HKD Infinity for Prompt-Conditioned Video Production: Exactness, Conditional Cycle Superiority, and Measured Benchmarks | IJCT Volume 13 – Issue 5 | IJCT-V13I5P59

We establish an exactness theorem for deterministic prompt-conditioned video computation with semantics-preserving state reuse, a lossless prompt–residual reconstruction theorem, and an explicit sufficient condition for at least 1000× hardware-cycle superiority over a specified comparator. These are conditional mathematical statements, not a proof that the current HKD implementation beats Runway or all state-of-the-art systems. Available empirical evidence consists of a single matched self-hosted CogVideo kettle pair: 659.412 seconds with reference validation versus 644.553 seconds with HKD validation and dispatch, a wall-time ratio of 1.02305. The decoded RGB hashes agree. No matched Runway generation, provider cycle counters, successful three-to-five-minute training run, or universal face/body fidelity result is available. We give the actual benchmark driver and the executable subset-sum verification code, distinguish counted operations from hardware cycles, and state precisely what additional evidence a stronger claim requires.