FROM COHERENCE TO DISCLOSURE Phase, Resonance, Cohesion, and Future-Sufficient Physical Computation

Abstract

Quantum Computational Theory + exact analytic study + preregistered computational benchmark protocol Central thesis For a specified future task, physical protection need preserve only those relational distinctions whose loss can still alter that future through the remaining dynamics. Design principle Design backward from the future. Evolve forward through coherence. Protect only what the future can still use. Quantum-coherent systems are commonly protected by attempting to preserve states or encoded information against environmental disturbance. Yet a specified future task need not depend on every distinction represented by the instantaneous physical state. We develop a future-sufficient framework in which terminal observables are propagated backward through the remaining dynamics to determine which present distinctions can still alter the requested future. For a terminal observable family A_T and channel Φ_{T:t}, the backward future-relevance space is the span of the adjoint images Φ†_{T:t}(A). Present states that agree on this relevance space are future-equivalent for the declared task. The construction separates physical coherence from future-relevant coherence and organizes the physical narrative as Coherence → Phase → Resonance → Cohesion → Structure → Partial Closure → Disclosure. In an exactly solvable three-mode quantum model, equal-magnitude coherence terms possess unequal future value; resonant mixing changes which phase relations are relevant; and equal global state disturbance produces unequal terminal damage. Under stated assumptions, protection devoted exclusively to a strictly future-null sector is dominated whenever it has positive physical cost and cannot couple back into future relevance. Conversely, when the target and admissible dynamics generate the complete operator structure, no nontrivial exact future-sufficient compression remains. The framework therefore proposes not maximal preservation of coherence, but future-sufficient preservation of relational structure. A matched optimal-control benchmark is specified prospectively to test whether the formal representational advantage survives graded relevance, leakage, bounded controls, and explicit physical costs. The benchmark has not been used to generate the schematic curves in Figures 7 and 8; those figures state hypotheses and boundary conditions rather than numerical results. Keywords quantum coherence; relative phase; resonant control; partial closure; future sufficiency; quantum control; decoherence; model reduction; physical computation; task-relative protection Highlights · A terminal task defines a backward-generated operator space of presently relevant distinctions. · Physical coherence can be nonzero while being exactly future-null for a specified task. · Resonant dynamics can continuously activate or suppress phase relevance. · Equal global state disturbance can produce unequal task-relative damage. · Protection of strictly future-null structure is dominated when it carries positive cost and cannot feed back into relevance.