The observable
Features are chosen explicitly. If the answer changes with them, that is part of the result.
Controlled Quotient Testing
To simplify — without losing what
made the comparison meaningful.
CQT emerged from a practical nuisance: two structures may look identical after a convenient coarse-graining even though an important distinction has already disappeared.
The method forces us to state in advance what is observed, which transformations are allowed, and when a comparison is meaningful at all.
1Source objectsWhat exactly are we comparing?
→
2Controlled quotientWhat are we allowed to forget?
→
3Independent oracleDid the required class survive?
→
VALIDorINVALID
01
Four commitments
What CQT does not allow us to hide
Admissible forgetting
A quotient is not a technical detail. It determines which distinctions we agree to lose.
Independent checking
The mechanism that created a label should not be its only witness.
The right to INVALID
Sometimes the correct answer is that the selected observation channel does not support the comparison.
The most useful inconvenient answer
INVALID is not a failed computation
If a distinction disappeared before it was tested, the system must not pretend that it found a meaningful match. INVALID keeps the method’s boundary of applicability visible.
This is where CQT becomes not only an algorithm but a research ethic: do not present information loss as a discovered law.
02
Where it is used
From an internal discipline to an instrument of its own
Structural sandboxesComparing graphs, classes, and transitions.
Numerical modelsTesting regime stability across representations.
Transition corporaReproducible collections of VALID and INVALID cases.
Project methodologyA shared language for the boundaries of observability.
This page is an entry point, not a replacement for technical documentation. Before publication it will include the release, manuscript, corpus version, and a minimal reproducible example.