From Fensome et al., 2019:
Cordosphaeridium? trompetum (Cookson and Eisenack, 1982, p.47, pl.4, fig.22) Lentin and Williams, 1985, p.74. Holotype: Cookson
and Eisenack, 1982, pl.4, fig.22. Originally Polysphaeridium, subsequently (and now) Cordosphaeridium?.
Questionable assignment: Lentin and Williams (1985, p.74). NIA. Age: Paleocene.

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Original description: [Cookson and Eisenack, 1982] (translated from German):

Polysphaeridium trompetum n. sp.
Plate 4, Fig. 22

Type: The specimen shown on Plate 4, Fig. 22 and preserved in specimen Rivernook 26.

Diagnosis: Almost spherical in shape, with numerous short, funnel-shaped, evenly distributed striations. The appendages are very thin-walled and have fine longitudinal striations in the lower cylindrical part, which diverge into the upper, expanded part. A fairly large opening could be an archaeopyle, but this is doubtful.

Material and dimensions: One specimen. Diameter of the spherical shell approx. 81 x 76 μm, length of the appendages approx. 10-14 μm, width of the funnel-shaped opening up to approx. 10 μm.

Occurrence: Rivernook Bed.

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Transfer to Cordosphaeridium: [Lentin and Williams, 1985]:

?trompetum (Cookson and Eisenack, 1982) comb. nov.
1982 Polysphaeridium trompetum Cookson and Eisenack, p.47, p1.4, fig.22.
Paleocene. We herein questionably include this species in Cordosphaeridium.