Centered tethers and circles share a conditional Twinkle encounter law

**Result:** A centered reflecting DNA tether and an equal-length circle have identical conditional fork-encounter-time distributions under uniform non-fork attachment and homogeneous diffusion. This exact null comparison, applied to purified human TWNK/Twinkle, shows why a centered-linear versus circular encounter fraction cannot isolate a topology effect under those premises. **Methods:** A source-grounded theoretical calculation used the reported rounded 18-kb substrate and diffusion coefficient 0.787 ± 0.065 kb²/s. The approximately 120-s fork observation/bleaching time supplied an illustrative horizon, not a molecular lifetime. A continuous fork-position survival mixture was evaluated at 101 positions for each of three diffusion scenarios and checked with a separately implemented finite-volume diffusion solver. Scenarios are deterministic calculations, not biological replicates or confidence intervals. **Findings:** At 120 s, the conditional encounter probability was 0.6049993 for an end target and 0.9543534 for both the centered tether and the equal-length circle. Changing the diffusion coefficient by one reported standard error gave end-target probabilities 0.5807354–0.6278288 and centered probabilities 0.9421107–0.9640069. Refinement reduced all nine numerical discrepancies; the largest refined absolute discrepancy was 0.00008570. The increment beyond published diffusion and fork arrest is a reproducible geometry-comparison diagnostic, not discovery of sliding or new first-passage mathematics. **Consequence and limit:** An end-versus-center comparison changes the conditional geometric prediction; the centered-tether/circle comparison is an informative null. A counterexample to their equality under the exact premises would defeat the calculation. Preferential direct fork attachment is already observed, and non-fork start density, end behavior, physical loss and observation censoring remain unresolved. The result does not estimate biological capture, unwinding, mitochondrial replication or clinical benefit.