Tile vocabulary

What it is

The project uses one fixed table of 23 positional Wang tiles. Fourteen named generalized tiles describe exact rectangular groupings of those atomic IDs for explaining the Yang–Zhang construction.

Why it exists

Solvers need a small, immutable vocabulary with unambiguous edge colors and identifiers. The generalized view helps people recognize gadgets, but it does not create a second tileset or change the atomic domain seen by a solver.

Inputs and outputs

The atomic input is the compiled TILESET; its snapshot contract records IDs and (N,E,S,W) colors. The generalized specification maps each of 14 shapes to an exact arrangement of those 23 IDs. It outputs presentation metadata only, with no SAT, UNSAT, or UNKNOWN status.

Mechanism

Two neighboring square tiles match when their touching edge colors are equal. Rotation and reflection are not allowed. The generalized recognizer checks the entire atomic pattern before drawing a contour, so a partial resemblance is never promoted to a generalized occurrence.

Primary animation

generalized_sheet is deliberately static: a tile vocabulary has no execution timeline to animate. The canonical sheet is the primary reduced-motion-safe asset, followed by its atomic legend.

A sheet of fourteen Yang-Zhang generalized tiles with internal seams and atomic identifiers. — **canonical-construction.** The exact 14 generalized tiles decomposed into 23 positional atomic IDs. Source contract: `wang-generalized-tiles-v1+wang-tileset-snapshot-v1`.

A semantic legend for twenty-three positional Wang tiles and their edge colors. — **canonical-construction.** All 23 atomic IDs with symbolic paper colors and generalized roles. Source contract: `wang-generalized-tiles-v1+wang-tileset-snapshot-v1`.

Position in the pipeline

The vocabulary is an immutable input to region construction and all three Wang decision paths. Generalized labels flow only to explanation and visualization; they are not semantic solver input.

Observed example

The named pipeline_sat.cm13 capture binds the same tileset identity into the region, both native trace manifests, Wang Z3 summary, solution, and rendered views. The displayed sheet is canonical construction data, not an observed solver trace.

Trust boundary

The tile table and matching rule define local compatibility. They do not prove that a region is tileable, that a reduction is correct, or that a rendered witness is valid. Those claims belong to construction tests, solvers, and the independent verifier.

Artifacts and references

See the static snapshot contract, the reduction note, and the Yang–Zhang builder contract. The public C table is defined in include/wang/tile.h and src/core/tile.c.