{"id": "c355", "title": "600-year translation of retained E relations", "filename": "490d_C355_Shem_Lifespan_Translation_of_E_Relations_20260924.md", "role": "Research action", "step": 355, "sha256": "c0fd7d0588d29b9f9225282a971c65e6f9b6f78f93c3676e898683c8a50ad5db", "bytes": 3399, "origins": ["C01–C479/packets/C355/490d_C355_Shem_Lifespan_Translation_of_E_Relations_20260924.md"], "download": "/sources/c0fd7d0588d29b9f9225282a971c65e6f9b6f78f93c3676e898683c8a50ad5db.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "490d C355 — Shem-lifespan translation of E relations\n\n24 September 2026. Step 2 of 10 in the C354–C363 authorization.\n\nOne nontrivial E relation survives a600-year source translation at both retained primary placements. Its fixed endpoint moves from SP Noah birth to the same-Gear SP Flood start. The input moves from re", "content": "# 490d C355 — Shem-lifespan translation of E relations\n\n24 September 2026. Step 2 of 10 in the C354–C363 authorization.\n\n**One nontrivial E relation survives a600-year source translation at both retained primary placements.** Its fixed endpoint moves from SP Noah birth to the same-Gear SP Flood start. The input moves from restored-MT Noah birth to restored-MT Flood start; the output moves from SP Shem birth to SP Shem death.\n\n| Fixed SP Flood | Restored-MT Flood input | SP Shem death output | Expanded gap |\n|---:|---:|---:|---|\n|3106 |2646 |2606 |460→500 |\n|3108 |2648 |2608 |460→500 |\n\nThus `3106+(25/23)(2646−3106)=2606`, with every node already present and typed in the frozen register. The MT input retains Cainan ON, Terah+60 and full430; the SP endpoints retain native Cainan OFF, base Terah and full430. In particular,2646 is the same-Gear Flood, not the adjacent2648 endpoint of the first529 rectangle.\n\nThe identity is translation covariance: shifting an affine map and its fixed point together by600 preserves its slope. Here the translation is dictated by existing600-year source paths. It introduces neither a fitted fixed point nor a new global translation operator.\n\nAll four forward E_N relations in each eleven-node field were checked. Besides the translated fixed point, only M→S retains a full source triple. Translating R→H gives2048→1956 and2050→1958: the Shem deaths are sourced, but2048/2050 are absent from this register. Translating H→F gives1956→1856 and1958→1858, again incomplete. This does not deny endpoints in other corpora; the domain is the frozen regular Noah/Shem/Flood register.\n\nConsequently, the650-year Shem birth separation also exists between matched deaths, but the original598→650 affine construction does not carry along with both sourced inputs. The proven transfer is the460→500 arrow only.\n\n## Verification and limits\n\n14 main checks and 15 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 source translation is a partial comparison; it does not preserve every member of the eleven-node field or establish a total group action.\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**C356, proposed and unexecuted:** Test the same three retained E_N arrows at the five same-Gear SP source-event pivots: Noah birth, Shem birth, Flood start, Noah death and Shem death. Use only translations determined by those existing source events.\n\nThe600 translation supplies a fully sourced reuse. The remaining existing lifecycle pivots provide a finite test of whether this is isolated or part of a smaller repeated source grammar.\n"}