Pith Number

pith:JH57O2NF

pith:2026:JH57O2NF75WPJERG5PUDMXRQ2D

not attested not anchored not stored refs pending

Characterization of the alternating and symmetric groups by the order and conjugacy class sizes

Andrey V. Vasil'ev, Ilya Gorshkov

arxiv:2606.29866 v1 · 2026-06-29 · 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{JH57O2NF75WPJERG5PUDMXRQ2D}

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	2026-06-30T02:17:38.878539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49fbf769a5ff6cf49226ebe8365e30d0e03356c0f639c3e33f217e7770b1e44c

Aliases

arxiv: 2606.29866 · arxiv_version: 2606.29866v1 · doi: 10.48550/arxiv.2606.29866 · pith_short_12: JH57O2NF75WP · pith_short_16: JH57O2NF75WPJERG · pith_short_8: JH57O2NF

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/JH57O2NF75WPJERG5PUDMXRQ2D \
  | 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: 49fbf769a5ff6cf49226ebe8365e30d0e03356c0f639c3e33f217e7770b1e44c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07adb90b8b9d3e089e119033b4fb62a8bc428dc800cec30628f1258e52ae66b3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-06-29T07:01:44Z",
    "title_canon_sha256": "5f4bce338f1f06d6bdca296c9485a7f8255aa5899f6ae2f5b82faaf781e55398"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.29866",
    "kind": "arxiv",
    "version": 1
  }
}