Pith Number

pith:LI3IRT2C

pith:2017:LI3IRT2C7ZJRWINQM4YY73K5LE

not attested not anchored not stored refs pending

Every group is the outer automorphism group of an HNN-extension of a fixed triangle group

Alan D. Logan

arxiv:1709.06441 v2 · 2017-09-19 · 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{LI3IRT2C7ZJRWINQM4YY73K5LE}

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	2026-05-17T23:41:47.115873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a3688cf42fe531b21b067318fed5d590afd69e6571fbc078a3225b5f3022d4d

Aliases

arxiv: 1709.06441 · arxiv_version: 1709.06441v2 · doi: 10.48550/arxiv.1709.06441 · pith_short_12: LI3IRT2C7ZJR · pith_short_16: LI3IRT2C7ZJRWINQ · pith_short_8: LI3IRT2C

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/LI3IRT2C7ZJRWINQM4YY73K5LE \
  | 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: 5a3688cf42fe531b21b067318fed5d590afd69e6571fbc078a3225b5f3022d4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1eb28baec08ab7fe402b9cdc225fbedbd5973d67d0763758a5569f52cbe9ea15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-09-19T14:14:13Z",
    "title_canon_sha256": "8994818bdf3cadd65ba0391e5cfaca1ecfec89b7865d5115b48482f5d59c318c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.06441",
    "kind": "arxiv",
    "version": 2
  }
}