Pith Number

pith:Q5PWXAUE

pith:2026:Q5PWXAUEMOJDAZ3QJFFLVN6ZPY

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The $r^\sharp$ invariant as a discriminant for the survival of the H-flux under T-duality on product manifolds

Alexander Pigazzini, Magdalena Toda

The cohomological invariant r^sharp determines whether the H-flux converts to geometric flux or survives under T-duality on product manifolds.

arxiv:2605.13603 v1 · 2026-05-13 · math.DG

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Claims

C1strongest claim

We show that the cohomological invariant r^sharp, introduced in [1] as a lower bound for the off-diagonal holonomy dimension of metric connections with totally skew torsion on product manifolds, predicts the behaviour of the torsion 3-form under both dimensional reduction and Buscher T-duality.

C2weakest assumption

The manifold is a product M = Σ_g × M_2 equipped with a product metric, and the parallel-form strata are identified via the de Rham splitting theorem when r^sharp = 0.

C3one line summary

r^sharp discriminates between regimes where H-flux survives T-duality or converts to geometric flux on product manifolds with product metrics.

References

9 extracted · 9 resolved · 1 Pith anchors

[1] Cohomological Calibration and Curvature Constraints on Product Manifolds: A Topological Lower Bound 2025 · arXiv:2509.11834

[2] A. Pigazzini, M. Toda,Local topological constraints on Berry curvature in spin–orbit coupled BECs, accepted in JGA (Springer) (2026) 2026

[3] Buscher,A symmetry of the string background field equations, Phys 1987

[4] Buscher,Path integral derivation of quantum duality in nonlinear sigma models, Phys 1988

[5] P. Bouwknegt, J. Evslin, V. Mathai,T-duality: topology change fromH-flux, Com- mun. Math. Phys.249(2004), 383–415 2004

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:22.893354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

875f6b82846392306770494abab7d97e3eee94d7533971ed9095deb64c5a6953

Aliases

arxiv: 2605.13603 · arxiv_version: 2605.13603v1 · doi: 10.48550/arxiv.2605.13603 · pith_short_12: Q5PWXAUEMOJD · pith_short_16: Q5PWXAUEMOJDAZ3Q · pith_short_8: Q5PWXAUE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q5PWXAUEMOJDAZ3QJFFLVN6ZPY \
  | 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: 875f6b82846392306770494abab7d97e3eee94d7533971ed9095deb64c5a6953

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6585dacbcfc9d9956b57d16e5615deecfae3805daaac194fc1c8cfc2470a6a3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-13T14:36:28Z",
    "title_canon_sha256": "067c78b4286308a8955d4f176c934551050029c9c25e449fa3fc7ea3ba63eef4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13603",
    "kind": "arxiv",
    "version": 1
  }
}