Pith Number

pith:2UM3CBWR

pith:2019:2UM3CBWRRU7YEU3UJAMWL43CM3

not attested not anchored not stored refs pending

The Ellis semigroup of bijective substitutions

Johannes Kellendonk, Reem Yassawi

arxiv:1908.05690 v3 · 2019-08-15 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2UM3CBWRRU7YEU3UJAMWL43CM3}

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	2026-07-05T01:54:41.135652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d519b106d18d3f825374481965f36266c8a44bab7e24fc5edd78be89242480d6

Aliases

arxiv: 1908.05690 · arxiv_version: 1908.05690v3 · doi: 10.48550/arxiv.1908.05690 · pith_short_12: 2UM3CBWRRU7Y · pith_short_16: 2UM3CBWRRU7YEU3U · pith_short_8: 2UM3CBWR

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/2UM3CBWRRU7YEU3UJAMWL43CM3 \
  | 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: d519b106d18d3f825374481965f36266c8a44bab7e24fc5edd78be89242480d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd721ec9797a41161ba8543c78546403040fe31d3ff2ed20933bafd3bb5ecbfd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-08-15T18:04:03Z",
    "title_canon_sha256": "2e59f47bb476c826c3b4d968b225b31ae23a9b8c31887ded8edd2d85de670dd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.05690",
    "kind": "arxiv",
    "version": 3
  }
}