GCTS / experiments

Careful demonstration · recorded from the solver

The marking begins empty.
Failure writes the rule.

A Hat placement is tried with ordinary geometric constraints. If it creates an immediate dead frontier, GCTS extends a sparse A₂ marking just far enough to make that placement mismatch—then verifies that the entire accepted prefix still matches.

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Preparing the recorded run

start
Search patch accepted trial

Loading the trace generated by the Python search.

Tiles
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Failures learned
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Prefix replay
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What is—and is not—being learned

A geometric certificate, not a branch ID

  1. 01

    Try geometry first

    The search starts with one unmarked Hat. A trial is failed only when placing it exposes a frontier point with no legal Hat continuation.

  2. 02

    Find a mismatch witness

    The learner searches overlapping A₂ site/channel pairs. It adds only the local sites needed for at least one unequal value across the failed contact.

  3. 03

    Protect the prefix

    All contacts in the accepted patch are equality constraints. A proposed update is committed only if the full prefix replays without a marking conflict.

  4. 04

    Reuse geometrically

    The learned marking transforms with every Hat orientation. A later placement with the same forbidden local geometry is rejected before lookahead.

Recorded run

One deterministic audit trail

This run demonstrates the learning invariant; it does not claim that the resulting finite marking is a universal Hat matching rule. The support search is sparse and direction-sensitive, with a configurable finite horizon for this demo.