{"id": "c319", "title": "Four-case sensitivity of the paired two-year selections", "filename": "490d_C319_Independent_Two_Year_Choice_Sensitivity_20260924.md", "role": "Research action", "step": 319, "sha256": "772477aca20028496cab603ac0a81b076c649f98d53f0e3d3d011e4e1cafc4da", "bytes": 3338, "origins": ["C01–C479/packets/C319/490d_C319_Independent_Two_Year_Choice_Sensitivity_20260924.md"], "download": "/sources/772477aca20028496cab603ac0a81b076c649f98d53f0e3d3d011e4e1cafc4da.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "490d C319 — Independent two-year choice sensitivity\n\n24 September 2026. Step 6 of the ten-step authorization C314–C323.\n\nThe two17K transports do not force the paired two-year selection. With all source contexts held fixed, define S=p−460+a, R=f−460+b, with a,b independently0 or2. The cumulative annual choice is a; the", "content": "# 490d C319 — Independent two-year choice sensitivity\n\n24 September 2026. Step 6 of the ten-step authorization C314–C323.\n\n**The two17K transports do not force the paired two-year selection.** With all source contexts held fixed, define `S=p−460+a`, `R=f−460+b`, with a,b independently0 or2. The cumulative annual choice is a; the regular Gear-coordinate choice is b. q and n are unchanged.\n\n| a /b | Left/right short spans | S→R | q→n | Joint source rows | All-K rows |\n|---|---|---:|---:|---:|---:|\n|0 /0|1060 /1060|8993|8993|5|0|\n|0 /2|1060 /1058|8995|8993|3|0|\n|2 /0|1058 /1060|8991|8993|3|0|\n|2 /2|1058 /1058|8993|8993|3|3|\n\nThe exact formulas are short spans1060−a and1060−b, with cross-width matrix[[8993+b−a,10053−a],[7933+b,8993]]. Thus two17K paths require a=b, allowing both00 and22. Requiring the all-K subdivision selects22 within this fixed four-choice domain.\n\nAll20 annual and40 same-phase configurations are enumerated. Fourteen annual and28 phase configurations are source-admitted; eight annual cases have two17K paths, and three have the all-K form. The00 choice is source-valid across all five rows. In the mixed choices one side can fail its endpoint domain independently; the22 upper failures remain.\n\nThe result is a sensitivity test, not a randomization or a probability estimate. Conditional uniqueness under the all-K requirement is not a source rule selecting that requirement or the matching annual/Gear choices. It does show exactly which extra choices convert a source-valid1060 rectangle to the1058 rectangle. The three all-K rows here are the i3…5 subset; C287's separately admitted i2 row has not disappeared.\n\n## Verification and limits\n\n121 main assertions and 15 frozen-input/predecessor checks passed. A second main replay produced byte-identical DATA and RESULTS. Separate review scope and agreement are recorded in the evidence. All frozen originals and standing controls remain unchanged. These are verification counts, not independent-witness counts.\n\nNo statistical claim or prescribed selection rule. Distinct choices and source states remain labelled; conditionalallKuniqueness does not canonize them.\n\nMirror/529 remains the focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction x=1 January AD2; no civil year zero. Regular Gears remain Noah/Shem/Flood only. SP minus-one companion is local to SP Noah/Shem. No cumulative/upstream Gear, new endpoint or phase, fitted anchor, global axis, z-law, canonical or graph edit. Capture now; canonize later. Source state, event identity, generated coordinate and phase ancestry remain distinct. Exact arithmetic and source membership do not establish intention or independent historical witnesses.\n\n## Decision after this result\n\n**C320, proposed and unexecuted:** Close the finite coverage boundary: census all eight retained LXX_OFF Shem/Flood annual pairs against the existing regular Noah/Flood contexts under the same17K transport. Explicitly locate the omittedSPG1 companion and any LXX aliases, without new endpoints or variants.\n\nThe five-case test cannot represent the whole admitted rectangle family. Completing this small held-domain census will explain which source rows are excluded by the earlier reversed500 requirement and prevent a subset count being mistaken for the fullC287 domain.\n"}