Does renaming internal nodes change a decision?
A controlled test that fixes the question, answer candidates and abstract graph while changing the assignment of names to internal relationships.
What changes—and what stays fixed
Every world has 512 non-root nodes and four roots. Three topology families provide different attachment patterns. Four identical branches beneath each root make the answer candidates structurally interchangeable before the target question is considered.
| Condition | Internal names | Question and candidate identifiers | Identifier-role frequencies |
|---|---|---|---|
| Original | Unchanged | Fixed | Unchanged |
| Unrestricted | 503 names reassigned | Fixed | May change |
| Frequency-constrained | The same 503 names reassigned | Fixed | Preserved exactly |
All treatments preserve the abstract graph, correct answers, record positions and state length. The constrained treatment also preserves the complete word and punctuation multiset. This does not guarantee identical contextual tokenization inside the service.
What the experiment measures
The primary statistic is disagreement between original and renamed answers minus disagreement between matched exact-request copies. It is computed within each forest, then summarized across the three topology families. Negative values are retained. Shuffled root and fourth-ancestor questions form the two primary endpoints.
Root-grouped layouts, signed accuracy changes and immediate-parent controls are secondary. Grouping is computed preprocessing and can expose membership directly; success there would not establish that the model traverses the graph.
The 9,216 main requests are supplemented by 4,608 separate direct-parent controls. Every distinct body has two copies. The final schedule allows all six-condition permutations, including adjacent copies, and uses mirrored orders to balance mean condition positions. Pair-gap distributions are reported without assuming equal elapsed time.
Validation and precision
The independent literal parser and downward traversal verified 13,824 exact question oracles, 1,152 candidate-orbit sets and 768 constrained multiset comparisons. All state strings are 24,230 bytes. The code tests use explicitly synthetic response fixtures, including failures, missing maps and malformed labels.
The smallest effect of engineering interest is ten percentage points. At 384 worlds, planning calculations vary substantially with the assumed between-world variance. They are sensitivity calculations, not a power guarantee. No result is implied by preparing a large request manifest.