Pith Number

pith:7CWOWOTJ

pith:2025:7CWOWOTJ5E4BWPT24MDG2XM4KG

not attested not anchored not stored refs pending

The VC-dimension of random subsets of finite groups

Anurag Sahay, Brad Rodgers

arxiv:2506.14219 v1 · 2025-06-17 · math.CO · math.NT · 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{7CWOWOTJ5E4BWPT24MDG2XM4KG}

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	2026-07-05T11:22:51.193223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8aceb3a69e9381b3e7ae3066d5d9c51938a942938eecae0ccd2cfd84e33c6c1

Aliases

arxiv: 2506.14219 · arxiv_version: 2506.14219v1 · doi: 10.48550/arxiv.2506.14219 · pith_short_12: 7CWOWOTJ5E4B · pith_short_16: 7CWOWOTJ5E4BWPT2 · pith_short_8: 7CWOWOTJ

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/7CWOWOTJ5E4BWPT24MDG2XM4KG \
  | 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: f8aceb3a69e9381b3e7ae3066d5d9c51938a942938eecae0ccd2cfd84e33c6c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "988ba255576620e2adce4eb5e8e22eb6e60dadc566529333fa5e973669f87720",
    "cross_cats_sorted": [
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-17T06:14:30Z",
    "title_canon_sha256": "2e3dab9eb3a21a0a5ddffd5190cef1fb4ee66aca83dd5a88fbe2698d0e8b0e59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.14219",
    "kind": "arxiv",
    "version": 1
  }
}