De-tracing: recovering the design system inside an auto-traced logo

This is the final deliverable of the verification pipeline: a symmetric-difference map of the original logo against the parametric rebuild, computed in-browser by SVG cross-masking. Blue is agreement. Green is what the rebuild added (a uniform 36-unit stroke reaching past the source's thin passages). Red is what it removed (hand-drawn excess at corners and letter feet). The colors are orthogonal RGB channels because the sets are disjoint — if any two classes overlapped, additive mixing would betray it as yellow. No yellow exists in this image; its absence is the correctness proof.

The method hypothesizes a parametric model, renders it, compares against the source raster, and lets the residual drive the next update. Three properties distinguish it from gradient-based vectorization (DiffVG-class methods): fits are closed-form, so the output is interpretable constants rather than Bézier soup; model selection happens inside the loop — a hypothesis can be rejected and replaced, not merely tuned; and the critic is perceptual, catching failures that pixel metrics structurally cannot.

Coordinate descent over components — walls, then lips, then bottom topology, then letters — each verified locally before the next. The loss:

Cross-sections of the traced walls fit straight lines with slopes 0.5506 and 0.5510 — the designer meant 0.55. The midline sat at 255.3 on a 512 canvas — they meant 256. Perpendicular stroke thickness clustered at 32; letter arm lines landed on 370 / 427.5 / 485 with the S's lobes at radius 28.75 and the C's lobe at exactly twice that. The original had a design system; the tracing had buried it. The rebuild's entire geometry is those recovered constants plus tangency math — corner fillets solved exactly, symmetry by mirrored coordinates rather than by drawing.

Gradient methods tune a hypothesis; they cannot reject one. This loop did, three times — each caught by measurement or by looking, each replacing a model class, not a parameter:

Three defects passed every numerical assertion and fell only to a vision check in the real rendering context: a WebKit thumbnail bug that dropped an element cairosvg rendered fine; blind probe points that sampled gaps in the geometry and reported success; and a CSS-class refactor that was leaner and degraded catastrophically in CSS-less rasterizers. The generalizable result: loops with derivable ground truth close themselves; perceptual-quality loops need a vision oracle — and knowing where that boundary sits is worth more than pretending it isn't there.

That boundary is directly load-bearing for production document-AI: OCR training loops can self-evaluate (render → rasterize → recognize → compare gives free ground truth), while layout fidelity, rendering QA, and "does this extraction look right" sit on the oracle side. The same architecture I run for clients — automated metrics for what is derivable, model-vision review for what is perceptual.

The rebuilt mark animates: a seamless 4-second loop where bubbles detach from the liquid under constant-flux inflation (r ∝ t^1/3), rise under Stokes drag toward a terminal velocity that equals the conveyor's handoff speed — the physics lands the animation constraint for free — and ring with a damped quadrupole wobble. The liquid surface is a translating sine strip: a traveling wave is its own shape in uniform translation, so the loop seals by periodicity, not by careful keyframing. Theming collapsed to a single input: currentColor drives structure, liquid strata, and effects through masks that encode alpha, not color — one asset, every theme, verified by pixel-sampling through the actual CSS inheritance path.

Fifty seconds, stop-motion: model states are the parametric builder with components progressively unlocked; every chart datum is computed by rasterizing that frame and counting pixels. Yellow appears exactly three times — at the falsifications.

Method framing, honestly calibrated: this is human-in-the-loop iterative refinement with closed-form fits and an AI vision critic — one documented execution of a method, not a theory. The execution trace, assets, and per-frame data are available on request.