Foundation 1

A load-bearing starting point. It is not on the same axis of confirmation as theorems: foundation and storeys are not ranked, only bearing and borne. It may not have logical premises; it is propagated downstream as a foundation-dependency set.

Theorem 14

A mathematical or logical result with a proof: it must carry proof links (Lean, Coq, paper, appendix, textbook) or an external anchor in established mathematics.

Empirical 1

A result obtained by measurement: it should carry data links and a cross-check by an independent method.

Structural inference 3

An inference from structural argument that has not yet been formalised as a theorem.

Interpretive 2

An interpretive reading within the framework; not a theorem and not a basis for computation.

Lexical 2

A dictionary-level correspondence with the vocabulary of another discipline; it asserts translatability, not structural identity.

Engineering 2

A tool, software or model. It is not on the cascade scale and may not serve as a logical premise; it may serve through an instrument edge.

Programmatic 2

A research programme or a goal still being written; the argument is not complete. It is never featured on the home page.

Rejected 3

A statement that has been examined and should be rejected; listed publicly with reasons. It may not be a logical premise of a non-rejected claim.

Cascade rules

1. The tier of a conclusion = min(tier of its premises, rigor of the inference). Only logical edges take part; instrument, context and refutes edges do not.
2. Scale: foundation 6, theorem 6, empirical 5, structural 4, interpretive 3, lexical 2, programmatic 1; engineering and rejected are off the scale.
3. Conservative declarations propagate downstream: the effective strength of a premise is the lesser of its declared tier and its computed ceiling.
4. Logical cycles are not errors: an unguarded cycle caps its whole strongly connected component at structural inference; if every member has a guardedness certificate there is no cap.
5. The cascade checks consistency, not truth; the rigor of an inference is self-reported by the author.