# Coordinate Control — an executable claim, with a measured boundary

We can turn one of the supplied visual coordinates into an executable edit: move an image's chromatic centroid while preserving six source hue-family chroma totals, per-pixel OKLab lightness and a protected central region. The implementation computes a bounded edit, verifies the exported file, or provides a numerical infeasibility witness. It does not merely describe the change in a prompt.

This is a demonstrated, narrow engineering capability. It is not proof of a new image model, a new optimizer, aesthetic improvement, general semantic control, or superiority over commercial editors.

## Results

Seven fixed coordinate requests on each of six existing library reproductions: Matisse, Degas, Gauguin, then an unchanged-controller validation on Klimt, Rothko and Jeong Seon. The first three and additional three remain separate in the raw records. Six further all-controls-locked contradictions are excluded from the 42 ordinary requests.

| Outcome | Coordinate-only ablation | Constrained controller |
|---|---:|---:|
| Ordinary requests | 42 | 42 |
| Solved | 42 | 22 |
| Infeasible under that method's locks | 0 | 20 |
| Full contract verified in original 8-bit exports | 0 | 16 |
| Full contract verified in 16-bit diagnostic exports | 0 | 22 |
| All-controls-locked contradictions correctly refused | 6 / 6 | 6 / 6 |

All 42 ablation outputs hit their targets in 16-bit but violate the hue-family budgets. The worst hue-family drift is 31.706%. All 22 computed candidate masters pass: worst normalized-coordinate error 0.000001486, worst hue-family budget drift 0.001555%, and worst absolute OKLab L drift 0.0001448. The protected region is pixel-exact. These are measurements of a specific color operator, not success percentages for general image editing.

All 20 candidate refusals and six candidate contradictions have verified support-bound witnesses. The solver reported no optimization failures. Forty-seven behavioral checks pass, including no-op pixel identity, detecting one altered protected pixel, detecting a wrong target on an unchanged source, and checking contradiction/out-of-range certificates.

The comparator uses identical controls, bounds and quadratic objective with the six hue-budget constraints removed. This isolates what those constraints do. It is an ablation, not an expert-workflow trial; it cannot establish that our system outperforms a competent artist or competing software. The preservation/coverage tradeoff is explicit: 22 fulfilled requests and 20 refusals, not 42 successful edits.

## A more consequential finding: selective undo can conflict with preservation

For this Degas reproduction, a (+0.025,+0.025) chroma-centroid displacement is feasible with the hue budgets locked. A (0,+0.025) displacement is not. Therefore removing only the horizontal decision while retaining the vertical decision is infeasible in this control family. The support witness verifies the obstruction; the UI retains the last accepted edit.

This does not mean undo is universally impossible. It means edits are coupled by the remaining constraints, and a control system should detect that conflict rather than silently relax a preservation promise. On Matisse, the same sequence and rollback are feasible; separately recomputed rollback/direct remaining states produce identical decoded pixels. Gauguin rejects the combined state before rollback becomes applicable. The raw records preserve these distinctions.

## Export failures: the coordinate must survive delivery

The primary 8-bit study solved eight requests and verified all eight. Additional-image validation solved fourteen and verified eight. Five Jeong Seon exports failed their centroid tolerance: this nearly monochrome image's small chroma signal is disproportionately affected by 8-bit rounding. One Klimt export exceeded the maximum lightness tolerance.

These six failures were not discarded or repaired by retuning. A post-hoc precision experiment exported exactly the same solved parameters at 16-bit, retaining the original requests and gates. All 22 candidate masters passed. The viewer uses those verified 16-bit masters; original 8-bit files and failure records remain available.

The low-chroma example also exposes a conceptual limit: accurately controlling a tiny reproduction tint is not necessarily a meaningful artistic action. A future interface should distinguish mathematically measurable change from perceptually useful change. No perceptual study was run here.

## What was actually built

- A signed, normalized image-coordinate representation based on raw OKLab chroma.
- A 72-control spatial chroma operator with source-dependent gamut bounds and a fixed protected region.
- Linear feasibility, quadratic minimum-change optimization and separating-bound witnesses.
- Independent reload-and-measure acceptance of written image files.
- Reversible coordinate state evaluated from immutable source pixels.
- A live local editor, reachable-region display, comparison viewer and failure history.

Five color-conversion functions were extracted verbatim from Color Kernel v0.4.8; the notebook was not executed. ISR's existing fields and summary functions provide supplementary readouts. Neither source library nor supplied notebooks were modified. New code connects those components to SciPy's existing solvers; it is not a replacement or imitation implementation of ISR.

## Claim boundaries

The implemented coordinate is the center of chromatic emphasis, not object location. The operator changes chroma at fixed pixels. It does not generate content, move a subject, restore an exact fabric, recover a scene graph or separate lighting from materials. Preserving six hue-family totals does not preserve every color histogram detail. Fixed OKLab L does not preserve all ISR fields; expected display-luma and mass changes are reported rather than mislabeled as failures or hidden.

The protected rectangle was fixed geometrically before the run, not inferred as an object or selected by an artist. Requests are numerical; no automatic language compiler is claimed. Maximum working dimension is 512; no production-resolution or video test was run. Source reproductions are not color-calibrated originals. The three validation images were selected after the primary results, before their own run; this is not an external randomized benchmark.

The candidate contact sheets were visually inspected. Geometry and fine drawn structures remain recognizable, with visible changes in regional saturation. Acceptance is numerical, not a judgment that these interventions improve the paintings. Near-neutral Jeong Seon changes have limited visual significance. No blind artist preference or correction-time study was performed.

## What we can say now

**A measured visual property can serve as an executable control target, with explicit preservation constraints and a verifiable refusal boundary.** That is a stronger implementation claim than structured prompting. Within this operator family, feasibility-aware revision also explains why some selective reversals cannot honor all remaining decisions.

The next substantial extension is a second operation family—actual geometry—with the same verified state and conflict handling. The test is whether coupled geometric/color edits retain the promised properties on unseen inputs, compared with existing constrained editing methods. The current results justify that experiment; they do not establish a market or research lead.

## Prior work and delivery

Image-space optimization and coordinate-based control are established. Relevant primary references include [DiffVG](https://people.csail.mit.edu/tzumao/diffvg/), [DragDiffusion](https://yujun-shi.github.io/projects/dragdiffusion.html), and [OKLab](https://bottosson.github.io/posts/oklab/). No novelty claim is inferred from integrating them with our measurements.

- Live editor: `http://127.0.0.1:8050/`.
- Run: `OPENBLAS_NUM_THREADS=2 OMP_NUM_THREADS=2 python src/server.py` from the project folder (local solver, not included here).
- Frozen design: `PROTOCOL.md`; additional-image design: `VALIDATION_PROTOCOL.md`.
- Original results: `reports/results.json`, `reports/results-validation.json`.
- Precision diagnosis: `reports/precision.json`; behavior checks: `reports/behavior-tests.json`.
- Sources/hashes: `data/provenance.json`, `data/provenance-validation.json`.
- Live user experiments are saved separately under `reports/live/` and `renders/live-*`; they never overwrite frozen results.