Arithmetic Soul (5e Subclass)

Arithmetic Soul

Sorcerer Subclass

Your mind has been opened to the great Universal Equation which suffuses the multiverse. In all things you catch glimpses of arithmetic expressions guiding their workings. With this aptitude comes the ability to manipulate the Weave, the raw fabric of magic, to subtly tweak the laws of physics and fate according to mathematical principles.

Arithmagic Spells

Starting at 1st level, you learn additional spells when you reach certain levels in this class, as shown on the Arithmagic Spells table. Each of these spells counts as a sorcerer spell for you, but it doesn't count against the number of sorcerer spells you know. These spells can’t be replaced when you gain a level in this class.
Whenever you gain a sorcerer level, you can replace one spell you gained from this feature with another spell of the same level. The new spell must be a divination or transmutation spell from the bard, sorcerer, or wizard spell list.
Additionally, you may choose to use Intelligence in place of Charisma as your spellcasting ability for your sorcerer spells, owing to the fact that your magic is derived from your understanding of the Universal Equation. You can use your Intelligence whenever a spell refers to your spellcasting ability and your Intelligence modifier when setting the saving throw DC for a sorcerer spell you cast and when making an attack roll with one.

Arithmagic Spells

Sorcerer Level	Spells
1st	catapult, identify, magnify gravity
3rd	enlarge/reduce, immovable object
5th	blink, slow
7th	divination, fabricate
9th	telekinesis, wall of force

Mathematical Magic

Starting at 1st level, whenever you finish a long rest, choose an Expression from the Universal Equation table that has a corresponding number less than or equal to your sorcerer level. You may use this Expression once, after which you must complete a long rest to do so again. You may also regain a use of this Expression when you complete a short rest by expending a number of sorcery points equal to half of the chosen Equation's number, rounded up. You can only have one Expression chosen this way at a time.

Numerical Insights

Beginning at 6th level, the pattern of the universe becomes clear to you in bursts, according to your study of sacred geometry. You gain an Equation die, a d6, which you roll before choosing your mathematical magic effect at the end of a long rest. Record the number rolled; you can expend an Equation die to use the Expression corresponding to the number rolled on that die once.
When you gain certain levels in this class, you acquire additional Equation dice. You gain a d8 at 8th level, a d10 at 10th, and a d12 at 12th.

Universal Equation Table

Number	Expression Name	Effect Description
1	Arcane Addition	When a creature within 30 feet that you can see makes an ability check or saving throw, you use your reaction to let it roll 1d4 and add the number rolled to the result. You must decide to do so before the roll is made.
2	Arcane Subtraction	When a creature within 30 feet that you can see makes an ability check or saving throw, you use your reaction to force it to roll 1d4 and subtract the number rolled from the result. You must decide to do so before the roll is made.
3	Stable Constant	When you make an ability check or saving throw, you use a 12 in place of your d20 roll. You must decide to do so before making the roll.
4	Probability Collapse	When you make a saving throw, you call a coin flip to determine the result. You can choose to do so after seeing the result of the roll, but before learning whether it succeeds or fails.
5	Equivalent Reprisal	When you take damage from a creature that is within 10 feet of you, you use your reaction to emanate magical energy. The creature that dealt damage to you must make a Strength saving throw against your spell save DC. On a failed save, the creature is pushed up to 10 feet away from you.
6	Derivative Deduction	You gain truesight out to a range of 60 feet until the start of your next turn.
7	Numeric Bane	When you or a creature you can see within 60 feet of you makes an attack roll, ability check, or saving throw, you impose disadvantage on that roll using your reaction. You must decide to do so before the roll is made. If the roll succeeds, you do not expend a use of this feature.
8	Numeric Boon	When you or a creature you can see within 60 feet of you makes an attack roll, ability check, or saving throw, you give advantage on that roll using your reaction. You must decide to do so before the roll is made. If the roll fails, you do not expend a use of this feature.
9	Multiplicative Force	When you hit a target with a spell attack that isn't a critical hit, it becomes one.
10	Vector Acceleration	When you cast a line spell, creatures in its area are forcibly pushed 10 feet directly away from the origin point.
11	Unstable Variable	When you or a creature you can see within 30 feet makes an attack roll, ability check, or saving throw, you can force it to reroll the result using your reaction. You can choose to do so after you see whether it succeeds or fails. The target must use the result of the second roll.
12	Power Exponentiation	When you cast a spell using a spell slot higher than its minimum level, the range of the spell increases by 10 feet per spell slot level above minimum (unless it has a range of self), and you can cause one creature affected by the spell to either take 1d8 force damage or gain 1d8 temporary hit points per level above minimum.
13	Esoteric Superaddition	When a creature within 60 feet that you can see makes an ability check or saving throw, you use your reaction to let it roll 2d4 and add the number rolled to the result. You can choose to do so after you see whether it succeeds or fails.
14	Esoteric Supersubtraction	When a creature within 60 feet that you can see makes an ability check or saving throw, you use your reaction to force it to roll 2d4 and subtract the number rolled from the result. You can choose to do so after you see whether it succeeds or fails.
15	Resonant Nullification	If the target of a spell you cast is affected by any other spells, you learn what those spells are, and you can end the effects of one a spell of your choice on the target by spending a number of sorcery points equal to the spell's level.
16	Divide By Zero	As a reaction at the end of a turn, each creature of your choice within 120 feet of you takes 50 force damage.
17	Scaled Norm	For 1 minute, whenever you make an attack roll, ability check, or saving throw, you can treat a d20 roll of less than half your sorcerer level, rounded down, as a 12.
18	Transformation Matrix	You transform sorcery points into a spell slot with a level equal to the number of points expended (no action required). You may create spell slots up to 8th level this way, and these spell slots vanish after you complete a long rest.
19	Unbound Operator	When you make an ability check or saving throw, you use 4d6 in place of your d20 roll. You can decide to do so after rolling and seeing if you succeed or fail.
20	Universal Epiphany	You gain 20 sorcery points. These can exceed your normal limit for sorcery points, and disappear if not spent after you complete a Short or Long Rest.

Note: Unless specified otherwise, an Expression doesn't require an action to use.

Functional Metamagic

At 14th level, you gain access to the following Metamagic options:

Iterative Spell

When you cast a spell that requires you to make an attack roll and you miss, you can spend 2 sorcery points to remake the attack roll. You may do so multiple times for the same spell, paying a cumulative +1 sorcery point cost each time you do so.

You can use Iterative Spell even if you have already used a different Metamagic option during the casting of the spell.

Harmonic Spell

When you cast a spell that has a casting time of 1 action or 1 bonus action and that you also cast on your last turn, you can spend a number of sorcery points equal to half the spell's minimum level, rounded down, to cast the spell as though you had used a spell slot 1 level higher than the one used to cast the spell. You can't use this Metamagic option with cantrips or 9th-level spells.

Linear Spell

When you cast a spell that effects an area defined by a radius centered on a point, you can spend 1 sorcery point to cause the spell's area to instead become a 10-foot wide line originating from you with a length equal to twice the normal radius of the spell.

Transcendent Spell

When you cast a spell, you can spend 1 sorcery point to cause the spell to effect targets on both the Ethereal and Material Planes as if they were on the same plane as you.

You can use Transcendent Spell even if you have already used a different Metamagic option during the casting of the spell.

Prime Protection

Starting at 18th level, when the result of your d20 roll for a saving throw is a prime number (1, 2, 3, 5, 7, 11, 13, 17, or 19), you gain an amount of temporary hit points equal to 25 minus the number rolled; this occurs before any other effects of making the saving throw.

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