Pith Number

pith:62S2XXAD

pith:2012:62S2XXAD6MEUPP646YOBIUG2I7

not attested not anchored not stored refs pending

The Outer Automorphism Groups of Two-Generator One-Relator Groups with Torsion

Alan D. Logan

arxiv:1206.2765 v4 · 2012-06-13 · 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{62S2XXAD6MEUPP646YOBIUG2I7}

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	2026-05-18T00:02:28.624076Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6a5abdc03f30947bfdcf61c1450da47f72b732d0467c402a5cc6e318073dc01

Aliases

arxiv: 1206.2765 · arxiv_version: 1206.2765v4 · doi: 10.48550/arxiv.1206.2765 · pith_short_12: 62S2XXAD6MEU · pith_short_16: 62S2XXAD6MEUPP64 · pith_short_8: 62S2XXAD

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/62S2XXAD6MEUPP646YOBIUG2I7 \
  | 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: f6a5abdc03f30947bfdcf61c1450da47f72b732d0467c402a5cc6e318073dc01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62322e488f63ada5bef35e27802755b1f35bad62e4697c947f8bcf8dd6bd61cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-06-13T11:01:02Z",
    "title_canon_sha256": "158d88fcabc233d8c2afd9ffe021996decc48db7e673077779ddce35b3a27c75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.2765",
    "kind": "arxiv",
    "version": 4
  }
}