17 Remaining conjectural extensions
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The finite theory closes several operator identities but does not settle the corresponding universal continuum questions.
Conjecture 17.1: Transfer-semigroup realization
Every sufficiently regular realization of the seed calculus whose transfer stage is local in time admits a closed generator on a completed state space, and the packet analysis maps form a compatible system for its semigroup or evolution family.
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Conjecture 17.2: Uniform refinement control
For a nested family of physically or analytically meaningful discretizations, there exist norms and constants independent of resolution such that
on every bounded time interval. Summable generator defects would then produce a coherent inverse-limit evolution.
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Conjecture 17.3: Latent-packet closure
For a stable infinite packet system, exact elimination of unresolved packets produces a causal memory kernel whose Laplace transform is the limiting packet self-energy. A Markovian closure exists precisely when this self-energy is constant, or can be represented by finitely many additional state packets.
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Boundary 17.4: What remains outside Paper VI
The following issues are not proved here:
existence and uniqueness for arbitrary stochastic differential equations;
posterior consistency or asymptotic normality in infinite statistical models;
domain invariance for unbounded fractional operators;
tightness and compactness required for stochastic continuum limits;
nonlinear PDE well-posedness beyond the stated finite and linear models;
an optimal packet choice for a general Markov, Bayesian, or PDE problem.
These belong to later realization-specific work or to external analytic theory.
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