Pith Number

pith:OVGDJONJ

pith:2025:OVGDJONJAQQSLUEBEWC4RXZS7F

not attested not anchored not stored refs pending

Determining subgroups via stationary measures

Andrew Zimmer, Dongryul M. Kim

arxiv:2512.12966 v4 · 2025-12-15 · math.GT · math.DS · math.GR · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OVGDJONJAQQSLUEBEWC4RXZS7F}

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	2026-07-13T01:20:04.915625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

754c34b9a9042125d0812585c8df32f94fac98cea444d52512214b3c9558b929

Aliases

arxiv: 2512.12966 · arxiv_version: 2512.12966v4 · doi: 10.48550/arxiv.2512.12966 · pith_short_12: OVGDJONJAQQS · pith_short_16: OVGDJONJAQQSLUEB · pith_short_8: OVGDJONJ

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/OVGDJONJAQQSLUEBEWC4RXZS7F \
  | 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: 754c34b9a9042125d0812585c8df32f94fac98cea444d52512214b3c9558b929

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c2ca7e8021cf4741f38968265081057a196567df3b33e6e0637f2411e77f579",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2025-12-15T04:08:02Z",
    "title_canon_sha256": "578462201be99ea0b7e83c6fc0de73e90c61f3004f3798b19ec2813e3fada999"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.12966",
    "kind": "arxiv",
    "version": 4
  }
}