The BB(6) Cryptid Frontier: Certified Templates, Ledger Reductions, and a Unified p-adic Return Problem

A self-contained research artifact on the BB(6) busy-beaver frontier: paper-style writeups (certified trace-template reductions of the cryptid machines; exact p-adic run-structure theorems with a Lean 4 formalization; a gate/structure/protection classification), a one-command verification battery re-checking every proof-path certificate, and the supporting lab notes including the novelty audit and the full corrections trail. No cryptid is decided; every claim carries an explicit epistemic label. Methodology: AI-assisted under a strict zero-false-proof discipline (adversarial red-teams, independent re-verification), documented in the notes.