Typed mixed graph

Quadratic Supplementary Laws: theorems and conservative definitions

Proof arrows, theorem-to-definition arrows, and conservative definition-to-definition arrows are intentionally different relations. Only theorem-proof arrows participate in premise paths.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Sparse modes suppress visual objects only. Every local proof and notation relation remains in the selected-node panel; external prerequisites and their exact release evidence appear on each individual theorem page.

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Proof arrows run from prerequisite to dependent; notation arrows run from a theorem or definition to the conservative definition it uses. Select a node to inspect every direct relation.

theorem definition proof dependency uses definition

dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged.

Constructive numerical example

Finite browser arithmetic illustrates the displayed formulas; it is not a theorem certificate.

Evidence and release boundary

Both complete supplementary-law endpoints and all 28 displayed bounded Euler-criterion, Gauss-lemma, modulo-four, and modulo-eight prerequisites were first enrolled in Alpha v15 and are independently kernel- and Lean-verified Alpha v34 checked-use theorems; none is admitted to Stable.

Alpha v30 contains 28 of 30 displayed theorem bodies, including 28 independently verified alpha_closed checked-use theorems from 3222 checked release theorems; no displayed theorem is admitted to Stable. Historical replay experiments have no persisted certificate and do not change release evidence, checked-use authority, or Stable admission.