Pith Number

pith:P6GXRMKY

pith:2012:P6GXRMKYEDXYEFDGGYBW2VAMCA

not attested not anchored not stored refs pending

Invariant random subgroups of the free group

Lewis Bowen

arxiv:1204.5939 v6 · 2012-04-26 · math.DS · 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{P6GXRMKYEDXYEFDGGYBW2VAMCA}

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	2026-05-18T02:54:14.494190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f8d78b15820ef82146636036d540c1027a407e0b5777cd107458481f05567a9

Aliases

arxiv: 1204.5939 · arxiv_version: 1204.5939v6 · doi: 10.48550/arxiv.1204.5939 · pith_short_12: P6GXRMKYEDXY · pith_short_16: P6GXRMKYEDXYEFDG · pith_short_8: P6GXRMKY

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/P6GXRMKYEDXYEFDGGYBW2VAMCA \
  | 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: 7f8d78b15820ef82146636036d540c1027a407e0b5777cd107458481f05567a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa01cc3de83fae4c44e0e5d5f597aabe870c6b771989686f34a4fc4fcddca569",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-04-26T14:30:11Z",
    "title_canon_sha256": "a1ab9a0e88031355ca8be5f46d124d791c01e3e47b7d1a990a5d32bf9f26797c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5939",
    "kind": "arxiv",
    "version": 6
  }
}