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what they are:
Nexus says negative energy is 10 less
deathless says it absorbs the first 10points of negative energy
how the fit on your character:
the benefit from the nexus crystal is untyped and nonslotted, while the deathless armor property is tied to armor.
what my question is:
while wearing the armor and holding the crystal, is negative energy reduced by 20pts or 10pts?

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This armor protects its wearer from harmful negative and positive energy, including channeled energy. The armor absorbs the first 10 points of positive or negative energy damage per attack that the wearer would normally take. The wearer has a 25% chance to ignore negative levels from any attack. Deathless armor does not block healing of any kind and does not protect against positive or negative energy effects that do not deal damage or bestow negative levels.
This black crystal feels cold to the touch. Simply carrying this crystal provides protection against negative energy. Whenever the bearer takes damage from negative energy, such as channel energy or an inflict spell, she takes 10 less points of damage. This reduction is applied after any saving throw is made. The crystal may possess other powers, but they are unknown at this time.
Protection from energy grants temporary immunity to the type of energy you specify when you cast it (acid, cold, electricity, fire, or sonic). When the spell absorbs 12 points per caster level of energy damage (to a maximum of 120 points at 10th level), it is discharged.
Protection from energy overlaps (and does not stack with) resist energy. If a character is warded by protection from energy and resist energy, the protection spell absorbs damage until its power is exhausted.
This abjuration grants a creature limited protection from damage of whichever one of five energy types you select: acid, cold, electricity, fire, or sonic. The subject gains resist energy 10 against the energy type chosen, meaning that each time the creature is subjected to such damage (whether from a natural or magical source), that damage is reduced by 10 points before being applied to the creature's hit points.
So, imagine you had Protection from Energy (fire) up with 10 points of absorption remaining, and you were under the effects of Resist Energy (fire). Then you are exposed to 30 points of fire damage from something.
The Protection spell absorbs the first 10 points, then expires. The Resist spell then kicks in, and you resist the next 10. You end up taking 10 points of fire damage.
I believe the Deathless ability and the Nexus Crystal would work the same way (essentially eliminating 20 points or less of negative energy damage). I read Deathless as being akin to Protection from Energy, and the Nexus Crystal as being akin to Resist Energy.

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Deathless wrote:This armor protects its wearer from harmful negative and positive energy, including channeled energy. The armor absorbs the first 10 points of positive or negative energy damage per attack that the wearer would normally take. The wearer has a 25% chance to ignore negative levels from any attack. Deathless armor does not block healing of any kind and does not protect against positive or negative energy effects that do not deal damage or bestow negative levels.Nexus Crystal wrote:This black crystal feels cold to the touch. Simply carrying this crystal provides protection against negative energy. Whenever the bearer takes damage from negative energy, such as channel energy or an inflict spell, she takes 10 less points of damage. This reduction is applied after any saving throw is made. The crystal may possess other powers, but they are unknown at this time.Protection from Energy wrote:Protection from energy grants temporary immunity to the type of energy you specify when you cast it (acid, cold, electricity, fire, or sonic). When the spell absorbs 12 points per caster level of energy damage (to a maximum of 120 points at 10th level), it is discharged.
Protection from energy overlaps (and does not stack with) resist energy. If a character is warded by protection from energy and resist energy, the protection spell absorbs damage until its power is exhausted.
Resist Energy wrote:This abjuration grants a creature limited protection from damage of whichever one of five energy types you select: acid, cold, electricity, fire, or sonic. The subject gains resist energy 10 against the energy type chosen, meaning that each time the creature is subjected to such damage (whether from a natural or magical source), that damage is reduced by 10 points before being applied to the creature's hit points.So, imagine you had Protection from Energy (fire) up with 10 points of absorption remaining, and you were under...
I agree with that interpretation of the rules.