Formal Sciences
The bedrock layer — abstract structure, formal system, and necessary inference. Mathematics, logic, computation, and systems theory: the languages in which every other domain is written.
Fields
Mathematics
The science of pure structure — pattern, quantity, and form reasoned from first principles, from arithmetic to category theory.
Computer Science
Computation as a way of knowing — information, algorithm, and the limits of what can be mechanically constructed.
Logic
The architecture of valid inference — proposition, proof, and the formal systems on which all certain knowledge rests.
Systems Theory
The meta-discipline — elements, feedback, emergence, and equilibrium, the patterns that recur across every domain at once.
Synthesis
What the 4 fields of Formal Sciences look like together — read live from the typed substrate. The field pages diagnose one field at a time; this is the cross-field view.
Epistemic coverage
Each field × lens cell counts how many of the field's notes have been authored through that episteme. A whole column left dark is a lens the entire domain is blind to.
Field landscape
Fields ranked by how far they are modeled. The bar is each field's maturity mix; the chips are the downstream features its substrate can already power.
How formal sciences connects
The relation types its concepts are wired with — the domain's structural signature.
causescomposesgeneralizestransformsdepends-onis-tool-forequilibratespart-ofis-acontradictsMost connected concepts
The hubs — concepts the most relations pass through.
Structural echoes
Notes whose relational shape matches — the same proof-skeleton recurring in different places. An exact histogram match is an isomorphism; a near match, an analogy. The seed of analogical transfer across the domain.
Frontier
Where the domain is structurally absent — the most leveraged places to author next.