Graph of thoughts: verify the artifacts you combine

Current snapshot

Follow artifacts through a dependency graph

Graph of Thoughts represents information as vertices connected by dependencies, allowing outputs from multiple branches to be combined and refined. This lab demonstrates that structure with executable integer arrays. It does not call an LLM, expose private reasoning, implement an ADK API or reproduce the paper’s experiments. Input flows into Partition, which supplies Branch A and Branch B. Aggregate depends on both branches. Refine consumes the aggregate; Verify depends on both the original input and the refined artifact. Each card names its parents so that a later decision can be traced to the actual data used. Branches are independent subproblems, not evidence of statistically independent errors.

Choose inputs and inject a branch failure

Input dataset selects Mixed values [7,2,5,2,9,1,4,1], Duplicate pairs [3,3,2,2,1,1,0,0], or Descending values [8,7,6,5,4,3,2,1]. Partition splits after four items, and each branch executes insertion sort. Branch B fault either leaves that result alone, reverses it, or drops its first item. Dropping an item is data loss even when the remaining values are sorted. With Mixed values and no fault, A is [2,2,5,7] and B is [1,1,4,9]. Removing B’s first item leaves [1,4,9]; the missing second 1 must remain visible in the multiplicity audit.

Compare aggregation and bounded refinement

Aggregation chooses a two-pointer merge or concatenation. Merge repeatedly consumes the smaller head, and therefore requires sorted inputs; it does not automatically correct a faulty branch. With the mixed default, merge produces [1,1,2,2,4,5,7,9]. Concatenation produces [2,2,5,7,1,1,4,9], which has a descending adjacent pair from 7 to 1. Refinement selects no repair or one complete insertion-sort pass over the aggregate. Try concatenation with insertion refinement: it repairs the order and the full verifier accepts. Then drop an item in B. Refinement still sorts the result but cannot recreate the missing occurrence. Graph composition and extra transformations are useful only when their contracts preserve the problem’s requirements.

Challenge the verification gate

Verification gate selects Order and multiplicity or Order only. The independent audit always computes both: adjacent inversions reveal ordering errors, while count differences show missing or extra occurrences of each value relative to the original input. A positive missing count means input items were lost; a negative count means extra items appeared. Use Mixed values, Drop first item, Merge and No refinement. The output [1,2,2,4,5,7,9] is ordered but lacks one 1. The full gate rejects it. Order only accepts it, and the decision prominently reports FALSE ACCEPT. Acceptance under a weak check must never be confused with a correct permutation. These exact finite checks work for this integer sorting task; they do not establish truth for arbitrary generated prose.

Inspect time, controls and saved evidence

Play reveals eight nodes across sixty inspection seconds. Pause freezes the timeline; Next node moves to the next seven-and-a-half-second boundary. Restart rewinds without changing the chosen inputs or speed. Time seeks and pauses; Speed selects quarter, half, normal or double pace. Changing a scenario input rewinds and pauses. Hiding the tab pauses too. Artifacts and the final verdict remain hidden until their inspection boundary, although the full fixture is precomputed. Export graph JSON saves the graph, its dependency edges and the currently inspected prefix. Capture baseline, Replace baseline and Clear baseline preserve or remove a comparison. Notebook observations persist locally; Export notes saves them. Expand experiment and Exit full screen change the view. The event history supports keyboard scrolling. Inspection seconds are teaching time, not measured model latency, cost or parallel execution duration.