Pith Number

pith:JFMQGO3U

pith:2011:JFMQGO3UPPZFN2M3OM6PTCNPTI

not attested not anchored not stored refs pending

Sofic dimension for discrete measured groupoids

David Kerr, Ken Dykema, Mikael Pichot

arxiv:1111.2842 v2 · 2011-11-11 · math.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JFMQGO3UPPZFN2M3OM6PTCNPTI}

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	2026-05-18T03:41:11.011827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4959033b747bf256e99b733cf989af9a0bb934427470d43e74800644e9c29e6e

Aliases

arxiv: 1111.2842 · arxiv_version: 1111.2842v2 · doi: 10.48550/arxiv.1111.2842 · pith_short_12: JFMQGO3UPPZF · pith_short_16: JFMQGO3UPPZFN2M3 · pith_short_8: JFMQGO3U

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/JFMQGO3UPPZFN2M3OM6PTCNPTI \
  | 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: 4959033b747bf256e99b733cf989af9a0bb934427470d43e74800644e9c29e6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dcf4146bf9d49bcc720bc6e1044d8eb5b69254605f2e5e85f3245fd26a73abd3",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-11-11T20:27:13Z",
    "title_canon_sha256": "ff2b369da2de3acf28552bccffbaa7392b259855a0d133cb606a6a38649ca7e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2842",
    "kind": "arxiv",
    "version": 2
  }
}