Pith Number

pith:TKU2INZO

pith:2011:TKU2INZOJNGU6GVAFVIEX72RIP

not attested not anchored not stored refs pending

Logic for metric structures and the number of universal sofic and hyperlinear groups

Martino Lupini

arxiv:1111.0729 v3 · 2011-11-03 · 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{TKU2INZOJNGU6GVAFVIEX72RIP}

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	2026-05-18T01:15:36.708755Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9aa9a4372e4b4d4f1aa02d504bff5143f05258bc34c8774aef73fcb6a23c3169

Aliases

arxiv: 1111.0729 · arxiv_version: 1111.0729v3 · doi: 10.48550/arxiv.1111.0729 · pith_short_12: TKU2INZOJNGU · pith_short_16: TKU2INZOJNGU6GVA · pith_short_8: TKU2INZO

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/TKU2INZOJNGU6GVAFVIEX72RIP \
  | 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: 9aa9a4372e4b4d4f1aa02d504bff5143f05258bc34c8774aef73fcb6a23c3169

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6bddff5943766f0ae6bce2b0d1ac2ecefe68005c58a0caf40d79b768f12e07f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2011-11-03T05:10:48Z",
    "title_canon_sha256": "9989b846c2576e315ec2c5f2c3e1388c7dfaeb579d476ed211fe60c94fb4129a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0729",
    "kind": "arxiv",
    "version": 3
  }
}