Pith Number

pith:YAWKKH2D

pith:2026:YAWKKH2DOHOGTFLLISIA742E2T

not attested not anchored not stored refs pending

The geometry of wreath and semi-direct products

Claudio Alexandre Piedade, Philippe Tranchida

Twisting and wreath products extend to coset geometries while preserving flag-transitivity, residual-connectedness and thinness, yielding regular polytopes and hypertopes for almost-simple groups with sporadic socles.

arxiv:2605.04646 v2 · 2026-05-06 · math.GR · math.CO

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\usepackage{pith}
\pithnumber{YAWKKH2DOHOGTFLLISIA742E2T}

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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.

Claims

C1strongest claim

we show that there exists regular polytopes and hypertopes for almost-simple group with socle a sporadic simple group.

C2weakest assumption

That the twisting and wreath product operations can be defined on arbitrary coset geometries so that flag-transitivity, residual-connectedness, and thinness are automatically preserved.

C3one line summary

Twisting and wreath products extend to coset geometries preserving key properties, enabling regular polytopes and hypertopes for almost-simple groups with sporadic socles.

Receipt and verification

First computed	2026-05-29T02:05:46.018672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c02ca51f4371dc69956b44900ff344d4ee2acc3e4219a86bc3f8bdf404c42cb4

Aliases

arxiv: 2605.04646 · arxiv_version: 2605.04646v2 · doi: 10.48550/arxiv.2605.04646 · pith_short_12: YAWKKH2DOHOG · pith_short_16: YAWKKH2DOHOGTFLL · pith_short_8: YAWKKH2D

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/YAWKKH2DOHOGTFLLISIA742E2T \
  | 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: c02ca51f4371dc69956b44900ff344d4ee2acc3e4219a86bc3f8bdf404c42cb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2932158df3b3670630a1f4b083861b6d86bda5a1b5e4ecc0ea952dcc0aa2e4e5",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-06T08:52:07Z",
    "title_canon_sha256": "ebf278da6723c338feea66c033231e746d0ef68a19198c5d436d5c33b7d381c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04646",
    "kind": "arxiv",
    "version": 2
  }
}