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.
Exact expanded first-order arithmetic statement
forall p. ((~(p = 1) /\ forall frm_prime_left_fslf_prime frm_prime_right_fslf_prime. p = frm_prime_left_fslf_prime * frm_prime_right_fslf_prime -> frm_prime_left_fslf_prime = 1 \/ frm_prime_right_fslf_prime = 1)) -> (exists fsl_a_fslf_prime fsl_b_fslf_prime fsl_c_fslf_prime fsl_d_fslf_prime. (p) = fsl_a_fslf_prime * fsl_a_fslf_prime + fsl_b_fslf_prime * fsl_b_fslf_prime + fsl_c_fslf_prime * fsl_c_fslf_prime + fsl_d_fslf_prime * fsl_d_fslf_prime)Constructive proof overview
Generated structural guide
Every natural prime has an unconditionally constructed four-square representation, using the checked bounded seed, all sixteen signed quaternion cases, and terminating multiplier descent.
The unchanged tactic script uses 2 declared prerequisites and contains 2 exact native proof lines.
dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged
Proof neighborhood
Direct dependencies
FS003M four_square_prime_from_odd_signed_quaternion FS0058 four_square_signed_centered_representationDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.