[S] (The salvage of the refuted confinement claim, same morning.) If primorial flanks survive at ~4.5/7 while random candidate pairs survive at ~1/100, then windows around primorials should carry elevated twin density — "twin-rich territory."
Sieved to 25×10⁶; twin density in windows of half-width W around each primorial vs the global 2C₂/ln²x prediction and vs random same-size windows in the same inter-primorial stretch:
| l | P | W | twins @P | expected | ratio | random |
|---|---|---|---|---|---|---|
| 11 | 2,310 | 735 | 32 | 32.4 | 0.99 | 21.1 |
| 13 | 30,030 | 9,702 | 244 | 241.0 | 1.01 | 170.0 |
| 17 | 510,510 | 168,168 | 2,557 | 2,570.7 | 0.99 | 1,963.8 |
| 19 | 9,699,690 | 3,216,213 | 32,988 | 32,815.0 | 1.01 | 30,039.2 |
Primorial neighborhoods carry exactly the global average density; the random windows match their own local prediction dead-on too. The global law holds everywhere tested, seam or no seam.
[F] The flank immunity is a two-address guarantee (P±1 only), diluted to invisibility at any window scale. The 4.5/7 flank survival was real immunity at a point, not a neighborhood effect. Measured alongside: the candidate share among odd addresses declines per layer ∏_{3≤p≤l}(1−2/p): 12.09% → 9.92% → 8.73% → 7.81% for l = 11 → 19 — "less p between gaps" at the candidate level, measurable and monotone.
This closes the spatial-localization branch of the twin question on the wheel toy: twins are uniformly distributed at the average rate everywhere tested, and what remains open (twin infinitude, desert growth) is not a statistics question enumeration can vote on — it is a single-configuration-at-infinity question.