FIRST_RUN.md step 3 to go live.Every card is a concept-specific configuration of one mechanic family. Cards are data; families are engine code. A card is playable as soon as its family·mode is implemented.
gear_ratio_gate · math · tuner.formula
Concept: Ratios & proportion
Player does: Set gear tooth counts so the portcullis rises at the target speed
Breaks: Ratios scale by adding the same amount
A ratio scales by multiplying both parts by the same factor, never by adding to them.
percent_shop · math · tuner.formula
Concept: Percent change
Player does: Apply successive markups and discounts to hit an exact price
Breaks: −20% then +20% returns to the start
Successive percent changes multiply, so a 20% drop and a 20% rise do not cancel.
graph_terrain · math · tuner.curve
Concept: Slope & intercept
Player does: Tune m and b so the ramp meets the ledge
Breaks: Slope is run over rise
Slope is rise over run, the vertical change divided by the horizontal change, not the other way around.
projectile_architect · math · tuner.curve
Concept: Quadratics (standard form)
Player does: Tune a, b, c so the arc threads the rings
Breaks: c changes how wide the parabola is
In standard form the leading coefficient a controls the parabola's width, while c only shifts the y-intercept.
move_the_arc · math · tuner.curve
Concept: Vertex form
Player does: Drag h, k, a to move the parabola onto its target
Breaks: (x − 3)² shifts the graph left
In vertex form, (x − h)² shifts the graph right by h, so (x − 3)² shifts right, not left.
reverse_growth · math · tuner.formula
Concept: Logarithms
Player does: Choose how many doublings reach the target population
Breaks: A logarithm is division
A logarithm answers how many times to multiply by the base to reach a value; it is the inverse of exponentiation, not division.
mirror_angles · math · tuner.formula
Concept: Reflection angles
Player does: Set mirror angles so the beam hits the crystal
Breaks: Light bounces straight back off any mirror
Light reflects so the angle of incidence equals the angle of reflection, not straight back unless it hit head-on.
pythagoras_bridge · math · tuner.formula
Concept: Pythagorean theorem
Player does: Cut the plank that spans the diagonal gap
Breaks: The hypotenuse is a + b
The hypotenuse's length is the square root of a² + b², not the simple sum of the legs.
scale_shifter · math · tuner.formula
Concept: Similarity; square-cube law
Player does: Grow ray: double your size, 8× your weight, too big for the gap
Breaks: Doubling length doubles volume
Volume scales with the cube of linear size, so doubling length multiplies volume by eight, not two.
volume_pour · math · tuner.formula
Concept: Volume
Player does: Fill differently shaped tanks to the same volume
Breaks: The taller container holds more
Volume depends on the full shape, not just height, so a shorter but wider container can hold more.
phase_gate · math · tuner.oscillator
Concept: Period
Player does: Dial the period so the vault rings lock
Breaks: A bigger b makes the period longer
The period of sin(bt) is 2π/|b|, so a bigger b squeezes the wave and shortens the period.
pulse_matcher · math · tuner.oscillator
Concept: Frequency
Player does: Match pulses per second to the beacon
Breaks: Frequency and period are the same number
Frequency is the reciprocal of the period: cycles per unit time, not time per cycle.
oscillation_reach · math · tuner.oscillator
Concept: Amplitude
Player does: Set the swing so the platform just touches each checkpoint
Breaks: Amplitude is peak-to-trough
Amplitude is the distance from the midline to a peak, half of the full swing.
wave_alignment · math · tuner.oscillator
Concept: Phase shift
Player does: Slide one wave in time until the peaks align
Breaks: sin(x + π/2) shifts right
Adding inside the argument shifts the graph left, because each output now happens earlier.
arc_builder · math · tuner.formula
Concept: Arc length s = rθ
Player does: Lay rope along the rim; the angle is arc ÷ radius
Breaks: An angle's radian measure depends on the circle's size
Radian measure is arc length divided by radius, so it is the same for any circle.
peak_efficiency · math · tuner.optimize
Concept: Optimization
Player does: Tune the parameter to maximize the machine's output
Breaks: The max is always at an endpoint
An optimum can occur at a critical point in the interior, not just at an endpoint of the domain.
linked_machines · math · tuner.formula
Concept: Related rates
Player does: Set how fast the radius grows so volume rises at the target rate
Breaks: Linked quantities change at the same rate
Related quantities change at rates connected by the chain rule, which usually differ rather than match.
Which socket each family mounts on in each genre (LIBRARY §5). The boss socket is always allowed. Hosts built tonight: dungeon, mystery, platformer.
| Family | Dungeon crawler boss: boss | Investigation adventure boss: accusation | Side-view obstacle course boss: boss | Grid puzzle / escape room boss: boss | Management sim boss: crisis |
|---|---|---|---|---|---|
| Truth Finder | chest / boss Treasure chests; the one bearing the false claim is a mimic | cross_exam / accusation One witness's claim contradicts the facts; object to the lie | gate / boss Three doors; the one with the false claim collapses | tile_board / boss Remove the odd tile to release the chain | event_card / crisis Advisors' claims; the false one tanks a stat |
| Sequencer | door / boss Glyph door pressed in process order | corkboard / accusation Rebuild the timeline on the corkboard | gap / boss Bridge planks in order; the wrong order leaves a gap | conveyor / boss Order the parcels on the conveyor | research_node / crisis Tech tree order |
| Tuner | door / boss Vault rings, catapult, or alchemy dials spinning on the function | lab / accusation Calibrate the instrument; set the lighthouse sweep | moving_platform / gate / boss Saw wheels, launch pads, a balloon that only lifts when tuned | lock / beam_board / boss Dial locks and gear trains | policy_dial / production_line / crisis Machine settings on the production line |
| Mapper | altar / enemy / boss Rune line on the altar floor, or an archery range on a number line | conversation / accusation At the auction, bid the right magnitude; pin the map | gap / boss The floor is a number line; land on the value | tile_board / boss Place the tile at its position on the axis | market / crisis Place goods on the price line |
| Sorter | enemy / boss Type-matched weapons; category-keyed doors | evidence / accusation File claims into case folders | gate / boss Only matching-category platforms are solid | goal_pad / boss Push crates onto category pads | market / crisis Route goods to districts |
| Linker | enemy / boss Chain lightning between pairs | corkboard / accusation String the board | pickup / boss Grapple anchors | pipe_board / boss Flow-style pairing | research_node / crisis Supply links |
| Investigator | door / boss Rooms are hypotheses; clues seal their doors | accusation / corkboard Pin clues, eliminate suspects, accuse | gate / boss Clues seal the doors of eliminated hypotheses | tile_board / boss Logic grid | event_card / crisis Policy debate with evidence |
| Function World | altar / boss Rune track whose floor height is f(x) | lab / accusation Sensor readings converging on a timestamp | gap / boss The terrain is y = f(x); the missing tile | tile_board / boss Track tiles that follow f | market / crisis Price curve over time |
| Balance | altar / boss Alchemy scale; spilled atoms become slimes | archive / accusation The ledger is off by one entry | switch / boss Seesaw bridge | lock / boss Cancel terms, DragonBox-style | ledger / crisis Balance budgets and flows |
| Simulator | enemy / boss Ecology rooms, reactor waves | lab / accusation Keep the patient stable overnight | moving_platform / boss Population or glucose lifts | beam_board / boss Place species so all are fed | crisis / policy_dial Run the economy or ecosystem |
| Builder | forge / boss Craft a molecule, circuit, or golem program | lab / accusation Build the compound or circuit | switch / boss Wire the elevator; word-block bridge | tile_board / boss Valence grid, Lightbot | production_line / crisis Lay out the factory |
| Transformer | forge / boss Crafting-bench machines | lab / accusation Decode the letter or cipher | pickup / gate / boss Power-up machine, cipher platforms | conveyor / pipe_board / boss Route through machines | production_line / crisis Processing chain |
| Accumulator | forge / boss Fill the reservoir to forge the key | archive / accusation Rebuild totals from rate logs | gap / boss Fill the pit; velocity ghost | conveyor / boss Fill tanks | production_line / crisis Output over time |
| Recall | enemy / boss Spells are flashcards, cooldowns are spacing | conversation / accusation Riddle-keeper interrogation | pickup / boss Type the term to double-jump | tile_board / boss Timed word tiles | research_node / crisis Quick recall boosts research |