LOREBOOK: MATH HANDLING

Trigger words: coherence load, soul resilience, overflow, stack penalty, cross-domain, CL, SR, calculation, math, formula, fusion math, star sum, chip cost, concept cost, resilience, overflow tier, stable, partial success, mixed success, catastrophic

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PURPOSE

This lorebook contains every formula the Arbiter uses to evaluate fusion attempts, soul status, and progression mechanics. It is the authoritative mathematical reference for the Conceptual Deck system. When a fusion is attempted, the Arbiter pulls from this lorebook to calculate outcomes with precision and transparency.

All math is shown openly to the player. The numbers are not hidden. The player deserves to understand exactly why an outcome occurred.

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CORE VARIABLES

Before any calculation begins, the Arbiter identifies and states the following values:

Components: the list of distinct carded items, overlays, and conceptual inputs entering the fusion. Each component has a star level (S) from 1 to 10.

N: the total count of distinct components and overlays being applied simultaneously to the same target.

SumStars: the arithmetic sum of all component star levels.

StackPenalty: the nonlinear cost of applying multiple components simultaneously.

CrossDomainMismatches: the count of incompatible ontological categories present in the fusion. Categories are: living, inanimate, location, abstract. Each pairing of incompatible categories counts as one mismatch.

CL (Coherence Load): the total pressure the fusion places on the system.

SR (Soul Resilience): the player's current tolerance for coherence pressure.

Overflow: the difference between CL and SR. The primary determinant of outcome tier.

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FORMULA 1 — COHERENCE LOAD (CL)

CL = SumStars + StackPenalty + CrossDomainMismatches

SumStars:

SumStars = S₁ + S₂ + S₃ + ... + Sₙ

Add every component's star level together. Simple arithmetic. No weighting.

StackPenalty:

StackPenalty = (N − 1)²

N is the number of distinct components. The penalty is nonlinear — stacking grows expensive fast. Two components produce a penalty of 1. Three components produce 4. Four produce 9. Five produce 16. This is intentional. Brute-force stacking is mechanically punished. Elegant low-component fusions are mechanically rewarded.

CrossDomainMismatches:

CrossDomainMismatches = count of incompatible ontological category pairings present

The four ontological categories are: living, inanimate, location, abstract.

Any pairing of categories that don't share a register counts as one mismatch. Evaluate all pairings present in the fusion, not just adjacent ones.

Examples:

• Inanimate + inanimate: 0 mismatches
• Living + inanimate: 1 mismatch
• Living + inanimate + abstract: 2 mismatches (living/inanimate, living/abstract — inanimate and abstract share no special incompatibility by default, but the Arbiter may rule otherwise based on context)
• Living + location: 1 mismatch
• Living + inanimate + location + abstract: up to 4 mismatches depending on pairings

The Arbiter evaluates cross-domain mismatches based on the specific components involved and the setting's logic. The count is stated explicitly before CL is calculated.

Self-Application modifier: When the player is the target of the fusion — their own body, mind, or soul is a substrate — double the CrossDomainMismatches value before adding to CL.

CL (self) = SumStars + StackPenalty + (CrossDomainMismatches × 2)

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FORMULA 2 — SOUL RESILIENCE (SR)

SR = SR_base + CardSlots + floor(HistoricalHighestStar / 2)

SR_base: 6. Fixed. Does not change except through soul scars (which reduce it permanently).

CardSlots: the player's current total card slot count. Starts at 3. Increases through star progression. Can decrease through catastrophic failure.

HistoricalHighestStar: the highest star level the player has ever carded, regardless of whether that card is still held. This value only ever increases — losing a card does not reduce historical highest star.

floor(): round down to the nearest integer. HistoricalHighestStar of 1 or 2 contributes 0. Star 3 or 4 contributes 1. Star 5 or 6 contributes 2. And so on.

SR at baseline (fresh player):

SR = 6 + 3 + floor(1/2) = 6 + 3 + 0 = 9

SR growth example (experienced player): Player has 6 card slots, historical highest star of 7:

SR = 6 + 6 + floor(7/2) = 6 + 6 + 3 = 15

SR is recalculated at the start of every fusion attempt. Soul scars reduce SR_base permanently — the Arbiter applies accumulated scars before calculating SR for any given attempt.

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FORMULA 3 — OVERFLOW

Overflow = CL − SR

If CL ≤ SR, Overflow = 0. The fusion is stable.

If CL > SR, Overflow = CL − SR. The fusion enters risk territory.

Overflow determines the outcome tier (see Outcome Tiers below).

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FORMULA 4 — CONCEPT CHIP COST

MinimumChipCost = star level of the highest-star component in the fusion

This is the minimum number of concept chips required to justify the fusion. Each chip must match the star level of the fusion link it justifies.

In practice: a fusion combining a ★3 component and a ★5 component requires at minimum one ★5 concept chip to proceed to Phase 2. Lower-star chips cannot substitute for higher-star requirements — a ★3 chip cannot justify a ★5 fusion link.

Additional chips beyond the minimum may be spent to strengthen the conceptual overlay, add secondary effects, or address specific conceptual gaps in the fusion design. Each additional chip consumed adds to the conceptual richness of the result but does not reduce CL.

Chips are consumed at Phase 2 declaration. They are non-refundable on failure.

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FORMULA 5 — SLOT PROGRESSION

New slot granted IF: NewCardStar > HistoricalHighestStar

One slot is granted per new historical high. The same star tier cannot trigger a second slot. The slot is granted immediately before the card occupies it.

Updated HistoricalHighestStar = max(current historical highest, new card star)

Slot loss from catastrophic failure does not reset historical highest star. The record of growth persists. The capacity does not.

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OUTCOME TIERS — FULL REFERENCE

Tier 0 — Stable

Condition: Overflow ≤ 0

The fusion succeeds as designed. All chips consumed as declared. Physical and conceptual costs applied normally. No soul damage.

Soul scar: none. SR change: none. Card status: unchanged. Anomaly: none.

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Tier 1 — Partial Success

Condition: Overflow 1–3

The primary effect occurs. The fusion functions. A significant side effect accompanies it — an instability, a limitation, a degradation of one component of the result, or an unintended secondary behavior. The side effect is a direct mechanical or conceptual consequence of the specific overflow, not a random penalty.

Soul scar: −1 SR_base. Permanent. SR change: −1 (applied immediately, affects all future calculations). Card status: result card may carry a minor instability flag. Anomaly: none typically, though environmental residue is possible at the high end of this range.

The Arbiter names the side effect specifically and explains which component interaction caused it.

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Tier 2 — Mixed Success

Condition: Overflow 4–6

The fusion produces something, but not reliably what was intended. The result exists but exhibits unexpected behaviors. Consequences may delocalize — effects spread beyond the target to the environment, nearby entities, or other carded items. Card corruption is possible at this tier.

Soul scar: −2 SR_base. Permanent. SR change: −2. Card status: possible corruption. The Arbiter evaluates whether the result card, a component card, or both develop anomalous properties or behavioral drift. Anomaly: possible if consequences delocalize into the environment persistently.

The Arbiter describes what emerged rather than what was intended. The causal chain — which concepts conflicted, which substrates failed to hold — is stated explicitly.

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Tier 3 — Catastrophic Failure

Condition: Overflow 7+

The fusion backfires. The intended result does not form, or forms in a severely and dangerously distorted state. Severe consequences discharge into the player's body, soul, the environment, or all three simultaneously. An anomaly almost certainly forms.

Soul scar: −3 SR_base minimum. Permanent. Severity scales with overflow beyond 7 — overflow of 10 produces −4 SR_base, overflow of 14+ produces −5 SR_base. The Arbiter applies judgment at the extreme end. SR change: −3 minimum. Card status: one or more involved cards likely corrupted or destroyed. Possible permanent loss of one card slot. Anomaly: near-certain. The anomaly is assigned a star rating based on the energy of the failure — typically equal to the highest-star component involved, sometimes higher.

The Arbiter names the anomaly, gives it a physical description and behavioral signature, assigns its star, and adds it to the anomaly ledger. The soul scar is described in terms of what part of the player's identity or resilience was damaged and how that expresses going forward.

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SELF-APPLICATION MODIFIERS (SUMMARY)

| Parameter | Normal | Self-Application | |-----------|--------|-----------------| | CrossDomainMismatches | Standard count | × 2 | | Soul scar severity | Standard tier | +1 tier | | Overflow tier | Standard | Standard (CL/SR unchanged except via doubled cross-domain) |

Self-application is permitted at all times. The Arbiter calculates it accurately and presents the full math before the player commits. The confirmation prompt is mandatory:

"This fusion targets you directly. Cross-domain mismatches are doubled. Soul scar severity is one tier higher than the overflow would normally produce. The math is as follows: [display calculation]. Do you proceed?"

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WORKED EXAMPLES

Example A — Baseline fresh player, low-star fusion

Components: Lighter (★1), Hairspray (★1), Super Soaker (★1) N = 3, SumStars = 3, StackPenalty = (3−1)² = 4, CrossDomain = 0 CL = 3 + 4 + 0 = 7

SR: SR_base=6, CardSlots=3, HistoricalHighest=1, floor(1/2)=0 SR = 6 + 3 + 0 = 9

Overflow = 7 − 9 = −2 → Stable

Minimum chip cost: ★1 (highest component). Chips required: at minimum one ★1 chip per fusion link. Result: fusion succeeds cleanly. No soul damage.

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Example B — Mid-tier fusion, experienced player

Components: Medieval siege mechanism (★4), Modern explosive primer (★5) N = 2, SumStars = 9, StackPenalty = (2−1)² = 1, CrossDomain = 0 CL = 9 + 1 + 0 = 10

SR: SR_base=6, CardSlots=5, HistoricalHighest=5, floor(5/2)=2 SR = 6 + 5 + 2 = 13

Overflow = 10 − 13 = −3 → Stable

Minimum chip cost: ★5. Player must have at least one ★5 concept chip to proceed.

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Example C — Reckless high-star stack

Components: Ancient sword (★7), Living flame elemental (★6), Cursed mirror (★5), Abstract concept of Time (★8) N = 4, SumStars = 26, StackPenalty = (4−1)² = 9 CrossDomain: inanimate (sword) + living (elemental) + inanimate (mirror) + abstract (time) = 2 mismatches (living/inanimate, living/abstract) CL = 26 + 9 + 2 = 37

SR: SR_base=4 (2 soul scars accumulated), CardSlots=6, HistoricalHighest=8, floor(8/2)=4 SR = 4 + 6 + 4 = 14

Overflow = 37 − 14 = 23 → Catastrophic Failure

Soul scar: −5 SR_base (overflow far exceeds tier 3 threshold). Near-certain anomaly. Likely card slot loss. The Arbiter does not proceed without explicitly stating this math and requesting confirmation.

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Example D — Self-application, moderate components

Player fuses a healing salve (★3) with their own wounded arm (★3 as a living body part of a soul-tethered individual). N = 2, SumStars = 6, StackPenalty = 1 CrossDomain: inanimate (salve) + living (arm) = 1 mismatch. Self-application doubles: 2. CL = 6 + 1 + 2 = 9

SR: SR_base=5 (one prior scar), CardSlots=4, HistoricalHighest=4, floor(4/2)=2 SR = 5 + 4 + 2 = 11

Overflow = 9 − 11 = −2 → Stable

Soul scar: none. Self-application at stable overflow is clean, though the doubled cross-domain penalty narrowed the margin. One more component and this tips into partial success.

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ARBITER DISPLAY FORMAT

When resolving any fusion, the Arbiter displays the math in this format before narrating the outcome:

FUSION MATH
─────────────────────────────
Components: [list each with star]
SumStars: [value]
N: [value] → StackPenalty: [value]
CrossDomain mismatches: [count] [list pairings]
Self-application modifier: [yes/no — if yes, CrossDomain ×2]

CL = [SumStars] + [StackPenalty] + [CrossDomain] = [total]

SR = [SR_base] + [CardSlots] + floor([HistoricalHighest]/2) = [total]

Overflow = [CL] − [SR] = [value]
Outcome tier: [Stable / Partial Success / Mixed Success / Catastrophic Failure]

Minimum chip cost: ★[value]
─────────────────────────────

This display precedes the narrative outcome. It is not optional. It is how the system maintains transparency and internal consistency.

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ARBITER ROUNDING AND EDGE CASES

Floor function: always round down. floor(3/2) = 1, not 1.5 and not 2. This applies only to the HistoricalHighestStar component of the SR formula.

Zero components: a fusion with zero components cannot exist. Minimum fusion requires two inputs.

Negative overflow: treated as zero for outcome purposes. Overflow of −5 and overflow of 0 both produce a Stable outcome. The margin of safety does not grant bonus effects.

Fractional stars: star levels are always integers 1–10. There are no half-stars. If an edge case produces a fractional star through some unusual mechanic, round to the nearest integer, rounding up on 0.5.

SR floor: SR cannot fall below 1 through soul scars alone. SR_base minimum is 1. At SR_base = 1 with no card slots and a ★1 historical highest, SR = 1 + 0 + 0 = 1. A player at this state is extremely fragile. The Arbiter notes this condition explicitly and warns that any fusion with CL ≥ 2 enters overflow territory.

SR of zero or negative: if SR would calculate to 0 or below through some combination of conditions, treat SR as 1. The soul tether is fraying but not severed. The Arbiter treats this as a critical state and narrates accordingly.