HELIX Key Verification: Transition-Key Routing Across the NID / HELIX Conjecture Stack
HELIX Key Verification: Transition-Key Routing Across the NID / HELIX Conjecture Stack
This preprint presents the HELIX Key Verification package for routing transition-key equations across the NID / HELIX conjecture stack. The central key is kappa = log2(3), interpreted in the workbench as 3-pressure measured against 2-containment. The package separates direct kappa systems from shadow, local, conditional, and different-key systems.Lean verification. The Lean file HelixKeyRouter.lean verifies rational 3/2 power identities, Collatz affine lane shape, Furstenberg x2/x3 shape, Mahler 3/2 shape, Sierpinski 3-over-2 shape, Goldbach Tower-3 survival shape, and router tags.Sage audit. The Sage file helix_key_audit.sage audits kappa and delta values, Collatz c/o threshold tests, Mahler and Waring rewrites, Sierpinski dimension, Furstenberg multiplier ratio, Goldbach Tower-3 pressure at scale, Goldbach first-rescue samples, Brocard shadow gap, and router classifications.Router classifications. DIRECT_KAPPA: Collatz, Furstenberg_x2_x3, Mahler_3_2, Waring, Sierpinski. SHADOW_KAPPA: Brocard. LOCAL_KAPPA: Goldbach. DIFFERENT_KEY: Riemann-style 1/2 critical balance and mod-8 visibility for hidden twin primes / blind runs. CONDITIONAL_KAPPA: Beal and Polignac.Verification status. Lean: PASS. Sage: PASS. Final package status: HELIX_KEY_VERIFICATION_PASS.The record includes the preprint PDF, original framework PDF, HELIX verification zip, Lean router, Sage audit script, and README.