Typed mixed graph

Kummer’s Carry Theorem: 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

The exact binomial-carry endpoint, its carry-free corollary, and their minimal prerequisite closure were first enrolled in Alpha v14 as body_checked and are now independently kernel- and Lean-verified Alpha v34 checked-use theorems; none is admitted to Stable.

Alpha v30 contains 13 of 15 displayed theorem bodies, including 13 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.