Pith Number

pith:IYF4VXSQ

pith:2012:IYF4VXSQDEPQLW24Q42KJA3YFR

not attested not anchored not stored refs pending

Pathological and Omega-transitive Representations of Free Groups

Jorge Bruno

arxiv:1204.5615 v3 · 2012-04-25 · math.RT · 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{IYF4VXSQDEPQLW24Q42KJA3YFR}

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	2026-05-18T03:07:21.037963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

460bcade50191f05db5c8734a483782c4803d9701dda8e7655baeded9c45bacf

Aliases

arxiv: 1204.5615 · arxiv_version: 1204.5615v3 · doi: 10.48550/arxiv.1204.5615 · pith_short_12: IYF4VXSQDEPQ · pith_short_16: IYF4VXSQDEPQLW24 · pith_short_8: IYF4VXSQ

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/IYF4VXSQDEPQLW24Q42KJA3YFR \
  | 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: 460bcade50191f05db5c8734a483782c4803d9701dda8e7655baeded9c45bacf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2df19b0a2448bf90b23d08d73536e4d35116a9c4db8b39373046fecd1d18fd88",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-04-25T11:01:49Z",
    "title_canon_sha256": "d8f1e26870419d703fd3cad8df152e401547d9f4ab0ffd3f1f977ed17822af78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5615",
    "kind": "arxiv",
    "version": 3
  }
}