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2 about fundamental usage
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This is defined on Tome of Magic pg. 117:

PRESTIGE CLASS CASTING ADVANCEMENTS

When a shadowcaster gains new casting class levels from advancement within a prestige class, this includes the knowledge of new fundamentals, and the transformation of lower-level path mysteries into spell-like or supernatural abilities. It does not include gaining bonus feats for learning new paths or any other shadowcaster class features.

So yes, you get initiate and master paths as normal for a shadowcaster of a level equal to your shadowcaster level plus master of shadow level minus 1. Unfortunately, the question of whether or not your fundamentals grow in usage frequency is unclear: it specifies “knowledge of new fundamentals,” but not improvements in using fundamentals in general. It is probably intended to be included, since it’s from the same shadowcaster class feature, and because it would be inane to not include it, but you’ll have to double-check that with your DM.

This is defined on Tome of Magic pg. 117:

PRESTIGE CLASS CASTING ADVANCEMENTS

When a shadowcaster gains new casting class levels from advancement within a prestige class, this includes the knowledge of new fundamentals, and the transformation of lower-level path mysteries into spell-like or supernatural abilities. It does not include gaining bonus feats for learning new paths or any other shadowcaster class features.

So yes, you get initiate and master paths as normal for a shadowcaster of a level equal to your shadowcaster level plus master of shadow level minus 1.

This is defined on Tome of Magic pg. 117:

PRESTIGE CLASS CASTING ADVANCEMENTS

When a shadowcaster gains new casting class levels from advancement within a prestige class, this includes the knowledge of new fundamentals, and the transformation of lower-level path mysteries into spell-like or supernatural abilities. It does not include gaining bonus feats for learning new paths or any other shadowcaster class features.

So yes, you get initiate and master paths as normal for a shadowcaster of a level equal to your shadowcaster level plus master of shadow level minus 1. Unfortunately, the question of whether or not your fundamentals grow in usage frequency is unclear: it specifies “knowledge of new fundamentals,” but not improvements in using fundamentals in general. It is probably intended to be included, since it’s from the same shadowcaster class feature, and because it would be inane to not include it, but you’ll have to double-check that with your DM.

1
source | link

This is defined on Tome of Magic pg. 117:

PRESTIGE CLASS CASTING ADVANCEMENTS

When a shadowcaster gains new casting class levels from advancement within a prestige class, this includes the knowledge of new fundamentals, and the transformation of lower-level path mysteries into spell-like or supernatural abilities. It does not include gaining bonus feats for learning new paths or any other shadowcaster class features.

So yes, you get initiate and master paths as normal for a shadowcaster of a level equal to your shadowcaster level plus master of shadow level minus 1.