Pith Number

pith:RURZU7TG

pith:2025:RURZU7TG77BKTPM3WMPZM3RC4C

not attested not anchored not stored refs pending

Minimal sofic shift on a group that is not finitely-generated

Ville Salo

arxiv:2507.06599 v1 · 2025-07-09 · math.DS · math.GR · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RURZU7TG77BKTPM3WMPZM3RC4C}

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	2026-07-05T11:34:19.210037Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d239a7e66ffc2a9bd9bb31f966e22e08d9594d3e3c7a31c038f685168fc7105

Aliases

arxiv: 2507.06599 · arxiv_version: 2507.06599v1 · doi: 10.48550/arxiv.2507.06599 · pith_short_12: RURZU7TG77BK · pith_short_16: RURZU7TG77BKTPM3 · pith_short_8: RURZU7TG

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/RURZU7TG77BKTPM3WMPZM3RC4C \
  | 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: 8d239a7e66ffc2a9bd9bb31f966e22e08d9594d3e3c7a31c038f685168fc7105

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02761c423e3cf0c90bebd8eab8418f7e816cf52c1934bcdf722eb2bf7059ed05",
    "cross_cats_sorted": [
      "math.GR",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-07-09T07:19:10Z",
    "title_canon_sha256": "18c2df4b6f05781c88166adb18311f72a771f4d5b04bfcfcf7b9b8abc5c37d44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.06599",
    "kind": "arxiv",
    "version": 1
  }
}