Inputs
Domains, units, assumptions, initial state, parameters, and constraints are stated before execution.
Lab Space
Change the model. Inspect the consequence.
Endpoint Singularity labs are not animations with mathematical labels. Controls update canonical numeric state, outputs remain inspectable, and each experiment states what it does and does not establish.
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Boundary and transformation laboratories
The current V0 contains two real deterministic systems. They establish the interaction standard while the generalized MathBlock engine remains future work.
ExecutableLimits
Limit Microscope
Move toward zero by powers of ten. Compare removable singularities, divergent one-sided behavior, and floating-point cancellation.
ExecutableContinuity
Discontinuity Scanner
Compare left and right behavior for removable, jump, infinite, and oscillatory discontinuities.
ExecutableCalculus
Power-law Boundary Observatory
Vary p and ε in f(x)=x-p. Compare an unbounded endpoint value with convergence or divergence of the improper integral.
ExecutableLinear algebra
Vector Transformation Lab
Rotate and scale a two-dimensional vector, inspect the matrix-derived output, complete a guided target, and fork the state into Build Space.
Lab Contract
Every experiment must expose its limits.
A successful run means the defined objective was met under the current model. It does not automatically prove a theorem or validate a physical prediction.
Trace
Intermediate state, method, validation decisions, errors, and termination remain inspectable.
Result
Numeric output, visual projection, accessible alternative, interpretation, and limitations agree.