Pith Number

pith:3BRAAAA3

pith:2018:3BRAAAA3RKTMWSCHSCBF3QVHCM

not attested not anchored not stored refs pending

Cardinality of product sets in torsion-free groups and applications in group algebras

Alireza Abdollahi, Fatemeh Jafari

arxiv:1808.08708 v3 · 2018-08-27 · math.GR · math.NT · math.RA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3BRAAAA3RKTMWSCHSCBF3QVHCM}

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	2026-05-17T23:54:53.907758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d86200001b8aa6cb484790825dc2a71324297df7e273435b2ddf59ad0e3a08ab

Aliases

arxiv: 1808.08708 · arxiv_version: 1808.08708v3 · doi: 10.48550/arxiv.1808.08708 · pith_short_12: 3BRAAAA3RKTM · pith_short_16: 3BRAAAA3RKTMWSCH · pith_short_8: 3BRAAAA3

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/3BRAAAA3RKTMWSCHSCBF3QVHCM \
  | 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: d86200001b8aa6cb484790825dc2a71324297df7e273435b2ddf59ad0e3a08ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcbe021d4b039a60e27626fd185fd54a1b8e888889bfbfaa54b22c7895ef24a2",
    "cross_cats_sorted": [
      "math.NT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-08-27T07:11:38Z",
    "title_canon_sha256": "b8189ff1e1d9a7b88a0a610ca1ac20311e95205ee4f135db230d2e66ec7f0ef4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.08708",
    "kind": "arxiv",
    "version": 3
  }
}