Pith Number

pith:RR5XGRSV

pith:2012:RR5XGRSVNBKRKLT4YFDMZWLQ4P

not attested not anchored not stored refs pending

Measure free factors of free groups

Juan Alonso

arxiv:1202.0571 v2 · 2012-02-02 · math.GR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RR5XGRSVNBKRKLT4YFDMZWLQ4P}

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	2026-05-18T04:02:26.730249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c7b7346556855152e7cc146ccd970e3fadad2573b582d85f5cf22138060851c

Aliases

arxiv: 1202.0571 · arxiv_version: 1202.0571v2 · doi: 10.48550/arxiv.1202.0571 · pith_short_12: RR5XGRSVNBKR · pith_short_16: RR5XGRSVNBKRKLT4 · pith_short_8: RR5XGRSV

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/RR5XGRSVNBKRKLT4YFDMZWLQ4P \
  | 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: 8c7b7346556855152e7cc146ccd970e3fadad2573b582d85f5cf22138060851c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f68200179884b92ba1f704af478b7731506dbbe50d6572a6e52af1a9d5bf1f4",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-02-02T22:03:28Z",
    "title_canon_sha256": "a672fef09c7f7f4dca06de4c5dcfc3dd557e3eef88a790a9cbd76154b83ce48d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.0571",
    "kind": "arxiv",
    "version": 2
  }
}