Pith Number

pith:Q2N3KKJ7

pith:2013:Q2N3KKJ75QKYEUT3J4K6RQPL2K

not attested not anchored not stored refs pending

Free subalgebras of the skew polynomial rings k[x,y][t;\sigma] and k[x,x^{-1},y,y^{-1}][t;\sigma]

S. Paul Smith

arxiv:1308.1694 v1 · 2013-08-07 · 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{Q2N3KKJ75QKYEUT3J4K6RQPL2K}

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	2026-05-18T03:16:28.032432Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

869bb5293fec1582527b4f15e8c1ebd2a6ee905659922254c494b5a6e0fe1967

Aliases

arxiv: 1308.1694 · arxiv_version: 1308.1694v1 · doi: 10.48550/arxiv.1308.1694 · pith_short_12: Q2N3KKJ75QKY · pith_short_16: Q2N3KKJ75QKYEUT3 · pith_short_8: Q2N3KKJ7

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/Q2N3KKJ75QKYEUT3J4K6RQPL2K \
  | 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: 869bb5293fec1582527b4f15e8c1ebd2a6ee905659922254c494b5a6e0fe1967

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af52cc36ffd89aab6bbe719aebd30446579656133bc36d5a457fb794a798b7e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-08-07T20:50:39Z",
    "title_canon_sha256": "31963f368d596c076c30e8191586f902267179df7802b67fb42025b94a9d476e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.1694",
    "kind": "arxiv",
    "version": 1
  }
}