Formal Specification and Verification of the PhiLogos Genesis Clock Kernel.

This paper presents PHILOGOS_GENESIS_CLOCK_V1_16BIT_SEALED, a deterministic sequencing kernel that serves as a logical ordering primitive for distributed systems rather than a physical time source. The kernel is formally specified as a fixed-point Iterated Function System over the 16-bit domain b ∈ {0,…,65535} with seed v₀ = (b + 2)S, S = 10¹⁵, and a 23-step truncating contraction vᵢ₊₁ = ⌊vᵢ q / S⌋ using q = 339,949,771,344,778. The resulting tick sequence exhibits bounded forward differences Δ ∈ [16692,16694], which establishes strict monotonicity and injectivity across all N = 65,536 outputs (e.g., T₀ = 33,386 to T₆₅₅₃₅ = 1,094,021,571). We prove that 128-bit integer arithmetic is a formal requirement for correctness, as 64-bit arithmetic overflows at the 16-bit domain ceiling, and we provide an exact 23-step inverse whose worst-case fractional error (≈ 9.56 × 10⁻⁵) guarantees perfect recovery of the original input. For transport-stable and implementation-independent verification, the kernel commits its full behavioral sequence via SHA-256 over the big-endian 64-bit tick stream and seals the complete artifact using RFC 8785 canonical JSON together with SHA-256. These constructions yield a parser-agnostic, independently regenerable, and cryptographically sealed specification suitable for reproducible deployment across heterogeneous execution environments.