxiv_version: 1306.4711v4 · doi: 10.48550/arxiv.1306.4711 · pith_short_12: 7R3ZWDIEYQHL · pith_short_16: 7R3ZWDIEYQHLFOUI · pith_short_8: 7R3ZWDIE

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/7R3ZWDIEYQHLFOUIBO2AQC6ICL \
  | 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: fc779b0d04c40eb2ba880bb4080bc812e45e3e101321b883a54d073791699433

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b67e2608930202900732e7c89b08084f2179c23d79f4cf27b3974fa18c92c3be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-06-19T22:30:42Z",
    "title_canon_sha256": "eba4f2376f597bc7eaaa8b4ca985620e7204200952055e9e9333f9b8f05fbbe1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.4711",
    "kind": "arxiv",
    "version": 4
  }
}