# Study review and proposed continuation

## Assessment

Studies 01–03 establish a working mechanism on the saved synthetic cases: edit supported vector outlines, check the exported geometry, and use exact gap-violation locations to repair two failed edits. They are a completed exploratory stage. They do not yet establish reliability on fresh inputs, comparative efficiency, broad SVG applicability, perceptual steering, attribution, or research novelty.

This review adds evidence accounting and a prospective validation plan. It does not add experimental results or rerun optimization.

## How much independent evidence is here?

| Study | Named requests / cases | Distinct input SVG byte hashes | Geometry record entries | Distinct recorded SVG byte hashes |
|---|---:|---:|---:|---:|
| 01 | 1 | 1 | 3, including the input | 3 |
| 02 | 10 | 5 | 30 | 30 |
| 03 | 10 | 6 | 30 | 22 |

These are counts from saved records and SHA-256 values, not a count of independent experimental replications. Study 03 inherits many input geometries through exact subdivision; different SVG bytes do not necessarily imply a different curve. Eight of its refined workflow entries reuse the initial smooth artifact because no repair was performed. Across the three studies, 63 record entries refer to 55 distinct SVG byte hashes. The 12 replayed history entries comprise ten initial smooth entries and two repair entries; they are not twelve additional independent outcomes.

The 37 behavioral tests cover specified behavior and failure cases. They do not establish a population success rate. A fresh replay with the same checker establishes reproducibility of its decisions, not independent assurance that the checker is correct.

## Decision record

| Decision | Evidence that motivated it | Status |
|---|---|---|
| Separate target achievement from preservation | The area-only edit reached 45,000 but moved anchors by 25 units. | Implemented in Study 01. |
| Compare target-only, penalty and explicit constraints | Symmetry made the first mechanism unusually easy. | Implemented in Study 02; fixed configurations, not a method-family ranking. |
| Add feasibility bounds and tolerance sensitivity | Two difficult contractions failed; penalty edits narrowly missed strict area precision. | Added after observing results; original denominator retained. |
| Extend to connected segments | Single-cubic endpoint/gap bounds excluded useful requests. | Implemented in Study 03; two such requests have certified solutions in the expanded family. |
| Add witness-guided repair | Actual sampled smooth edits violated the gap between samples. | Added after observing those failures; both repair histories retained. |
| Validate before extending to general outlines | Fixtures are reused, refinement is post hoc, and replay uses the same checker. | Recommendation from this review; next study not yet run. |

## Proposed Study 04 — reliability and the value of verification feedback

**Primary question:** Does witness-guided refinement improve the proportion of independently verified edits on fresh supported inputs, compared with additional sampling or another solve under a comparable budget?

**Separate checker question:** Does the current interval checker agree with a second implementation on domain support, gap violations and acceptance boundaries?

### Freeze the design before producing results

1. Preserve Studies 01–03 as development evidence. Use their fixtures for debugging, not as the new evaluation set.
2. Develop and validate a fixture generator, then freeze its version, seeds, distributions and case assignments. Aim for at least 100 new input geometries as a proposed engineering target, not a statistical power calculation. Declare sample size and strata before the final run.
3. Include asymmetric and translated shapes; unequal segment widths; near-margin gaps; protected landmarks; feasible targets with verified witness shapes; independently proven impossible requests; and deliberately unsupported paths. Do not label a case feasible merely because no impossibility bound is known.
4. Fix tolerances, numerical scales, repair budget, selection rules and the primary endpoint before inspecting final evaluation outcomes. Separate exploratory tuning cases from the evaluation set.
5. Count outcomes per input/request pair. Shared starts, methods and repair histories are paired observations, not independent extra trials.

### Cross-check the checker independently

Implement a separate power-basis gap evaluator that finds all derivative roots in [0,1] and checks the endpoints and stationary points. Cubic gaps have quadratic derivatives. The numerical implementation must handle repeated roots, nearly degenerate coefficients and roots close to interval boundaries. For decisive near-threshold comparisons, isolate roots and evaluate with rigorous bounds; an ordinary floating-point minimum is not itself an exact certificate.

Do not import the current checker's subdivision or moment functions into this second implementation. Add independently constructed analytic fixtures, alternate area/moment formulas, and representation-preserving tests such as exact subdivision and translation with correspondingly transformed requests. Separate parser coverage from geometric claims. Resolve every acceptance disagreement before using the checker as evaluation ground truth. This is independent implementation checking, not formal verification or an external expert review.

### Compare the contribution of feedback

Retain the initial sampled smooth controller, then compare these follow-up workflows from the same candidate:

- Another solve with the same samples and a declared restart policy.
- A prespecified denser or nested uniform sampling policy.
- Exact violation-witness refinement.
- A stationary-point-based constraint approach, if its implementation and numerical safeguards are ready before the protocol freeze; otherwise defer it explicitly.

Use both a fixed evaluation/solve budget and a reported end-to-end time budget where practical. Include failed attempts, export, verification and repair costs. Do not compare only accepted cases or report medians that exclude costly failures. Position-only remains an omission control for continuity, rather than the primary competitor for a smoothness-constrained task.

### Record and report

Report full-request certification, witnessed violations, unresolved certificates, unsupported inputs, solver termination, feasibility class, repair counts, maximum residuals, and median plus tail costs. Measure geometric movement under the declared objective. Archive the protocol, generator, input/request files, all candidates, timestamps, environment and source hashes. Report changes to the protocol rather than silently folding them into the original plan.

Use paired summaries by case and stratum. If uncertainty intervals are reported, state the sampling model and unit of analysis; do not derive broad reliability claims from a deterministic convenience set.

### Decision gates

| Gate | Required evidence before advancing | What would change the recommendation |
|---|---|---|
| Checker consistency | No unresolved disagreements on acceptance or supported-domain claims in the frozen validation suite; boundary cases explicitly classified. | An accepted invalid candidate blocks broader assurance claims until explained and fixed. |
| Value of repair feedback | Paired results against the declared follow-up baselines, with all costs included. | If denser sampling or a simpler method performs as well, prefer the simpler method; the present study does not establish a unique advantage. |
| Useful coverage | Success and failure profiles across the declared fresh fixture strata, including difficult and unknown-feasibility cases. | If failures cluster near particular shapes or scales, narrow the supported domain or address that weakness before generalization. |
| Broader representation | A specific practical need that the two-graph model cannot express, plus a planned intersection/certificate method. | General outlines are a separate capability extension after the present mechanism has a credible validation baseline. |

## Resources and scope

The next validation work can begin with the current local code and mathematical sources. Broader claims would benefit from an external geometry review and an appropriately licensed external shape collection. Generative-image steering requires a model-specific experiment; training-data attribution requires a separate causal question and evidence-access plan. Neither follows from geometric conformance receipts alone.

Recommended sequence: independent checker cross-check → frozen fresh-input evaluation → budget-matched repair comparison → decide whether and how to generalize. The broad literature collection does not need to resume for its own sake; research should answer concrete gaps uncovered by that work.