{"id": "c332", "title": "Death-partition test of the coupled two-year selector", "filename": "490d_C332_Death_Partition_and_the_Coupled_Selector_20260924.md", "role": "Research action", "step": 332, "sha256": "48c1547e19ffd476855d3b26f91e8c42e9be5ae5ebf98494918ff69f655eec2b", "bytes": 4232, "origins": ["C01–C479/packets/C332/490d_C332_Death_Partition_and_the_Coupled_Selector_20260924.md"], "download": "/sources/48c1547e19ffd476855d3b26f91e8c42e9be5ae5ebf98494918ff69f655eec2b.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "490d C332 — Death partition and the coupled selector\n\n24 September2026. Step9 of10 in the C324–C333 authorization.\n\nThe new death partition supplies a precise one-sided condition, not an independent rule coupling both+2 choices. Within C319's held menu,950+108 selects the regular choice b=2. Adding actual MT-Noah→SP-No", "content": "# 490d C332 — Death partition and the coupled selector\n\n24 September2026. Step9 of10 in the C324–C333 authorization.\n\nThe new death partition supplies **a precise one-sided condition, not an independent rule coupling both+2 choices**. Within C319's held menu,950+108 selects the regular choice b=2. Adding actual MT-Noah→SP-Noah-death490 selects the primary rail. The cumulative choice a remains0 or2. Adding the existing two17K condition then selects22 conditionally.\n\nC319 defines S=p−460+a and R=f−460+b with a,b independently0 or2, while SP Noah N is fixed. Matched SP death D=N−950 gives:\n\n`D−R = 110−b`.\n\nThus D−R=108 is equivalent to N−R=1058 once Noah950 is held. It restates the right2K edge. Actual same-Gear MT Noah M gives M−D=490 for primary SP stations and491 for companions, independently of a and b.\n\n| a /b | Source-admitted rows | With950+108 | With490 | With both | All-K rows |\n|---|---:|---:|---:|---:|---:|\n|0 /0|5|0|3|0|0|\n|0 /2|3|3|2|2|0|\n|2 /0|3|0|2|0|0|\n|2 /2|3|3|2|2|3|\n\nThe two primary rows i3 and i5 retain both new conditions in **02 and22**. In each matched pair the N,M,D,R coordinates and source identities are identical; only the cumulative S member changes. For i3,02 uses S=−6347 while22 uses S=−6345. Both use N3706, M3246, D2756 and R2648. The new death path cannot by itself decide between those two existing cumulative endpoints.\n\nThe additional two17K requirement is R−S=N−q=8993, which C319 already shows requires a=b. Combined with b=2 and primary490, it leaves precisely22 at i3 andi5. This is a valid conditional uniqueness result. It does not establish an independent source prescription for imposing or coupling the conditions, and the new108 arithmetic does not add a constraint beyond the right2K edge from which it follows.\n\nAll20 inherited annual controls and40 same-phase components are retained. Fourteen annual controls are jointly source-admitted. Six admitted rows have950+108; nine have490; four have both; two have both plus the two17K condition. Formal upper rows whose R or S is absent remain unadmitted. In particular, a missing Gear4 MT Flood is not created to retain108.\n\nThis is C319's i3…7 slice. C287's separately admitted i2 companion row remains preserved in C331; it was not rejected by this narrower control domain. The complete four-row2K result and the three-row all-K subset in this menu must not be confused.\n\nThe result preserves the useful source-qualified950/108 and primary490 partitions while locating the remaining choice exactly: the cumulative+2 selection must be justified through an additional stated condition or source rule. Arithmetic alone does not supply that historical prescription.\n\n\n## Verification and limits\n\n163 main checks and 17 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. Independent review and its scope are recorded in the evidence. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.\n\nFinite condition testing within an inherited menu. Conditional22 uniqueness remains valid when all stated requirements are imposed; it is not a newly sourced selector or a probability claim.\n\nMirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.\n\n## Decision after this result\n\n**C333, proposed and unexecuted:** Synthesize C324–C332, verify the sealed report/evidence chain and source integrity, and publish the final C333 checkpoint, reading index and recovery packages. Do not execute C334.\n\nThe bounded source, geometry, context, modal, dependency and529-control questions are complete. A verified synthesis is the remaining authorized step and will preserve both the positive new partitions and their exact scope.\n"}