Pith Number

pith:CK64O7CO

pith:2012:CK64O7COTZDWYPGCBIJKOHXSIM

not attested not anchored not stored refs pending

Finite symmetry group actions on substitution tiling C*-algebras

Charles Starling

arxiv:1207.6301 v3 · 2012-07-26 · math.OA · 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{CK64O7COTZDWYPGCBIJKOHXSIM}

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	2026-05-18T03:16:06.448866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12bdc77c4e9e476c3cc20a12a71ef2431b04f9f4778da3ac35a8f6d6c6fd983d

Aliases

arxiv: 1207.6301 · arxiv_version: 1207.6301v3 · doi: 10.48550/arxiv.1207.6301 · pith_short_12: CK64O7COTZDW · pith_short_16: CK64O7COTZDWYPGC · pith_short_8: CK64O7CO

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/CK64O7COTZDWYPGCBIJKOHXSIM \
  | 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: 12bdc77c4e9e476c3cc20a12a71ef2431b04f9f4778da3ac35a8f6d6c6fd983d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66bdd1c76e0cf5b3fe939b08dd102a340417c6d410e992e902515cb937600934",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-07-26T15:35:19Z",
    "title_canon_sha256": "e0363158d7d033db9646cff085bfb80cc0eaa05cd8bec2b091595d2dca11e3f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6301",
    "kind": "arxiv",
    "version": 3
  }
}