Typed mixed graph
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.
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.
dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged.
Finite browser arithmetic illustrates the displayed formulas; it is not a theorem certificate.
The complete universal Lagrange four-square theorem, representation of every prime, complete eight-variable Euler identity and signed-conjugate identity, explicit multiplicative closure, constructive modular seeds for every prime, all sixteen signed centered orientations, and bounded strict prime-multiple descent were first enrolled in Alpha v13 as body_checked; the universal endpoint and its exact prerequisite closure are now independently kernel- and Lean-verified Alpha v34 checked-use theorems, without Stable admission.
Alpha v30 contains 178 of 217 displayed theorem bodies, including 178 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.
Previously independently replay-verified empty-context experiments. Those experiments persisted no certificates and granted no release authority; current Alpha checked use follows separately sealed, independently verified proof bundles. This browser does not replay proofs or alter Stable membership.
67 verified campaign nodes visible in this proof family; the campaign denominator includes rows shared with other maps.
Older parent rows: 23 / 23 independently replay-verified outside this candidate map. Total sealed-slice obligations experimentally verified: 103 / 219.