{"id": "c359", "title": "Two-segment E and 300/299 realization of the primary 529 side", "filename": "490d_C359_Primary_529_Side_to_SP_Shem_Lifespan_Comparison_20260924.md", "role": "Research action", "step": 359, "sha256": "9d4410c88223ed0e3232dcdc09133d595ddfa108860851db19a169a631d9b8ee", "bytes": 3586, "origins": ["C01–C479/packets/C359/490d_C359_Primary_529_Side_to_SP_Shem_Lifespan_Comparison_20260924.md"], "download": "/sources/9d4410c88223ed0e3232dcdc09133d595ddfa108860851db19a169a631d9b8ee.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "490d C359 — Primary529 side to SP Shem lifespan comparison\n\n24 September 2026. Step 6 of 10 in the C354–C363 authorization.\n\nThe primary2K side has an exact two-segment image in the matched SP Noah/Shem biography. The first leg uses E=25/23; the second uses the established300/299 gap conversion:\n\n460+598=1058 → 500+600", "content": "# 490d C359 — Primary529 side to SP Shem lifespan comparison\n\n24 September 2026. Step 6 of 10 in the C354–C363 authorization.\n\n**The primary2K side has an exact two-segment image in the matched SP Noah/Shem biography.** The first leg uses E=25/23; the second uses the established300/299 gap conversion:\n\n`460+598=1058 → 500+600=1100`.\n\n| Placement | Original source chain | Resulting source chain |\n|---|---|---|\n| i3 | SP Noah3706 → restored-MT Noah3246 → adjacent restored-MT Flood2648 | SP Noah3706 → SP Shem birth3206 → SP Shem death2606 |\n| i5 | SP Noah3708 → restored-MT Noah3248 → adjacent restored-MT Flood2650 | SP Noah3708 → SP Shem birth3208 → SP Shem death2608 |\n\nLet N,M,R denote the input chain and S,T the SP Shem birth/death. The upper formula is `N+(25/23)(x−N)`. The lower formula is `S+(300/299)(x−M)`. Both send the shared input M to S, so the comparison is continuous at the join. The lower input is a598 cross-state Noah/Flood gap; the output is an actual600-year Shem lifespan. It does not change Shem’s source lifespan.\n\nThe endpoint R reaches T by another already sourced path: the Noah-held300/299 repair moves R to the same-Gear Flood V by−2, and C355’s SP-Flood-held E arrow moves V to T by−40. This agrees with the total42-year gain. Agreement concerns these endpoints; it does not equate the full composite affine function with the lower segment function.\n\nThe total ratio is550/529, a diagnostic consequence of adding the two transformed legs. It is not adopted as a global operator. No single affine map can send all three source nodes to their displayed outputs: fixing N and sending M to S forces E, which sends R to base-MT Shem birth H instead of SP Shem death T.\n\nThe two source gap ratios are inherited. Joining them in this way is a bounded comparison tested here, not an instruction found in the reviewed source passages. No claim of historical novelty or prescribed authorial construction is made.\n\n## Verification and limits\n\n14 main checks and 17 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.\n\nThe joined comparison is inferred, not source-prescribed. Two different slopes cannot be collapsed into one global affine map; scalar equality or endpoint agreement does not equate functions.\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**C360, proposed and unexecuted:** Test this two-segment source mapping against every C319 control, including SP companion and source-membership failures. Derive the exact endpoint residuals and determine whether it selects the cumulative settinga as well as the regular settingb.\n\nThe positive endpoint construction is exact at the two retained primary fields. The fixed control menu can distinguish structural selectivity from restating the existing regular2K condition.\n"}