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Hammer the Gap

When you take a full-attack action, each consecutive hit against the same opponent deals extra damage equal to the number of previous consecutive hits you have made against that opponent this turn. This damage is multiplied on a critical hit.

Manyshot

When making a full-attack action with a bow, your first attack fires two arrows. If the attack hits, both arrows hit. Apply precision-based damage (such as sneak attack) and critical hit damage only once for this attack. Damage bonuses from using a composite bow with a high Strength bonus apply to each arrow, as do other damage bonuses, such as a ranger's favored enemy bonus. Damage reduction and resistances apply separately to each arrow.

Emphasis mine

I think the important thing to notice here is that the text says Hammer the Gap is based on the number of hits against the same opponent and Many specifically states that if the attack hits, both arrows hit making it 2 hits. If Hammer the Gap said each consecutive attack Manyshot wouldn't work because it's one attack that hits twice.