Pith Number

pith:VJUPFIK4

pith:2026:VJUPFIK4GBXF32PI4LVCA4HV2H

not attested not anchored not stored refs pending

Panmagic permutations and N-ary groups

Jaeho Lee, Sergiy Koshkin

arxiv:2606.22221 v1 · 2026-06-20 · math.CO · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VJUPFIK4GBXF32PI4LVCA4HV2H}

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	2026-06-23T02:13:32.297093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa68f2a15c306e5de9e8e2ea2070f5d1e13ab699e0038e3e54b7b665665c8fe6

Aliases

arxiv: 2606.22221 · arxiv_version: 2606.22221v1 · doi: 10.48550/arxiv.2606.22221 · pith_short_12: VJUPFIK4GBXF · pith_short_16: VJUPFIK4GBXF32PI · pith_short_8: VJUPFIK4

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/VJUPFIK4GBXF32PI4LVCA4HV2H \
  | 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: aa68f2a15c306e5de9e8e2ea2070f5d1e13ab699e0038e3e54b7b665665c8fe6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06da0caa229d2a970199c73da9581ec99ebca46464f11bb5a7e4e617ed4dd97f",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-20T20:49:37Z",
    "title_canon_sha256": "fe9fe0f8bbe35269516f255fc6a5a69c1f75526573738ed95d6fd149437bdade"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.22221",
    "kind": "arxiv",
    "version": 1
  }
}