Pith Number

pith:UL4XFGH5

pith:2026:UL4XFGH5ECHPV2FSHAHMSYXXBP

not attested not anchored not stored refs pending

Conjugacy of Isometries in Real Orthogonal Groups

Ziyang Zhu

The paper classifies all real orthogonal transformations where linear conjugacy implies orthogonal conjugacy.

arxiv:2605.12083 v2 · 2026-05-12 · math.RT

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\usepackage{pith}
\pithnumber{UL4XFGH5ECHPV2FSHAHMSYXXBP}

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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 determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjugate in the orthogonal group.

C2weakest assumption

The quadratic space is finite-dimensional, non-degenerate, and the base field is the reals; the proof likely relies on standard canonical form theorems for orthogonal matrices over R without additional restrictions stated in the abstract.

C3one line summary

The paper classifies orthogonal transformations over real quadratic spaces such that GL-conjugacy implies O-conjugacy.

Receipt and verification

First computed	2026-06-09T02:08:43.801244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2f97298fd208efae8b2380ec962f70bf6da8b43bcb0a17e43446968603635db

Aliases

arxiv: 2605.12083 · arxiv_version: 2605.12083v2 · doi: 10.48550/arxiv.2605.12083 · pith_short_12: UL4XFGH5ECHP · pith_short_16: UL4XFGH5ECHPV2FS · pith_short_8: UL4XFGH5

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/UL4XFGH5ECHPV2FSHAHMSYXXBP \
  | 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: a2f97298fd208efae8b2380ec962f70bf6da8b43bcb0a17e43446968603635db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1603b6d150b9ecf5c3621c5286176f891c31a815edb7698fb15c5f4896edf182",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-05-12T13:07:22Z",
    "title_canon_sha256": "7a0718b7eeb9b7cb1d83935cdcf0f5c264bca1223f29e5589344214aa91902fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12083",
    "kind": "arxiv",
    "version": 2
  }
}