Sheet-Identity Admissibility, Developmental Time, and Observation Geometry in Coarse-Grained Turbulence

This independent research preprint develops and stress-tests a governed state/observation architecture for coarse-grained turbulence. The program begins from exact finite projection/non-commutation and coarse-graining non-identifiability benchmarks, then evaluates whether distinctions erased by coarse projection can be represented through sheet identity, simultaneous multi-channel state, developmental-time coordinates, and explicit observation geometry. The external numerical program uses the Johns Hopkins Turbulence Database (JHTDB) and preserves failed gates, implementation defects, and non-replicating numerical optima rather than tuning them away. A fresh pre-registered observation-operator replication on disjoint space-time support reproduces bounded same-point rank-3 directional reconstruction, long-horizon persistent partition events, and a three-primary/one-witness state architecture in bounded form. The fourth witness remains nonredundant, while finite-line numerical optima are support-dependent and angle diversity alone is not a universal ordering of sensor quality. The manuscript also reports a second independently frozen closure-translation campaign. The predecessor and fresh campaigns both fail to produce a robust promoted held-out SGS closure, although their internal model rankings differ. The resulting claim is deliberately limited: better state identifiability does not automatically imply stable closure transfer across the tested finite campaigns. A deployable scale-uniform resolved closure remains open. The work does not claim a universal LES closure, failure of RANS as a class, revision of Kolmogorov K41, a climate or supercell forecasting mechanism, physical spacetime self-intersection, a universal sheet-birth clock, Navier-Stokes regularity, or a Millennium-problem solution. Exact algebraic statements, directed numerical evidence, fresh replications, failed tests, and open questions are separated explicitly.