The Penalty Model

What sprite fetches cost, measured: a fixed 6-dot core, an alignment overhead set by (K + SCX) mod 8, an exact composition rule for stacked sprites, and two edge regimes — the prelude and the right edge.

Penalty by SPRITEX

Single-sprite and four-sprite penalty by SPRITEX (= OAM X; displayed X + 8), SCX=0 (dmg-sim measurement, gbmicrotest sprite ROMs; firing-scanline median minus non-firing median):

The single-sprite cost decrements exactly 1 dot per +1 SPRITEX over [8, 9]; the four-sprite penalty decrements a clean ~4.094 dots per +1 SPRITEX over the first three steps of [8, 13] (≈1 dot of alignment per sprite × 4 sprites). The SPRITEX=12 row (+27.646) carries a sub-dot wobble — its non-firing baseline itself drifts ~1 dot by tile-boundary alignment, so the 11→12 and 12→13 steps read −5.103 / −3.084 rather than the clean −4.094. At SPRITEX ∈ {14, 15} the sprites straddle a BG tile boundary and per-sprite alignment overhead re-enters in a form the linear model does not capture (dmg-sim measurement).

Stacked sprites at one X: the chain collapses to combinational

When N sprites share an OAM X byte, each runs its full fetch core but the inter-fetch gap collapses to gate delays: WUTY↑ᵢ → VEKU → TAKA↓ᵢ → SOWO↑ → TEKY↑ᵢ₊₁ with no clocked element on the path. SACU never resumes between fetches, the BG counter stays at 5, LYRY stays high — which is exactly what keeps the AND4 re-fire chain armed. Each completed fetch's per-slot fetched-flag DFF (EBOJ/CEDY/FONO family, clocked by WUTY) clears that slot's X latch, so the next unfetched same-X slot drives FEPO for the re-fire; the chain ends when no unfetched same-X slot remains.

Measured cadence (zero variance, 7 firing scanlines per N, the gambatte 10spritesPrLine K=167 chain):

mode3_ext(N, K, S) = single_sprite_penalty(K, S) + (N − 1) × 6.000 dots

The rule's measured anchors:

The Mooneye intr_2_mode0_timing_sprites calibration table (extras of 2/4/5/7/8/10/11/13/14/16 M-cycles for N = 1..10) is M-cycle rounding of this uniform 6-dots-per-sprite extension — there is no hardware shared-fetch alternation, and the BG fetcher plays no per-sprite role (it is frozen throughout the chain). Multi-group configurations compose per X-group: when PX passes from group A to group B, FEPO drops, SACU resumes, the BG fetcher advances normally, and group B re-pays its own first-sprite alignment.

The right edge: K = 167

At K = 167 the X match fires at the dot WODU would otherwise fire. The cost is not right-edge-special: (167 + 0) mod 8 = 7 puts the single sprite at the alignment model's 6-dot floor, and the stacked-composition rule applies unchanged — ext = 6.000 + (N − 1) × 6.000 per effective sprite. Measured (dmg-sim measurement, gambatte 10spritesPrLine_10xposA7 ROM — nine on-screen sprites — and N ∈ {1,2,3,4} patched variants, zero variance, 7 firing lines each):

The ~0.02-dot residual against exact N × 6 is the end-of-chain WODU rise arriving through the FEPO↓/XENA arm rather than the PX-decode arm. Per-sprite TEKY spacing in the long chain: 5.947 dots between #1 and #2, then exactly 6.000 between each subsequent pair, ending in a final TEKY glitch pulse too narrow for SOBU's capture as FEPO falls.

Sprites at SPRITEX < 8: the fetch hides in the prelude

When the X match fires before the first SACU↑, the whole fetch lands inside the AVAP→first-SACU prelude instead of between SACU pulses — same total cost, different shape. Measured at SPRITEX=0 (zero variance, 23 firing scanlines): the real TEKY fires at +11.255 dots from AVAP (the second LYRY-high event — the first is consumed by the TAKA carry-over clear), the fetch runs +11.766 → +17.399, the first SACU lands at +18.430 (vs 7.026 baseline), and total Mode 3 duration is identical to the SPRITEX=8 case.