Pith Number

pith:TW6A4F6S

pith:2014:TW6A4F6SUNWBLNNCHWS65KME7U

not attested not anchored not stored refs pending

Finite index subgroups without unique product in graphical small cancellation groups

Alexandre Martin, Dominik Gruber, Markus Steenbock

arxiv:1407.6850 v1 · 2014-07-25 · 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{TW6A4F6SUNWBLNNCHWS65KME7U}

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	2026-05-18T00:44:28.900361Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dbc0e17d2a36c15b5a23da5eea984fd303a89d0322a43c6bd3871f91f2dc50d

Aliases

arxiv: 1407.6850 · arxiv_version: 1407.6850v1 · doi: 10.48550/arxiv.1407.6850 · pith_short_12: TW6A4F6SUNWB · pith_short_16: TW6A4F6SUNWBLNNC · pith_short_8: TW6A4F6S

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/TW6A4F6SUNWBLNNCHWS65KME7U \
  | 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: 9dbc0e17d2a36c15b5a23da5eea984fd303a89d0322a43c6bd3871f91f2dc50d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74d671629678993c3cf4edea5521a8c6d153269d93732805883a9426078ff141",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-07-25T11:08:18Z",
    "title_canon_sha256": "8cb2e50c1e3524d3a00a33f01f63301e8570561a64de06158b3e228d86911684"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.6850",
    "kind": "arxiv",
    "version": 1
  }
}