Boundary History and Observability in Classical Fluid Dynamics: Prospective Numerical Tests, Classical Comparators, and Predictive Limits

A staged theoretical and numerical investigation of preparation-dependent response, partial boundary observation and inverse estimation in classical incompressible Navier–Stokes systems. An exact parallel-channel reduction is compared with a restricted three-pulse confined-cylinder study (DFG-like Re=20) and a distinct external-PIV reanalysis. Predeclared numerical tests R4.4 and R4.5 show bounded within-model predictive transfer. R4.4: predicted future drag difference −0.003722830610, numerical result −0.003974638900, relative discrepancy approximately 6.7639%; six-arc history-estimation RMSE OPT6=0.022554784994 and UNIFORM6=0.026181073247. Formal status: R4_4_HOLDOUT_PASS. R4.5: under simulated independent noise, OPT6/UNIFORM6=0.846611 and conventional A-opt6/OPT6=0.846165, an approximately 15.38% lower RMSE for A-optimal placement. Strong hypothetical error correlation reverses rankings. Formal status: R4_5_NUMERICAL_COMPARATOR_SUPPORTIVE. Additional GLS analyses are post-outcome exploration, not a new prospective PASS. Initial cylinder and transient FAIL records, separately frozen supplemental PASS results, and limitations are preserved. No BIG-specific dynamical term is added. BIG-specific added predictive value = NOT DEMONSTRATED. This is not independent laboratory validation of the Re=20 three-pulse history protocol. R4.4/R4.5 independent reviews primarily recompute archived outputs algebraically; they are not full reruns using an independent PDE solver. Local rank in a restricted three-parameter preparation family is not complete observability of arbitrary fluid states. The English main paper is authoritative. The Japanese companion is a reference summary, not a complete word-for-word translation. An English technical supplement, original numerical archives, source reports, source map, checksums, and reproduction guidance accompany the paper. Historical private Drive URLs inside immutable logs are provenance only; the principal evidence is downloadable from this record. Third-party PIV measurements are not redistributed; use the original dataset DOI 10.5281/zenodo.20765567. LICENSE SCOPE: CC BY 4.0 applies to Jun Lucis’s manuscripts, authored reports and authored numerical data. It does not relicense third-party software. Embedded scikit-fem 12.0.2 retains its BSD 3-Clause license and notices. No new software license is granted for original author source code where none was specified; see LICENSES.md for the component-level rights statement. Publication provides source for inspection and verification, not an assertion that every component is CC BY.