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From the Dyson Sphere Program Wiki

Proliferator Bonuses

Items with Proliferator marks receive various bonuses depending on the type of activity they are involved in. The amount of the bonus depends either on the Proliferator's Production Speedup or Extra Products parameter. Some of the activities also apply the item's Energy Consumption penalty to the building that processes the item.

Activity Bonuses Energy Penalty

Production Any production building (except the Fractionator) can get either Production Speedup or Extra Products bonus if all the recipe ingredients have the same-tier Proliferator mark, depending on the building settings, chosen by the player (the default is Extra Products). If one of the ingredients has lower-tier mark or no mark, the lowest or no bonus will be applied.

The exception is the production of Antimatter, Antimatter Fuel Rod and buildings that take other buildings as the ingredients (such as Mk.II and Mk.III Belts, Sorters or Assembling Machines. Production of these can only benefit from the Production Speedup bonus of the Proliferator.

The Production Speedup bonus is multiplicative with the building's Crafting Speed. For example, applying Proliferator Mk.III to an Assembling Machine Mk.III will result in Crafting Speed of 3 (+100% out of the building's 1.5).

Yes
Research When used in Research, proliferated Matrices produce bonus hashes according to the Proliferator's Extra Products bonus. Yes
Fractionation Proliferated Hydrogen will increase the Fractionator's conversion rate by the Proliferator's Production Speedup bonus. For example, a Proliferator Mk.III will yield a 2% conversion rate (+100%).

Note that passing through Fractionator does not remove the Proliferator marks from the Hydrogen unless it gets converted.

Yes
Proliferators Spraying the Proliferator itself gives more sprays in the Spray Coater, increased by the amount of Extra Products bonus. It's always worth it. No
Power Generation
(Dyson Sphere)
Proliferated Graviton Lenses increase Ray Receiver's maximum power collection rate by the Proliferator's Production Speedup bonus. This applies to both Power Generation and Photon Generation modes.

The Proliferator bonus is multiplicative with the innate bonus of the Lens, therefore using a Lens sprayed with the Proliferator Mk.III would result in 400% of the baseline generation (200% with Lens × Proliferator bonus)

No
Power Generation
(Generic Fuel)
Proliferated fuels (except Antimatter Fuel Rods and Full Accumulators) increase both the Fuel's energy capacity and the Power Generator's power output by the Proliferator's Extra Products bonus.

When burnt in the Mecha's Fuel Chamber, the Extra Products bonus applies to the Fuel Chamber Generation rate. The bonus is multiplicative with the Fuel's native Fuel Chamber Generation bonus, thus resulting in, for example, 187.5% Generation for Energetic Graphite with Proliferator Mk.III mark (150% × 1.25).

No
Power Generation
(Antimatter)
Proliferated fuels Antimatter Fuel Rods only increase the Artificial Star's power output, but by the amount of the Proliferator's Production Speedup bonus. It does not alter the Rod's fuel capacity, thus resulting in faster burn rate.

When burnt in the Mecha's Fuel Chamber, the bonus applies to the Fuel Chamber Generation rate instead. It is multiplicative to the innate bonus, thus resulting in 1200% Fuel Chamber Generation.

No
Full Accumulator Similar to Antimatter Fuel Rods, Full Accumulators get their Fuel Chamber Generation rate affected by the Proliferator's Production Speedup bonus, but only in the Mecha's Fuel Chamber.

Other Accumulator's abilities to store and transfer power are unaffected by the Proliferator bonuses in any way.

No
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