Certified equivalence class
193 graph forms share one complete game.
The map contains every observed order-7 Digraph Placement graph in this class. The neighborhood and specimen views compare their graph structure. Every form has the same complete-game digest and exact value.
Shared complete-game identity 830ef59c3454d13324e6841d466a702ef3e168bab7615bb4043d6e6d58e8fd66
01 · Complete class
All 193 forms grouped by directed-arc count. Column height records the observed count.
Use Left and Right Arrow keys to change arc-count columns, Up and Down Arrow keys to move within a column, Home and End to reach the limits, and Escape to return to the stable reference. Touch or click any graph to compare it.
02 · Neighborhood
Nine forms near the selection
Forms 93–101 of 193. Select one for an exact comparison below.
Selected form 97 of 193 with 23 directed arcs.
complete game 830ef59c3454d13324e6841d466a702ef3e168bab7615bb4043d6e6d58e8fd66Performed edit study
One certified form, edited 42 ways.
The author selected the class's only 17-arc form, toggled every possible loop-free directed arc once, and reverified every result. Gold cells retain exact value 1/2.
From one class to the full corpus
The study contains 21,697 certified graph forms.
The class above isolates 193 forms that share one complete game. This view widens to every quotient-distinct order-7 graph in the study, then regroups those forms by complete-game identity and exact combinatorial value.
The three panels have similar silhouettes for the displayed arc-count and node-count descriptors. The verifier establishes exact equality.
Select a mark to inspect it. With the canvas focused, use the Left and Right Arrow keys to move between forms and Escape to close the specimen. The layer controls and A, B, C case study provide shorter keyboard paths through the dataset.
Loading the checked atlas
Coordinates derived from the verified dataset · 2.3 MBThese counts describe the observed sample. The total number of representations for each value is unknown.
Evidence trail
Independent replay verifies the historical corpus behind the atlas.
These figures describe the independently replayed historical run used to build this atlas. The paper's primary held-out comparison is a separate 221,184-proposal experiment that rejected thirty corruption families.
Partizan proposes graph forms. The exact verifier computes each combinatorial-game value. The atlas exposes three identity levels: graph quotient, complete game, and exact value.
Stiller used computation to locate an endgame kernel. Elkies recomposed it as a chess study. Partizan follows the same division of labor: the machine enumerates certified forms, and a person chooses which representation to pursue.
The performed edit study begins with the unique 17-arc form and reports all 42 possible one-arc edits. Exact replay retained 33 variants at value 1/2.
Further exampleA → B → C, value 0Forms A, B, and C map to two complete games and one exact value.
Case study · value 0