{"id": "c296", "title": "Source members of the large self-Mirror widths", "filename": "490d_C296_Source_Members_20K_24K_Self_Mirror_20260924.md", "role": "Research action", "step": 296, "sha256": "0407017a949bef54e687c8dcc29792e1ca7a9801c7dbfab2f453d2ebf5aee4e1", "bytes": 2449, "origins": ["C01–C479/packets/C296/490d_C296_Source_Members_20K_24K_Self_Mirror_20260924.md"], "download": "/sources/0407017a949bef54e687c8dcc29792e1ca7a9801c7dbfab2f453d2ebf5aee4e1.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "C296 — Source members of the 20K and 24K self-Mirror widths\n\n24 September2026. Source audit of the large symmetric carriers.\n\n20K and24K have precise cumulative source members in the held fields; the nominal14K Noah case does not. The members occupy different annual indices, which must remain attached to the large widt", "content": "# C296 — Source members of the 20K and 24K self-Mirror widths\n\n24 September2026. Source audit of the large symmetric carriers.\n\n**20K and24K have precise cumulative source members in the held fields; the nominal14K Noah case does not.** The members occupy different annual indices, which must remain attached to the large widths.\n\nFor a BC pair with base B and signed center−B, its ordinary reflected pair has center+B. Their cross-Mirror width is2B. The audit covers28 records: the complete LXX OFF Flood and ON Shem fields, all six restored MT Flood boundaries, and all six SP Noah births in the held full430/OFF/Terah0 context.\n\n|Source|Annual member or role|B|Self-Mirror width|\n|---|---|---:|---:|\n|LXX OFF cumulative Flood|Opening, index0|5290=10K|10580=20K|\n|LXX ON cumulative Shem|Index2, not opening|6348=12K|12696=24K|\n|Restored MT regular Flood|G1 close|2645=5K|5290=10K|\n|Required SP Noah|3703 absent|7K required|14K unsupported in this register|\n\nThese are the only K-multiple self-Mirror widths in the28-record domain. Since529 is odd,529 divides2B exactly when it divides B. The bounded annual windows then identify the three qualifying members directly.\n\nThe24K result gives a specific source qualification to the6348 marker: the LXX ON Shem field opens at6350, and6348 is its third annual boundary. The20K result uses the LXX OFF Flood opening5290. The two markers therefore must not be described as identically indexed openings.\n\nTranslation by2B and ordinary Mirror produce the same output paired set at these members, but their component ancestry differs. Translation preserves the source component order; Mirror reverses it. Algebraically T2B(−B+ε)=M(−B−ε), not M(−B+ε). No physical seasonal labels are reassigned to erase that distinction.\n\nThe nearest held SP Noah birth is3705, not3703. Its self-Mirror width is7410=14K+4. Neither a generated7K position nor an abstract gcd supplies the missing source record.\n\nEighty-seven source-domain and exact phase checks and eight authentication checks pass; the complete28-record ledger replays identically. Author review only; no new source state, axis or graph edge.\n\n**Best next bounded step — C297:** compare the axis report's regular16K-to-reflected-Christ gap and cumulative24K-to-reflected-Conquest gap across all existing MT Flood boundaries. Determine whether the highlighted6000 equality extends through source-qualified annual members. High is sufficient.\n"}