Exact screening and artifact admission

This overview explains how the C12 through C16 sequence reduces repeated work while preserving reconstructible GF(2) artifacts. A faster internal construction path is meaningful only under its exact artifact contract and retained comparison scope. For this rank-one product, each cell is the and of one column entry and one row entry. With column one zero and row one one, the upper row receives two ones and the lower row two zeros. This is not the earlier exclusive-or of a row scalar and a column scalar. Check each of the four products against the target. All match. With several rank components, corresponding products are combined by exclusive-or, as required by arithmetic over the two-element field. The reconstruction operation must be specified before exactness can be judged. If the target's lower-right cell is one, these same factors fail. A high candidate score cannot repair that mismatch. Ranking proposes where to look; full reconstruction decides whether a proposed artifact is exact. C12 through C16 develop guarded dispatch, task-aware admission and reconstructible GF(2) artifacts. In C15, candidate construction repeats expensive layout and artifact work. C16 shares a layout per partition, evaluates required descriptors, and fully admits a bounded leading set. For a conceptual rank-one Boolean matrix, take column 10 and row 11. Their AND outer product is 11 / 00. A descriptor can record enough information to rank this candidate before constructing its full serialized artifact. The selected artifact must still pass strict admission and reconstruction. Screening does not mean skipping every losing partition without analysis. Later C39 and C40 confirm repository-internal C15-to-C16 improvements on their own frozen Windows cohorts. C41 separately tests implementation substitutions. These updates strengthen a scoped mechanism account; they do not establish a universal decomposition win or an external ABC comparison. C41's ablation effects are not additive causal percentages. Work a second complete case with row_index 0, column_index 1. Keep this assignment fixed throughout the calculation. Each symbol retains the meaning already introduced; a new value does not create a new logical rule. Select the upper row and the right column using zero-based indices. The corresponding entries of the column factor and row factor are both one. Their product is one. With a single rank component there is no second product to combine; with several components their products would be exclusive-or reduced. This case establishes a specific contrast. GF(2) multiplication uses AND products. Do not substitute XOR of row and column factors. Keep the input, intermediate values, and conclusion together when comparing it with the previous case. The calculated answer belongs to this complete assignment under the stated rule. Several candidate variants may share the same row and column layout. Constructing that descriptor once can avoid repeated preparation. The descriptor is an internal aid, not automatically a complete serialized artifact ready for use elsewhere. A screening stage can retain a bounded subset of promising candidates. That bounds the search effort but does not prove that the retained candidates satisfy format requirements or reconstruct correctly. Admission and exact verification remain explicit later steps. To study which refinement saves work, compare the baseline, each refinement alone, and both together under the same task. Their savings can overlap, so adding two isolated savings may overpredict the combined effect. The actual confirmation and substitution results remain separate retained experiments. Share eligible layout work and fully admit the required candidates. Keep internal improvements distinct from unmatched external comparisons or universal claims.