Pith Number

pith:HK5SHV3M

pith:2026:HK5SHV3MUHLI3EYEBHYUOVTSFE

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Geometries with parallel, skew-symmetric and closed torsion

Andrei Moroianu, Paul Schwahn

Riemannian manifolds admitting a metric connection with parallel skew-symmetric closed torsion locally split as products of standard factors.

arxiv:2605.13227 v1 · 2026-05-13 · math.DG

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\pithnumber{HK5SHV3MUHLI3EYEBHYUOVTSFE}

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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 prove that PSCT manifolds always locally split into a product of well-understood factors, allowing a complete local classification.

C2weakest assumption

The manifold admits a metric connection whose torsion is simultaneously parallel, skew-symmetric, and closed; if no such connection exists the classification statement is vacuous.

C3one line summary

PSCT manifolds locally split into products of well-understood factors for complete local classification, with analysis of almost Hermitian G-structures in Gray-Hervella classes.

References

26 extracted · 26 resolved · 4 Pith anchors

[1] I. Agricola, T. Friedrich:On the holonomy of connections with skew-symmetric- symmetric torsion, Math. Ann. 328, 71–748 (2004) 2004

[2] I. Agricola, A. C. Ferreira, T. Friedrich:The classification of naturally reductive homogeneous spaces in dimensionsn≤6, Diff. Geom. Appl. 39, 59–92 (2015) 2015

[3] de Arriba de la Hera, M 2024

[4] On Bismut--Ambrose--Singer manifolds · arXiv:2605.02485

[5] Pluriclosed manifolds with parallel Bismut torsion · arXiv:2406.07039

Receipt and verification

First computed	2026-05-18T02:44:49.620405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3abb23d76ca1d68d930409f14756722910994b5d3649b0e320dfd66b3055ad94

Aliases

arxiv: 2605.13227 · arxiv_version: 2605.13227v1 · doi: 10.48550/arxiv.2605.13227 · pith_short_12: HK5SHV3MUHLI · pith_short_16: HK5SHV3MUHLI3EYE · pith_short_8: HK5SHV3M

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HK5SHV3MUHLI3EYEBHYUOVTSFE \
  | 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: 3abb23d76ca1d68d930409f14756722910994b5d3649b0e320dfd66b3055ad94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ab3042af2112183589c3aa04e6e83bf32f6b1192b17d2740df72113d9ff8731",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-13T09:18:53Z",
    "title_canon_sha256": "29ac3bab9a732db5a083c370f3c12f045e2dea1021964a47bb0b48a99b62538e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13227",
    "kind": "arxiv",
    "version": 1
  }
}