{"id": "c122", "title": "C122 — The retained13K paths admit a3+8+2 refinement", "filename": "490d_C122_Three_Eight_Two_Refinement_20260922.md", "role": "Research action", "step": 122, "sha256": "9760eeaf02a4b1b6ba84c6c3ebd1013f795e4667f1585d095467b2eea85f0958", "bytes": 1786, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C119_C128_529_Conquest_Batch_20260922/C122/490d_C122_Three_Eight_Two_Refinement_20260922.md"], "download": "/sources/9760eeaf02a4b1b6ba84c6c3ebd1013f795e4667f1585d095467b2eea85f0958.md", "format": "md", "derived": false, "tags": [], "excerpt": "C122 — The retained13K paths admit a3+8+2 refinement\n\nThe four qualified Creation–Conquest–Flood prefix paths now contain the local8K construction explicitly. This inserts a generated comparison boundary into already admitted paths; it does not discover additional Flood states.\n\n| Arc | SP Creation BC base | Generated ", "content": "# C122 — The retained13K paths admit a3+8+2 refinement\n\n**The four qualified Creation–Conquest–Flood prefix paths now contain the local8K construction explicitly.** This inserts a generated comparison boundary into already admitted paths; it does not discover additional Flood states.\n\n| Arc | SP Creation BC base | Generated BC base | Reflected Conquest base | Reflected MT Flood base | Retained status |\n|---|---:|---:|---:|---:|---|\n| N01 | 4420 | 2833 | 1399 | 2457 | G2 close; partial expansion |\n| N02 | 4419 | 2832 | 1400 | 2458 | G2 start; full expansion |\n| N03 | 4418 | 2831 | 1401 | 2459 | G3 close; partial expansion |\n| N04 | 4417 | 2830 | 1402 | 2460 | G3 start; full expansion |\n\nEach chain is **1587+4232+1058=6877**, or **3K+8K+2K=13K**. Exact component checks agree. The BC middle boundary is generated by8K; its value is not an additional historical witness.\n\nC11’s qualifications remain binding. N02 and N04 support the complete earlier Creation expansion. N01/N03 support these prefix paths but require unsupported MT Noah births3055/3057 to extend the full earlier chain. N03 still has no complete retained Shem join. These are not repaired by the8K insertion.\n\nThe later native Conquest members1403–1405 would demand Flood2461–2463 for the2K continuation, outside the held ordinary MT field. The1406 closing boundary would demand2464. At the earlier edge, the native opening4421 reaches a1398 candidate, outside the Conquest field, although its13K Flood target2456 exists. Thus source membership, not numerical divisibility, bounds the four-row domain.\n\n26 checks passed, using the frozen C11 source records without rerunning its campaign. **Next:** isolate the equations needed for this refinement and its local complement symmetry. High sufficient.\n"}