ARM CN RESULTS — held-out-N contamination probe (construction vs recall)
Registered: arm_cn_preregistration.txt, commit 69a1642 (pushed before sampling, 2026-08-21).
Sampled: 2026-08-21, 75/75 invocations collected (5 cells x 15), no runtime deaths.
Scored once by arm_cn_analysis.py on the complete ledger; frozen in arm_cn_report.json.

VERDICT: P-CN1 HOLDS (construction). The closed form predicts the modal valid output at
held-out N: HIT at 4 of 5 evaluable cells, including 3 of 3 discriminating cells.
P-CN2 (recall) required <= 2 hits; observed 4. F-CN1 does not fire.

| N  | k* | branch | disc | valid/15 [Wilson 95%] | on-pred | modal value (count, margin) | verdict | k*-structure | rival | above argmax |
| 50 | 7  | V(7,1) | no   | 11 [0.48, 0.89]       | 4       | 3.5122554 (6, +2)           | MISS    | 10/11        | 0     | 0 |
| 58 | 8  | T      | yes  | 14 [0.70, 0.99]       | 12      | 3.6250000 (12, +11)         | HIT     | 14/14        | 0     | 0 |
| 62 | 8  | T      | yes  | 13 [0.62, 0.96]       | 13      | 3.8750000 (13, +13)         | HIT     | 13/13        | 0     | 0 |
| 65 | 8  | V(8,1) | no   | 13 [0.62, 0.96]       | 9       | 4.0258871 (9, +7)           | HIT     | 12/13        | 0     | 0 |
| 75 | 9  | T      | yes  | 12 [0.55, 0.93]       | 8       | 4.1666667 (8, +6)           | HIT     | 8/12         | 0     | 0 |

Every cell evaluable (>= 5 valid). No one-sample margins: smallest margin is +2 (N=50, the
miss); the four hits carry margins +6 to +13.

SECONDARIES.
  S-CN1 (k*-structure majority): 5/5 cells (predicted >= 4). Dominant radius gives k = k* in
    57 of 63 valid outputs pooled.
  S-CN2 (strong form): 0 rival-argmax emissions at the three discriminating cells (0/39 valid;
    predicted <= 1). 0 valid outputs above the family argmax at any cell (0/63).
  S-CN3 (validity): 63/75 valid at 1e-6 (84%); invalid rows are 9 overlaps (mostly hex-row
    attempts and over-packed rows), 1 unparseable (N=50 slot 9 emitted fraction literals such
    as 1/14 and (2**0.5 - 1)/14 — the arm-CH "radical literal" failure mode), and 2 count
    errors. No validity collapse at large N.

THE N=50 MISS, DECOMPOSED. Prediction V(7,1) = 3.5295867: a 7x7 grid at r = 1/14 plus one
filler of radius (sqrt2 - 1)/14 = 0.0296 in an interstice. Observed: 10 of 11 valid outputs
are the 7x7 grid with exactly one extra circle (k*-structure 10/11); 4 place the filler at the
registered interstitial radius (on-prediction, 3.5296), 6 place it in a container corner at
r ~ 0.0123 (3.5123, the cell's mode), 1 elsewhere. The selection (7x7 + 1 filler) is the
registered template in 10 of 11; the miss is filler execution, the same off-template failure
arm CH isolated (30 of 31 invalid CH attempts misplaced fillers). The cell therefore supports
the construction reading at the structural level while missing at the value level, and is
reported as a MISS under the registered value criterion.

N=75, THE LARGEST CELL. Modal T(9,75) at 8/12 valid; the four off-mode outputs are a 5x15
grid at r = 1/30 (2.5, twice), a hexagonal r = 0.05 layout (3.75) and a 12-column layout
(3.0625) — alternative constructions, none of them the family rival V(8,11) = 4.2847718.

INTERPRETATION (scoped). At five N with no published sum-of-radii packing to recall, the
proposer emits the nearest-square template at the registered value in four cells and at
the registered structure in all five. The recall reading predicted the anchor would not
survive the move to unpublished N; it did. This does not establish absence from the
pretraining corpus (unprovable) and does not bear on m >= 4 extend cells (already
disconfirmed, arm M). The square-arm corpus grows by 75 to 678 invocations.

PROTOCOL NOTES. All 75 rows used no tools (tool_uses = 0 on every invocation). Eleven rows
(N=65 slots 1, 3, 6, 8, 9, 10, 11, 12, 13, 14, 15) were transcribed into the ledger by reconstructing the
emitted 8x8 grid string from its fixed template plus the emitted filler triple; the
reconstruction is character-identical to the emission for these standard grids and is
disclosed here; on 2026-08-22 the ledger's per-row `reconstructed` flag was set to true on these eleven rows (it had been written false by the collector), with the raw field untouched.
