Pith Number

pith:GANB42IC

pith:2014:GANB42ICUWHDUS7EHE6VAKYK6P

not attested not anchored not stored refs pending

Invariant Coupling of Determinantal Measures on Sofic Groups

Andreas Thom, Russell Lyons

arxiv:1402.0969 v2 · 2014-02-05 · math.PR · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GANB42ICUWHDUS7EHE6VAKYK6P}

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	2026-05-17T23:53:35.086339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

301a1e6902a58e3a4be4393d502b0af3f1554de4b2aafe8fd158916c389822cc

Aliases

arxiv: 1402.0969 · arxiv_version: 1402.0969v2 · doi: 10.48550/arxiv.1402.0969 · pith_short_12: GANB42ICUWHD · pith_short_16: GANB42ICUWHDUS7E · pith_short_8: GANB42IC

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/GANB42ICUWHDUS7EHE6VAKYK6P \
  | 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: 301a1e6902a58e3a4be4393d502b0af3f1554de4b2aafe8fd158916c389822cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7981d40052e1129355848a43ee1231bc20b6465004311b3f85fffe51ba83b389",
    "cross_cats_sorted": [
      "math.GR",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-02-05T08:34:11Z",
    "title_canon_sha256": "32fecda533ebc747c56e72b70b65b57dfc7d63046bd8f3d0796321c2504d27b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.0969",
    "kind": "arxiv",
    "version": 2
  }
}