Pith Number

pith:GKLOG4L3

pith:2011:GKLOG4L3GRLP5QXS3IEN4FFUSQ

not attested not anchored not stored refs pending

Free subgroups within the images of quantum representations

Louis Funar, Toshitake Kohno

arxiv:1108.4904 v2 · 2011-08-24 · math.GT · 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{GKLOG4L3GRLP5QXS3IEN4FFUSQ}

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	2026-05-18T01:20:59.672285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3296e3717b3456fec2f2da08de14b4943f049c08976a24d1a5d4d964e8f6f254

Aliases

arxiv: 1108.4904 · arxiv_version: 1108.4904v2 · doi: 10.48550/arxiv.1108.4904 · pith_short_12: GKLOG4L3GRLP · pith_short_16: GKLOG4L3GRLP5QXS · pith_short_8: GKLOG4L3

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/GKLOG4L3GRLP5QXS3IEN4FFUSQ \
  | 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: 3296e3717b3456fec2f2da08de14b4943f049c08976a24d1a5d4d964e8f6f254

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69c8e35f0fa8e87d034dec5c23871cd275a8df004ae17243da9e854dbba26dd2",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-08-24T18:20:54Z",
    "title_canon_sha256": "3b53fee44cca9a44ceef7c47f7aa85f8e03002af8665705cdf10958796a7ad2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4904",
    "kind": "arxiv",
    "version": 2
  }
}