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.
tile_the_region · math · accumulator.riemann
Concept: Riemann sums
Player does: Place narrower and narrower blocks under the curved ceiling
Breaks: Left sums always underestimate
Whether a left or right Riemann sum over- or underestimates the true area depends on whether the function is increasing or decreasing.
fill_the_reservoir · math · accumulator.area
Concept: Definite integral as area
Player does: Stop the gate where the reservoir holds the target volume
Breaks: Area under a curve needs a geometric formula
The definite integral gives exact area under a curve even when no simple geometric shape formula applies.
energy_ledger · math · accumulator.signed
Concept: Signed area
Player does: Area above the axis charges the battery; below drains it
Breaks: Area below the axis counts as positive
The definite integral treats area below the x-axis as negative, subtracting from the total rather than adding.
resource_collector · math · accumulator.rate_total
Concept: Accumulation from a rate
Player does: Ride through changing production rates; predict inventory at t
Breaks: Total = rate × time even when the rate changes
When the rate changes, total accumulation is the integral of the rate over time, not a single rate times time.
rate_total_machine · math · accumulator.rate_total
Concept: Fundamental Theorem
Player does: Switch between the rate gauge and the storage tank; predict each
Breaks: Integrals and derivatives are unrelated
The Fundamental Theorem of Calculus links them directly: differentiation and integration are inverse operations.
integration_window · math · accumulator.area
Concept: Changing bounds
Player does: Drag the window's edges to hit the target total
Breaks: Swapping the bounds doesn't matter
Swapping the limits of integration flips the sign of the definite integral's value.
level_the_reservoir · math · accumulator.average_value
Concept: Average value
Player does: Flatten uneven water into a rectangle of equal area
Breaks: Average value is the average of the endpoints
The average value of a function over an interval is its integral divided by the interval length, not just the average of the endpoints.
rate_runner · math · accumulator.rate_total
Concept: Position from velocity
Player does: Sketch your ghost's velocity; position is the area under it
Breaks: The velocity graph shows the path's shape
A velocity-time graph shows speed and direction over time; its shape is not the shape of the object's actual path.
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 |