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Approximation Target Divergence Mapping

Refine an approximation by mapping where it diverges from the target, then focus improvement effort on the most consequential gaps.

Gap-fill role

This draft directly addresses the zero-any accepted-prime target refinement from queue position 24 of scaled_gap_fill_batch_003_queue.yaml. It operationalizes refinement as a target-relative divergence discipline: specify the target, snapshot the approximation, map consequential mismatch, and use that map to prioritize corrective improvement.

Pre-draft disposition conclusion

Disposition: drafted_full_archetype. The candidate has close neighbors in bounded_approximation, iterative_refinement_loop, progressive_refinement_from_core_model, divergence_detection_and_correction, tolerance_band_management, tolerance_stack_management, variance_reduction, quality_control, and the pilot benchmark_anchored_refinement variant. None clearly absorbs the full pattern, and no binding alias or duplicate-merge directive was found.

Review emphasis

Review this draft with the broader refinement family. Its most important boundary risks are component-only collapse into a generic gap map, overlap with iterative_refinement_loop, overfitting to benchmark targets, and false precision when target divergence is scored more exactly than the measurement supports.

Common Mechanisms

  • checkpointed_convergence_review
  • refinement_backlog_prioritization
  • regression_guarded_refinement_cycle
  • residual_error_heatmap
  • side_by_side_target_delta_review
  • tolerance_band_gap_scoring

Compression statement

Approximation-Target Divergence Mapping is the pattern of treating the difference between a current approximation and an intended target as a structured object. Instead of refining everywhere or reacting to the most visible defects, it specifies the target, snapshots the approximation, decomposes their divergence by dimension, distinguishes acceptable approximation error from material mismatch, and directs refinement effort toward the gaps whose correction most improves fit.

Canonical formula: refinement_priority_i := consequence(target_i - approximation_i) × tractability_i × confidence_i; refine gaps above the action threshold while preserving acceptable approximation bounds

Abstractions this archetype builds on — directly (a source ingredient) or as a related pattern. Links follow the typed catalog namespace.

Built directly on (1)

  • Refinement: Iteratively improving a candidate solution toward adequacy through repeated cycles of evaluation and adjustment that narrow the gap to a target, rather than deriving the answer in one shot.

Also references 26 related abstractions

Variants

Narrower or domain-specific specializations that share this archetype's core structure. Recognized variants are established; candidate variants are provisional.

Metric Residual Divergence Mapping · subtype · recognized

Map quantitative residuals between a model or process output and target values to guide selective refinement.

  • Distinct from parent: Narrower because the target gap is primarily quantitative.
  • Use when: Target dimensions can be measured or benchmarked; Residuals vary by region, case type, subgroup, or operating regime.
  • Typical domains: simulation refinement, machine-learning error analysis, quality control
  • Common mechanisms: residual error heatmap, tolerance band gap scoring, checkpointed convergence review

Qualitative Target-Gap Mapping · domain variant · recognized

Map divergence from a qualitative, interpretive, aesthetic, or experiential target using criteria rather than pure metrics.

  • Distinct from parent: Narrower because comparison depends on qualitative criteria.
  • Use when: The target includes style, meaning, user experience, judgment, or interpretive fit; Numeric scores are insufficient or misleading.
  • Typical domains: musical performance, design review, policy implementation
  • Common mechanisms: side by side target delta review, refinement backlog prioritization

Benchmark-Anchored Divergence Mapping · validation variant · candidate

Use benchmark cases or reference examples to decide which approximation-target divergences require refinement.

  • Distinct from parent: Narrower because the target is represented through test cases or exemplars.
  • Use when: Direct target measurement is difficult but benchmark cases exist; The approximation must perform across known regimes before being trusted.
  • Typical domains: scientific model validation, software acceptance testing, engineering calibration
  • Common mechanisms: benchmark case delta table, checkpointed convergence review

Regression-Guarded Refinement · risk or failure variant · candidate

Close one target gap while explicitly checking that already acceptable dimensions do not regress.

  • Distinct from parent: Narrower because regression control is the dominant constraint.
  • Use when: Refinement actions interact across dimensions; Local improvement can degrade prior target fit.
  • Typical domains: software releases, model tuning, service redesign
  • Common mechanisms: regression guarded refinement cycle, checkpointed convergence review

Near names: Target Divergence Mapping, Approximation Gap Analysis, Residual Gap Mapping, Gap-Directed Refinement.