Pith Number

pith:7GWQQTV6

pith:2010:7GWQQTV67VHPMTHKSTDJVLAPFY

not attested not anchored not stored refs pending

Generalizing Magnus' characterization of free groups to some free products

Brandon Seward, Khalid Bou-Rabee

arxiv:1004.0222 v5 · 2010-04-01 · 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{7GWQQTV67VHPMTHKSTDJVLAPFY}

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	2026-05-18T04:24:06.326224Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9ad084ebefd4ef64cea94c69aac0f2e2fbef8a7435069454873a9e82381bfe8

Aliases

arxiv: 1004.0222 · arxiv_version: 1004.0222v5 · doi: 10.48550/arxiv.1004.0222 · pith_short_12: 7GWQQTV67VHP · pith_short_16: 7GWQQTV67VHPMTHK · pith_short_8: 7GWQQTV6

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/7GWQQTV67VHPMTHKSTDJVLAPFY \
  | 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: f9ad084ebefd4ef64cea94c69aac0f2e2fbef8a7435069454873a9e82381bfe8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e18a5412916afe3cbe2c70c8ece0f82e5952df7c3554569f924341f8394d7168",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-04-01T19:57:27Z",
    "title_canon_sha256": "c41895be56295dec4372698f99757e80b15205ae1f147e0cb4ba005043bb420d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0222",
    "kind": "arxiv",
    "version": 5
  }
}